ZAKLJUČNO POROČILO O REZULTATIH OPRAVLJENEGA RAZISKOVALNEGA DELA NA PROJEKTU V OKVIRU CILJNEGA RAZISKOVALNEGA PROGRAMA (CRP) »KONKURENČNOST SLOVENIJE 2006 - 2013« I. Predstavitev osnovnih podatkov raziskovalnega projekta 1. Naziv težišča v okviru CRP: JAVNA AGC,\!C|. Konkurenčno gospodarstvo in hitrejša rast - Nacionalna in sektcj^l^;"^ Luve ■^ßn, LJUBIj.AN/ 3 0 -03- 2010 IPril.: VNOST wir" 2. Šifra projekta: Prejeto; V4-0409 3 ■ Naslov proj ekta: številka zadeve: , i T" Vrednost: Optimiranje proizvodnih postopkov za povečevanje dodane vrednosti v kmetijstvu i 3. Naslov projekta 3.1. Naslov projekta v slovenskem jeziku: 3.2. Naslov projekta v angleškem jeziku: 4. Ključne besede projekta 4.1. Ključne besede projekta v slovenskem jeziku: dodana vrednost, kmetijstvo, optimiranje, Slovenija 4.2. Ključne besede projekta v angleškem jeziku: value added, agriculture, optimisation, Slovenia 5. Sfaziv nosilne raziskovalne organizacije: Univerza v Ljubljani, Biotehniška fakulteta 5.1. Seznam sodelujočih raziskovalnih organizacij (R0): Kmetijski inštitut Slovenije 6. Sofinancer/sofinanceiji: Ministrstvo za kmetijstvo, gozdarstvo in prehrano 7. Šifra ter ime in priimek vodje projekta: 13487 Stane KAVČIČ Datum: 2. marec 2010 Podpis vodje projekta: Prof. dr. Stane Kavčič Podpis in žig izvajalca: Rektor prof dr. Radovan Stanislav Pejovnik, po pooblastilu dekan prof dr. Franc _Štarnpar_ IL Vsebinska struktura zaključnega poročUa o rezultatih raziskovalnega projekta v okviru CRP 1. Cilji projekta: 1.1. Ali so bili cilji prej ekta doseženi? ^ a) v celoti ] b) delno ] o) ne 1.2. Ali so se cilji projekta med raziskavo spremenili? m a) da 3 b) ne 2. Vsebinsko poročilo o realizaciji predloženega programa delah Deregulacija kmetijskih trgov vzporedno s pričakovanim postopnim umikom SKP, rastoče okoljske in družbene zahteve ter klimatske spremembe vodijo v vedno večja tržna nihanja, ki jih spremlja profesionalizacija kmetijstva. Gospodarski subjekti so zato čedalje bolj izpostavljeni proizvodnim in poslovnim tveganjem, to pa od njih zahteva prilagoditev poslovanja in učinkovitejše načrtovanje gospodarjenja. Ob intenzivnih strukturnih spremembah kmetijske pridelave v EU kot odziva na politično dogovorjene obveznosti (naklonjenost Komisije bioenergetiki in vse večji ne-prehranski uporabi žit) lahko pričakujemo postopno ponovno povečano povpraševanje po surovinah kmetijskega izvora in posledično dolgotrajnejše zvišanje cen večine pomembnejših poljedelskih kultur na ravni, ki bo višja kot v predkriznem obdobju. To naj bi v povprečnem letu tudi vsaj deloma izboljšalo ekonomski položaj kmetijstva. Na večini slovenskih kmetij pa se žita uporabljajo kot vhodna surovina (v živinorejski proizvodnji), zato v tem sektorju lahko pričakujemo dodatne zaostritve z vidika ekonomike. Spremenljivi stroški krmnega obroka se v govedoreji že danes gibljejo med 40 in 75 % skupnih spremenljivih stroškov reje, pri neprežvekovalcih pa je ta delež lahko tudi višji. Zato vodenje prehrane postaja ključni vzvod za uspešno in ekonomično rejo živali. Rejci bodo pri načrtovanju krmnih obrokov v prihodnje prisiljeni upoštevati vse večje število ciljev in dodatnih omejitev, s kakršnimi se do sedaj neposredno večinoma še niso srečali (Tozer in Stokes, 2001), jih pa lahko povzamemo z ekonomskim pojmom eksternalije. Tudi v živinoreji lahko pričakujemo razvoj v smeri zaostrenih zakonodajnih zahtev, kakršne v rastlinski pridelavi poznamo že nekaj let (izravnana bilanca hranilnih snovi: zahteve kolobarja, gnojilni načrti, obtežba površin ipd.). V živinoreji nedvomno postaja čedalje pomembnejša zahteva čim manjše obremenjevanje okolja z neizkoriščenimi hranili in minerali. Na področju navzkrižne skladnosti med pogoji dobrega počutja živali v prihodnje lahko pričakujemo večji poudarek tudi zagotavljanju ustrezno uravnoteženega krmnega obroka in minimiziranju možnosti za preskromno ali prekomerno oskrbo s hranljivimi snovmi. Predvsem neuravnoteženost v oskrbi z rudninskimi snovmi pogosto vodi do presnovnih bolezni in drugih anomalij, kar ne vpliva le na slabše počutje živali, ampak ima tudi negativne ekonomske posledice. Ob poudarjeni »multifunkcionalni« vlogi kmetijstva to prevzema tudi vse značilnosti drugih gospodarskih sektorjev, med katerimi postaja prilagajanje konkurenčnosti temeljni vzrok in vzvod izboljšav v proizvodnji. Proces odločanja na mikro (kmetijska gospodarstva), mezo (raven regionalnega svetovanja) in tudi makro ravni (nosilci odločanja v kmetijski politiki) je mogoče podpreti z razvojem primernih empiričnih orodij. Empirično orodje mora omogočiti simuliranje kompleksnih agro-tehničnih, okoljskih in ekonomskih razmer ter zadostiti kriterijem formalne optimizacije, ki gospodarskim subjektom v danih razmerah z različnih vidikov ovrednoti njihovo razvojno perspektivnost. Tem kriterijem v največji meri zadostijo različne metode in modeli matematičnega programiranja, ki spadajo na področje operacijskih raziskav. Metodika izvedenega projekta: Projekt je zasnovan modularno, posamezni moduli pa se medsebojno dopolnjujejo oziroma služijo kot podporna orodja preostalim modulom. Modul prilagodljivih modelnih kalkulacij za podporo ekonomsko-tehnoloških izračunov (modul 1) Tako z ekonomskega kot s tehnološkega vidika je zgrajeno orodje podprto z Modelnimi ^ Potrebno je napisati vsebinsko raziskovalno poročilo, kjer mora biti na kratko predstavljen program dela z raziskovalno hipotezo in metodološko-teoretičen opis raziskovanja pri njenem preveijanju ali zavračanju vključno s pridobljenimi rezultati projekta. kalkulacijami, razvitimi na Kmetijskem inštitutu Slovenije (Rednak, 1997). Modelne kalkulacije so samostojni simulacijski modeli, ki na podlagi opredeljenih (izbranih) vhodnih tehnoloških parametrov omogočajo oceno porabe proizvodnih vložkov in s tem stroškov proizvodnje pri posameznih kmetijskih proizvodih. Poraba vložkov je odvisna od intenzivnosti (pridelka), velikosti parcele ali črede, oddaljenosti, nagiba in ponekod še od nekaterih drugih tehnoloških parametrov. Za razliko od t.i. Kataloga kalkulacij (Jerič, 2001), ki je bil osnova pri razvoju podobnega, sicer bistveno manj kompleksnega optimizacijskega orodja v okviru projekta CRP-V4-0362, modelne kalkulacije po posameznih pridelkih neposredno vključujejo vse proizvodne stroške. S tem je omogočen tudi neposreden izračun polne lastne cene. Njihova prednost je tudi v tem, da količine posameznih vložkov v modelnih kalkulacijah niso določene po razredih intenzivnosti, temveč večinoma v obliki funkcijske odvisnosti (zvezno). To je še posebno pomembno pri optimiranju konkretnih kmetijskih gospodarstev, saj je paleta intenzivnosti na slovenskih gospodarstvih zelo pestra. Na Kmetijskem inštitutu Slovenije so za potrebe posodabljanja modelnih kalkulacij vzpostavili tudi interno bazo podatkov za vse parametre (cene inputov in pridelkov, plače, dajatve, proračunske podpore...), katere vse od leta 1994 mesečno posodabljajo. Z uporabo modelnih kalkulacij je zagotovljena aktualnost zgrajenega orodja (enostavno posodabljanje) in tudi verodostojnost vhodnih, s tem pa tudi izhodnih podatkov. Razvito orodje je zato primerno tudi za analizo aktualnega dogajanja na konkretnih kmetijskih gospodarstvih. Modul za izračunavanje prehranskih potreb (modul 2) Ta modul temelji na nadgradnji in nadaljnjem razvoju deloma že predhodno pripravljenega modela za izračunavanje potreb po hranilnih snoveh prežvekovalcev (Žgajnar in sod., 2007). V prihodnje bi ga lahko razširili tudi v smeri izračunavanja potreb za neprežvekovalce, vendar to področje ni tako strokovno zahtevno kot pri prežvekovalcih, zato nam ni predstavljal raziskovalnega izziva. Je pa ekonomika reje zaradi velikega deleža žit in močne krme v obroku še toliko občutljivejša na močna nihanja cen teh komponent obroka, ki jih rejci pogosto kupujejo. Optimizacija prehrane zanje lahko pomeni precejšnje znižanje stroškov in s tem izboljšanje ekonomskega položaja, kar smo na nekaterih primerih upoštevali v naslednjem modulu (področje prehrane prašičev). Modul za izračunavanje prehranskih potreb je izdelan tako, da omogoča izračun povprečnih dnevnih potreb, potreb na točno določen dan znotraj proizvodne dobe, potreb v definiranem obdobju sezone, potreb v celotnem obdobju pitanja ali vzreje oziroma v enem letu glede na vnaprej definirane proizvodne lastnosti. Na podlagi slednjih model izračuna tudi predvideno dobo vzreje plemenskih živali in živali v pitanju. S takšnim pristopom je omogočeno obravnavanje različnih tehnologij reje in vzreje, s katerimi se v praksi srečujemo. Posebna pestrost tehnologij je prisotna pri govejih pitancih, pri katerih se ta odraža poleg pestre pasemske strukture predvsem v različnih začetnih masah pitanja in intenzivnosti pitanja. To se odraža tako v povprečnem dnevnem prirastu, dobi pitanja, kot tudi v klavno zreli telesni masi. V okviru tega modula smo pripravili tudi nabor najpogosteje uporabljene krme in njene hranilne vrednosti. To omogoča predvsem enostavne in hitre analize posameznega kmetijskega gospodarstva, saj lahko na osnovi nekaj najpomembnejših standardnih parametrov približno ocenimo hranilno vrednost doma pridelane krme. Prednost zgrajenega modula za izračunavanje prehranskih potreb je tudi ta, da od potencialnih uporabnikov ne zahteva podrobnega poznavanja uporabljenih funkcijskih pristopov, pač pa le nekatere bistvene zakonitosti živinoreje in pridelovanja krme. Hkrati je enostaven in dovolj natančen izračun krmnih potreb edini način, s katerim lahko rejce prepričamo v smiselnost pogostejšega izračunavanja obrokov za njihove živali. Modul za optimiranje prehrane z več pod-moduli (modul 3) Pri izgradnji tega modula smo izhajali iz predpostavke, da je iskanje najcenejšega krmnega obroka, ki hkrati pokrije vse potrebe živali, temeljno vodilo vsakega sodobnega živinorejca. Temu v prid govori dejstvo, da stroški krmnega obroka pogosto presegajo polovico, ob visokih cenah krmnih žit pa pri nekaterih kategorijah živali celo dve tretjini skupnih spremenljivih stroškov. S primernim optimizacijskim programom zato lahko sestavimo cenejše krmne obroke, ki so v danih ekonomskih In tržnih pogojih za posamezno rejo ekonomsko najugodnejši. S pomočjo tehnik matematičnega programiranja smo znotraj tega modula razvili samostojna optimizacijska orodja, s pomočjo katerih je možna optimizacija krmnih obrokov za posamezno kategorijo živali. V okviru projekta smo tako pripravili optimizacijski model za optimiranje prehrane krav molznic, krav dojilj, bikov pitancev in prašičev pitancev. Za vse omenjene kategorije domačih živali smo ubrali podoben metodološki pristop, bistvene razlike nastopijo le pri optimiranju prehrane prašičev pitancev. Modele smo zasnovali na principu dvostopenjske optimizacije, ki temelji na principu dveh podmodeiov (Žgajnar in Kavčič, 2008). Prvi pod-model temelji na metodi klasičnega linearnega programiranja. Z njim iščemo najcenejši krmni obrok, ki v 'grobem' zagotavlja pokrivanje prehranskih potreb, izračunanih s prejšnjim modulom. Pri iskanju rešitve upošteva le najpomembnejše omejitve, saj se zlasti pri visoko-produktivnih živalih, zaradi poenostavitev (linearni odnosi) ter nasprotujočih se omejitev, lahko zgodi da sistem nima rešitve. Posledično to pomeni da je sistem enačb, s katerimi je opredeljen prehranski problem, relativno precej 'odprt', kar nekaterih primerih pripelje tudi do prevelikih odstopanj od ključnih normativov. Posledično je lahko dobljena rešitev za prakso neuporabna (prevelike prekoračitve posameznih parametrov krmnih obrokov in neustrezna razmerja med hranilnimi snovmi). Problem bi deloma lahko zaobšli z definiranjem novih omejitev, s katerimi bi preprečili prekomerne prekoračitve, vendar bi takšen pristop zahteval interaktivni pristop reševanja, ki pa zardi zahtevanega znanja ter tudi časa reševanja ni zanimiv. Poleg tega bi takšen pristop pomenil zelo 'zaprt sistem enačb', ki bi se pri visoko-produktivnih živalih še pogosteje izkazal kot nerešljiv. Pri ubranem pristopu je pomen linearnega programiranja poiskati najcenejši krmni obrok, pri katerem nas ne zanima sestava samega obroka pač pa podatek o ceni. Slednjo namreč potrebujemo v drugem pod-modelu, ki temelji na tehtanem ciljnem programiranju in dodatno nadgrajenem s kazensko funkcijo. Gre za metodo večkriterijskega programiranja, ki na podlagi večjega števila ciljev poišče optimalno rešitev. Torej s tem pristopom iščemo kompromisno rešitev med zastavljenimi cilji, vključno z izračunanim minimalnim stroškom krmnega obroka, kateremu se poskušamo približati. Dodana t.i. 'kazenska funkcija' pa nam omogoča, da tudi v skrajnih primerih lahko pridemo do smiselne rešitve. Z njo definiramo dovoljena odstopanja od postavljenih omejitev. Namreč ena izmed ključnih pomanjkljivosti tehtanega ciljnega programiranja je da ne razlikuje med mejnimi spremembami oziroma ne loči med obsegom odstopanj od posameznih ciljev. S prehranskega vidika to pomeni, da dobimo prehransko bolj uravnotežen krmni obrok, ki pa se po stroškovni strani minimalno razlikuje od najcenejšega možnega, ki bi teoretično zagotavljal doseganje zastavljene proizvodnosti živali, v praksi pa pri njihovem doslednem upoštevanju zaradi porušenih medsebojnih razmerij tega pogosto ne dosegamo. Na ta način izračunani krmni obroki (bodisi dnevni/mesečni/polletni/letni) lahko vstopajo nazaj v živinorejske modelne kalkulacije. S tem vsaj teoretično lahko zagotovimo njihovo večjo fleksibilnost - prilagodljivost analiziranemu primeru. Vendar tega postopka ni mogoče popolnoma avtomatizirati, se je pa s pomočjo takšnega pristopa mogoče bolj približati stanju na konkretnem kmetijskem gospodarstvu. V primeru uporabe orodja za pomoč pri vodenju konkretnega kmetijskega gospodarstva lahko na ta način vnaprej ocenimo, katere kulture so za konkretno kmetijsko gospodarstvo v danih pogojih najbolj donosne. Uporabnik bi tako lahko svoje proizvodne vire razporedil tako, da bi kar najbolje pokril potrebe svojih živali. Prav alokacijska učinkovitost pa je poleg tehnične učinkovitosti ključen element ekonomske učinkovitosti (Farrell, 1957). Pri uporabljenem pristopu gre za podporo kratkoročnim odločitvam, ki pa pogosto lahko podkrepijo dolgoročno načrtovanje in usmeritev kmetijskiln gospodarstev. Optimizacija prehrane lahko pomeni precejšnje znižanje stroškov in s tem izboljšanje ekonomskega položaja. V prihodnje bi kazalo uporabljen pristop razširiti na dodatne živinorejske aktivnosti In ga s tem približati večjemu številu kmetijskih gospodarstev v Sloveniji. Modul za optimiranje kmetijskih gospodarstev (modul 4) Za podporo pri odločanju na ravni kmetijskih gospodarstev v Sloveniji je bil že razvit deterministični statični linearni program v okviru projekta »Spletni informacijski sistem za podporo odločanju na kmetijskih gospodarstvih« (CRP-V4-0362). Optimizacija je izvedena po načelu maksimiranja skupnega doseženega pokritja na ravni kmetije, ki jo opredelimo preko vnosa precej obširnega nabora podatkov in izklapljanja tistih aktivnosti, ki na konkretnem gospodarstvu niso realna alternativa. Model temelji na podatkih iz Kataloga kalkulacij. Kot je bilo že omenjeno, ima takšen pristop pomanjkljivost predvsem z vidika posodabljanja cenovnih razmerji in nezveznosti vključenih aktivnosti. To se je izkazalo kot pomanjkljivost tudi v fazi testiranja optimizacijkega modula (CRP-V4-0362). Zato smo v okviru tega projekta optimizacijski model nadalje razvili v smislu enostavnejšega posodabljanja kot tudi vklapljanja novih aktivnosti. Za precejšen del proizvodnih parametrov, stroškov in prihodkov smo pripravili izračune, ki preko funkcijskih povezav oblikujejo matriko za načrtovanje na konkretnem kmetijskem gospodarstvu. Formiranje matrike še vedno temelji na pokritjih, naknadno pa je mogoče od dobljene rešitve odšteti ocenjeno vsoto stalnih stroškov ali pa te izračunati na podlagi modelnih kalkulacij. Tak pristop omogoča podrobnejšo finančno analizo konkretnega kmetijskega gospodarstva. Zaradi krčitve finančnih sredstev projekta tega koraka nismo izpeljali do faze, da bi bil celoten preračun avtomatiziran, bi pa bil takšen postopek tudi z vidika potrebne strojne opreme (zmogljivosti računalnika) razmeroma zahteven, saj bi bil potreben iterativni pristop, torej večkratni zagon optimizacije, da bi dobili optimalno rešitev. Z vidika končnega uporabnika pa bi to pomenilo pristop, ki bi zagotovo večino odvrnil od njegove uporabe. V prehranskem delu razširjen in natančnejši model omogoča tudi dodatne analize s področja ekonomike prehrane. S ponovnim definiranjem namenske funkcije smo naredili tudi primerjalno analizo med optimalno rešitvijo, ki jo dobimo pri maksimiranju pokritja in med optimalno rešitvijo, če z namensko funkcijo minimiramo krmne stroške. Ugotovili smo, da je ob istih omejitvah korelacija med dobljenimi rešitvami zelo visoka. Za izvedbo projekta smo uporabili predvsem metode matematičnega programiranja. Zaradi modularnega pristopa k izvedbi projekta smo lahko uporabili njim najbolj ustrezne metode. Na podlagi pregleda literature smo izbirali med metodami matematičnega programiranja, ki so bile vsaj teoretično predhodno že aplicirane za različne obratoslovne probleme. V modulih, kjer je izvedena formalna optimizacija, smo uporabili tehniko klasičnega determinističnega linearnega programiranja. Pri praktičnem reševanju optimizacijskih problemov pa se skoraj vedno izkaže, da je fokusiranje zgolj na en cilj kot edini in najpomembnejši (ekonomski) pregroba poenostavitev in je posledično dobljena rešitev za prakso povsem neuporabna. Zato smo na podlagi dognanj (Rehman in Romero, 1984, 1987; Lara, 1993; Lara in Romero, 1994 in kasneje tudi drugih) probleme skušali streti s pomočjo večkriterialnega pristopa in iskali rešitev, ki nam ne omogoča le ekonomske optimizacije, ampak ob tem zasleduje tudi druge cilje, ki so prav tako pomembni za načrtovanje odločitve (Zadnik Stirn, 2001). V okviru projekta smo tako pri nekaterih modulih uporabili tehtano ciljno programiranje. Gre za posebno obliko linearnega programiranja. V primerjavi s klasičnim linearnim programom, kjer naenkrat lahko optimiramo le en cilj, ostale zahteve pa zajamemo v omejitvah, lahko s ciljnim programom iščemo rešitev, ki zadosti večjemu številu zastavljenih ciljev. Želene toge omejitve klasičnega linearnega programa tako preoblikujemo v cilje. Dosežemo jih lahko v celoti, deloma, v skrajnih primerih pa nekaterih izmed njih sploh ne dosežemo. Metoda torej dopušča odstopanje od zastavljenega cilja, ki pa naj bi bilo čim manjše. Zagotovo je namreč v praksi bolje, da dobimo »dovolj dobro« rešitev, kot pa da dobimo optimalno in povsem nerealno oziroma je sploh ne dobimo. Nadgrajen klasičen linearni program v ciljni program omogoča večjo fleksibilnost in v večini primerov pripelje do realnejše rešitve. Z njim minimiziramo neželeno odstopanje od zastavljenih ciljev in ne minimiziramo oziroma maksimiramo ciljev samih (Ferguson in sod., 2006). Kvaliteta modela je tako v največji meri odvisna od definiranja zastavljenih ciljev in pripadajočih uteži k posameznemu cilju. Zato je pri večkriterialnem modeliranju nujno sodelovanje strokovnjakov iz vpletenih področij ali celo uporaba druge metode za čim manjšo pristranskost pri definiranju pomena posameznega cilja. Za definiranje uteži bi namreč lahko uporabili metodo analitičnega hierarhičnega procesa (AHP). Ta se je pri reševanju večkriterialnih problemov že izkazala kot učinkovito orodje pri definiranju uteži ciljev. V zgrajenih modulih tega projekta pa ta metoda še ni bila uporabljena. Z uporabo tehnike ciljnega programiranja pridemo do kompromisne rešitve, ki pa vsaj v nekaterih primerih lahko pomeni preveliko odstopanje od zastavljenega cilja in zato iz praktičnega vidika takšna rešitev ni sprejemljiva. Da smo prehranske potrebe živali ohranili znotraj želenih mej, smo ciljni program nadgradili s t.i. kazensko funkcijo (Rehman in Romero, 1984). Vsako odstopanje od želenega cilja (želimo ga doseči 100 %) smo na ta način obravnavali po vnaprej definirani večstopenjski kazenski lestvici, ki ni dopuščala večjega odstopanja od meje definiranih intervalov. Namenska funkcija tehtanega ciljnega programiranja, nadgrajenega s kazensko funkcijo, je na ta način merila celotno 'kazen', pridobljeno z odstopanji od posameznih ciljev. Intervale kazenske lestvice, s katerimi smo definirali dovoljeno odstopanje od zastavljenih ciljev, pa smo vključili v nabor omejitev. Rezultati: Operativni cilj izvedenega projekta je aplikacija metode matematičnega programiranja za reševanje problemov večkriterijskega odločanja na ravni kmetijskih gospodarstev. Večji del raziskovalnega dela, opravljenega v okviru projketa, je bilo predstavljeno v obliki prispevkov na šestih znanstvenih konferencah (od tega štiri na mednarodni ravni, eden na svetovni ter eden na nacionalni ravni) in v mednarodnih znanstvenih revijah. Primer optimiranja obrokov za bike pitance ter opis uporabljenga pristopa je podrobno predstavljen v Žgajnar in Kavčič (2008b) ter Žgajnar in Kavčič (2008c). Metodološko podoben pristop je bil apliciran tudi na primeru sestavljanja obrokov za krave molznice (Žgajnar in Kavčič, 2009d; Žgajnar in sod. 2009), kjer je bil poudarek na formuliranju dnevnih krmnih obrokov. Pri sestavljanju ter analiziranju prehrane prašičev pitancev je bil uporabljen metodološko podoben pristop, ki pa je temeljil na treh pod-modelih (Žgajnar in Kavčič, 2009a; Žgajnar in Kavčič, 2009b in Žgajnar in Kavčič, 2009c). Pri slednjih se je namreč izkazalo, da je ekonomičnost reje - tehnologije pitanja zelo odvisna od energetske koncentracije obroka. Zadnji korak pa na podlagi preprostega algoritma izbere najučinkovitejšo rešitev. Na primeru pitanja bikov smo analizirali tudi, kako 'zunanje' spremembe na političnem in ekonomskem področju prispevajo k izrazito poslabšani stabilnosti ekonomike pitanja govedi (Žgajnar in Kavčič, 2008a). Naša hipoteza je bila, da se z zviševanjem cen krme (poslabšanje cenovno-stroškovnih razmerij) kot posledice dodatnega povpraševanja (bio-energija, bio-masa), manjše proizvodnje in liberalizacije trgov, spreminja tudi (racionalna) sestava krmnega obroka. Analizo smo opravili s pomočjo metod matematičnega programiranja, ki temeljijo na principu omejene optimizacije. Za simuliranje odzivov na zunanje (eksogene) spremembe je bila uporabljena metoda pozitivnega matematičnega programiranja (PMP). V okviru projekta razvito modularno orodje povezuje številne dejavnike, ki so predmet različnih področij in skupaj krojijo kratkoročno odločanje in dolgoročno načrtovanje kmetijskih gospodarstev, s poudarkom na prehrani. To je namreč podočje, kateremu je bilo v dosedanjih agrarno-ekonomskih raziskavah posvečeno (pre)malo pozornosti, je pa ključno pri analizi živinorejskih tipov kmetijskih gospodarstev. Orodje je ob vključitvi najsodobnejših tehnik linearnega programiranja razdeiano do te mere, da omogoča simulacijo realnih rezultatov in je zato lahko v dejansko pomoč pri obratoslovnih odločitvah. Zaradi kompleksnosti dejavnosti kmetijstva je bilo delo ob upoštevanju časovnih, človeških in finančnih omejitev projekta omejeno le na del gospodarskih aktivnosti in s tem prilagojeno za odločanje na določenem tipu kmetijskih gospodarstev. Model lahko apliciramo na kmetijska gospodarstva, ki se ukvarjajo predvsem z rejo prežvekovalcev. Orodje omogoča razrešitev nekaterih vprašanj nadaljnje profesionalizacije, proizvodne preusmeritve, izbire ukrepov kmetijske politike ter trajnostne rabe proizvodnih virov na ravni tovrstnih kmetijskih gospodarstev. Z morebitnim podaljšanjem projekta bi zgrajeno orodje lahko nadgradili v smeri večje univerzalnosti (dopolnjevanje z dodatnimi usmeritvami: neprežvekovalci, dodatne poljedelske kulture, trajni nasadi, zelenjadarstvo ipd.). Z izvedbo projekta smo omogočili izboljšave posameznih korakov načrtovanja na mikro in mezo ravni. V prvi vrsti z zgrajenim orodjem lahko optimiramo proizvodnjo na konkretnih kmetijskih gospodarstvih, na podlagi rezultatov tipičnih kmetijskih gospodarstev znotraj izbranih regij pa ima orodje napovedovalno moč tudi za simulacije razvojnih učinkov na regionalni in nacionalni ravni. 3. Izkoriščanje dobljenih rezultatov: 3.1. Kakšen je potencialni pomen^ rezultatov vašega raziskovalnega projekta za: a) odkritje novih znanstvenih spoznanj; b) izpopolnitev oziroma razširitev metodološkega instrumentarija; c) razvoj svojega temeljnega raziskovanja; d) razvoj drugih temeljnih znanosti; e) razvoj novih tehnologij in drugih razvojnih raziskav. K 3.2. Označite, s katerimi družbeno-ekonomskimi cilji (po metodologiji OECD-ja) sovpadajo rezultati vašega raziskovalnega projekta: a) razvoj kmetijstva, gozdarstva in ribolova - Vključuje RR, ki je v osnovi namenjen razvoju in podpori teh dejavnosti; b) pospeševanje industrijskega razvoja - vključuje RR, ki v osnovi podpira razvoj industrije, vključno s proizvodnjo, gradbeništvom, prodajo na debelo in drobno, restavracijami in hoteli, bančništvom, zavarovalnicami in dragimi gospodarskimi dejavnostmi; c) proizvodnja in racionalna izraba energije - vključuje RR-dejavnosti, ki so v funkciji dobave, proizvodnje, hranjenja in distribucije vseh oblik energije. V to skupino je treba vključiti tudi RR vodnih virov in nuklearne energije; d) razvoj infrastrukture - Ta skupina vključuje dve podskupini: • transport in telekomunikacije - Vključen je RR, ki je usmeijen v izboljšavo in povečanje varnosti prometmh sistemov, vključno z varnostjo v prometu; • prostorsko planiranje mest in podeželja - Vključen je RR, ki se nanaša na skupno načrtovanje mest in podeželja, boljše pogoje bivanja in izboljšave v okolju; 3 e) nadzor in skrb za okolje - Vključuje RR, kije usmegen v ohranjevanje fizičnega okolja. Zajema onesnaževanje zraka, voda, zemlje in spodnjih slojev, onesnaženje zaradi hrupa, odlaganja trdnih odpadkov in sevanja. Razdeljen je v dve skupini: f) zdravstveno varstvo (z izjemo onesnaževanja) - Vključuje RR - programe, ki so usmeqeni v varstvo in izboljšanje človekovega zdravja; g) družbeni razvoj in storitve - Vključuje RR, ki se nanaša na družbene in kulturne probleme; h) splošni napredek znanja - Ta skupina zajema RR, ki prispeva k splošnemu napredku znanja in ga ne moremo pripisati določenim ciljem; i) obramba - Vključuje RR, ki se v osnovi izvaja v vojaške namene, ne glede na njegovo vsebino, ali na možnost posredne civilne uporabe. Vključuje tudi varstvo (obrambo) pred naravnimi nesrečami. Označite lahko več odgovorov. 3.3. Kateri so neposredni rezultati vašega raziskovalnega projekta glede na zgoraj označen potencialni pomen in razvojne cilje?_ Olajšani so določeni postopki načrtovanja prehrane na kmetijskih gospodarstvih, predvsem izračunavanja obrokov za različne kategorije domačih živali. Izračunavanje obrokov temelji na razpoložljivi krmi in potrebah živali, bistveni prispevek tega projekta pa je optimiranje tehnologije prehrane živali, ki je podkrepljeno z ekonomskimi izračuni. Na ta način je omogočena časovna/delovna razbremenitev kmetijskih gospodarjev, predvsem pa izračunani obroki omogočajo skozi vgrajeno stroškovno optimizacijo doseganje višje dodane vrednosti v živinorejski proizvodnji, vendar nikakor ne na škodo okolja.__ 3.4. Kakšni so lahko dolgoročni rezultati vašega raziskovalnega projekta glede na zgoraj označen potencialni pomen in razvojne cilje?_ Razvoj orodij matematičnega programiranja v smeri, ki je precej prijazen do uporabnikov, omogoča prenos teoretičnih dognanj v vsakodnevno prakso kmetovanja in na daljši rok omogoča preko dviga dodane vrednosti (skozi večjo stroškovno učinkovitost) izboljšanje konkurenčnosti slovenskega kmetijstva. Ker razvita orodja omogočajo bolj natančno izravnavo zaužitih in potrebnih hranilnih snovi v obrokih (domačih vrst) živali, z uporabo razvitih orodij lahko dosežemo tudi pozitivne okoljske učinke (manjše izločanje neizkoriščenih hranilnih snovi v okolje, manjši izpusti toplogrednih plinov na enoto prireje ipd.)._ 3.5. Kje obstaja verjetnost, da bodo vaša znanstvena spoznanja deležna zaznavnega odziva? a) v domačih znanstvenih krogih; b) v mednarodnih znanstvenih krogih; ^ c) pri domačih uporabnikih; d) pri mednarodnih uporabnikih. 3.6. Kdo (poleg sofinancegev) že izraža interes po vaših spoznanjih oziroma rezultatih? Neposredni uporabniki (predvsem mlajši kmetijski gospodarji) in Kmetijsko-gozdarska zbornica Slovenije. 3.7. Število diplomantov, magistrov in doktorjev, ki so zaključili študij z vključenostjo v raziskovalni projekt?_ v fazi izdelave je ena diplomska naloga in ena doktorska disertacija. Prva predstavlja primer neposredne uporabe razvitih orodij v praksi (z iskanjem izboljšav v drugih fazah proizvodnih postopkov na kmetiji), druga pa znanstveno-metodološko poglobitev dela na področju optimizacije odločanja na kmetijskih gospodarstvih._ 4. Sodelovanje s tujimi partnerji: 4.1. Navedite število in obliko formalnega raziskovalnega sodelovanja s tujimi raziskovalnimi institucijami._ Pri projektu, ki je predmet tega zaključnega poročila, nismo imeli formalnega raziskovalnega sodelovanja s tujimi raziskovalnimi institucijami. 4.2. Kakšni so rezultati tovrstnega sodelovanja? 5. Bibliografski rezultati^: Za vodjo projekta in ostale raziskovalce v projektni skupini priložite bibliografske izpise za obdobje zadnjih treh let iz COBISS-a) oz. za medicinske vede iz Inštituta za biomedicinsko informatiko. Na bibliografskih izpisih označite tista dela, ki so nastala v okviru pričujočega projekta. 6. Druge reference'^ vodje projekta in ostalih raziskovalcev, ki izhajajo iz raziskovalnega proiekta: 3 Bibliografijo raziskovalcev si lahko natisnete sami iz spletne stram:http:/www.izum.si/ * Navedite tudi druge raziskovalne rezultate iz obdobja financiranja vašega projekta, ki niso zajeti v bibliografske izpise, zlasti pa tiste, ki se nanašajo na prenos znanja in tehnologije. Navedite tudi podatke o vseh javnih in drugih predstavitvah projekta in njegovih rezultatov vključno s predstavitvami, ki so bile organizirane izključno za naročnika/naročnike projekta. COBISS Kooperativni online bibliografslci sistem in servisi COBISS COBISS Kooperativni online bibliografski sistem in servisi COBISS STANKO KAVČIČ [13487] Osebna bibliografija za obdobje 2007-2010 ČLANKI IN DRUGI SESTA VNl DELI 1.01 Izvirni znanstveni članek 1. ŽGAJNAR, Jaka, ERJAVEC, Emil, KAVČIČ, Stane. Optimisation of production activities on individual agricultural holdings in the frame of different direct payments options. Acta agric. Slov.. [Tiskana izd.], 2007, letn. 90, št. 1, str. 45-56. [COBISS.SI-ID 2215048] 2. /(iA.I\' \R, Jaka, KAVČIČ, Stane. Spremembe sc>^lave kmniih obrokov goveje pitance Ciuinges of beef ratii>n eoniposilioii : primer uponibe norinaliMiih in pozitivnih matenuitieiiih metod : an c.xaniple of utilizing nunnatiw and positive nialheinatical methods. .kia üi^nc. Shv..\ risicana i/.iL]. 20()S. let^^)2- si. 1, sir. 20-40. iCOBlSS.SI-ID 2108328] (Žgajnar in Kavčič, 2008a) 3. ŽGAJNAR, Jaka, ERJAVEC, Emil, KAVČIČ, Stane. Change in farm production structure within different CAP schemes - an LP modelling approach. An. Univ. "Duncearea de Jos" Galati, Fasc. IEcon. inform, apl, 2008, fasc. 1, str. 31-36. [COBISS.SI-ID 23914321 4. /GAJNAR. Jaka. IC.-WCIC, Stane, üpliniizalion ol' bulls fattening ratitm ap]ilying niatlicmaiieal determini.«;tic programming approach. Buhj;. J. (igric. sei., 2008. vol. 14, no. 1, sir. 76-86. fCOBlSS.SI-lD 228.S0f)S] (Žgajnar in Kaveic, 2()0Sb) 5. ŽCJAJNAR. Jaka, Jl'VANX'lC, lAika. KAVČIČ. Staue. Combination of linear and weighted goal progfumming with penalty iimction in optimisation of daily dairy cow ration ^ Kojnbinacc Hncdrniho a vu/eneho ciloveho programovani s trcstnou liinkci pfi stanovcni deiini krmne davky pro doinice. Zemcd. ckon.. 20W. \-ol. 55, no. 10, str. 402-500. [COBlSS.Si-lD 2524040] (Žgajnar in sod., 2008) 1.04 Strokovni članek 6. KAVČIČ, Stane. Loterija se nadaljuje : izplačila ukrepov kmetijske politike. Krneč, glas, 2007, letn. 64, št. 10, str. 6-7. [COBISS.SI-ID 19941201 7. BUITEN, Ab van, JERIČ, Damjan, KAVČIČ, Stane. Smernice za kmetovanje s kvoto in premijami. Sodob. kmet., 2007, letn. 40, št. 1, str. 14-19. [COBISS.SI-ID 1994888] 8. KAVČIČ, Stane. Stroški gor, odkupne cene dol. Sodob. kmet., 2008, letn. 41, št. 1, str. 6-7. [COBISS.SI-ID 2273160] 9. KAVČIČ, Stane, JERIČ, Damjan. Se mi bo naložba v prirejo mleka obrestovala?. Krneč, glas, 2009, letn. 66, št. 12, str. 12-13. [COBISS.SI-ID 2441352] 10. KAVČIČ, Stane, JERIČ, Damjan. Možnosti za izboljšanje gospodarnosti prireje mleka. Krneč, glas, 2009, letn. 66, št. 50, str. 8-9, 2009, letn. 66, št. 52, str. 8. [COBISS.SI-ID 25568081 11. KAVČIČ, Stane, JERIČ, Damjan. Možnosti za izboljšanje gospodarnosti prireje mleka. Krneč glas, 2010, letn. 61, št. 1, str. 7. [COBISS.SI-ID 2557064] 1.06 Objavljeni znanstveni prispeveli na konferenci (vabljeno predavanje) 12. JERIČ, Damjan, KAVČIČ, Stane. Možnosti racionalizacije stroškov v prireji mleka = Possibilities for cost reduction in milk production. V: ČEH, Tatjana (ur.), KAPUN, Stanko (ur.). Zbornik predavanj -18. Mednarodno znanstveno posvetovanje o prehrani domačih živali "Zadravčevi-Erjavčevi dnevi" : Radenci, 5. in 6. november 2009. Murska Sobota: Kmetijsko gozdarska zbornica Slovenije, Kmetijsko gozdarski zavod, 2009, str. 58-70. [COBISS.SI-ID 25294161 1.08 Objavljeni znanstveni prispevek na konferenci 13. LEEUVEN, Myma van, BARTOVÄ, Lubica, M'BAREK, Robert, KAVČIČ, Stane. EU agricultural markets outlook - AGMEMOD approach. V: ŠEVARLIČ, Miladin (ur.), TOMIČ, Danilo (ur.). Development of Agriculture and Rural Areas in Central and Eastern Europe : proceedings of plenary papers and abstracts. Zemun: Serbian Association of Agricultural Economists, 2007, str. 1-8. [COBISS.SI-ID 2082440] 14. KOVAČ, Mateja, ERJAVEC, Emil, KAVČIČ, Stane. Production and income outlook for Slovene agriculture. V: ŠEVARLIČ, Miladin (ur.), TOMIČ, Danilo (ur.). Development of Agriculture and Rural Areas in Central and Eastern Europe : proceedings of plenary papers and abstracts. Zemun: Serbian Association of Agricultural Economists, 2007, str. 1-9. [COBISS.SI-ID 20819281 15. LEEUVEN, Myma van, BARTOVÄ, Lubica, M'BAREK, Robert, KAVČIČ, Stane. EU agricultural markets outlook - AGMEMOD approach. V: TOMIČ, Danilo (ur.), ŠEVARLIČ, Miladin (ur.). lOOth Seminar of the EAAE, Novi Sad, Serbia, 21st-23rd June 2007. Development of agriculture and rural areas in Central and Eastern Europe : thematic proceedings. Novi Sad: Regional Chamber of Commerce, [2007?], str. 121-128. [COBISS.SI-ID 2244232] 16. KOVAČ, Mateja, ERJAVEC, Emil, KAVČIČ, Stane. Production and income outlook for Slovene agriculture. V: TOMIČ, Danilo (ur.), ŠEVARLIČ, Miladin (ur.). lOOth Seminar of the EAAE, Novi Sad, Serbia, 21st-23rd June 2007. Development of agriculture and rural areas in Central and Eastern Europe : thematic proceedings. Novi Sad: Regional Chamber of Commerce, [2007?], str. 293-301. [COBISS.SI-ID 22444881 17. ŽGAJNAR, Jaka, ERJAVEC, Emil, KAVČIČ, Stane. CAP reform policy alternatives and farm decisions' optimization : the case of Slovenia. V: IFMA 16 : congress 2007, Ireland. [S. 1.: s. n., 2007?], str. 199-208. [COBISS.SI-ID 2091144] 18. KOVAČ, Mateja, ERJAVEC, Emil, KAVČIČ, Stane. Napovedovanje dodane vrednosti v dejavnosti kmetijstva = Forecasting the value added in agriculture. V: KAVČIČ, Stane (ur.). Slovensko kmetijstvo in podeželje v Evropi, Id se širi in spreminja. 1. izd. Ljubljana: Društvo agrarnih ekonomistov Slovenije - DAES, 2007, str. 269-276. [COBISS.SI-ID 2264456] P). Zii:\}K\R. Ji:k;i. KI-.RMAl'M^R. Ajda. KAVČIČ. Staiu-. \lodol /a occiijc\anjc pruliranskih [K^rcb prcŽ\ckovulcov in opliiniranjckrninih obrokov -= Hslimation orvuniinanis' nulrilional raiiiircmoin-s and li\LNUick ration optimisation. KA\'ČIČ. Stane (ur.). Slovci!sl:o kuu.njslvo in podeželje i' Evropi, ki sc širi in spreminja. 1. i/el. Ljubljana: Drušl\o am-arnih ckonouiisiov Slovenije - D.MIS, 200". str. 270-28S. [COBISS.Sl-ID 22647 LI I (Žgajnar in sod., 2007) 20. Ž("i'\J\AI^, .laka. KAVČIČ, Stane. Spreadsheet tool for leasi-eosi and nutrition balanced licef ration ibmuilation - Orodje /a načrtovanje najcenejših prehransko i/ravnaiiili obrokov /a pitance. JM-TRIČ, Nczika (ur.). L'rn'pw^tna reja domačih živali. (Acta agrieulturae sloveniea. Suplunent. Supplement. 2). V Ljubljani: liiotelini.ska fal\ulteta. 2008, str. 1S7-I^M. [COlBfSS.SI-ID 23655761 (/-ajnar in Kavčič, 200.Se) 21. /Ci.-\.fNAR. Jaka, K.AVČiČ, Stane, lliree pba.se feed-mix optimization for growing pigs. V: irM,\ 17. July ! 0-24 Bloomington, Illinois, l-'ood, fiber and ener-^y for the j'uturc. | S. 1.: s. n.. 200')?J. Str. [199-2101. [COBIS^S.SI-ID 24^660.41 li0 (4) Korak 2: «-C, (5) >0,= % (6) K»rak3: MaxZ =-(a+Q,5ßxf)Xi tako, daje (7) A,x,0 (9) Namenska funkcija, definirana z enačbo (1), predstavlja vsoto zmnožkov tržnih cen (-c,) ter polnih lastnih cen (-c;) z-te krme s količino izbrane z-te krme v sestavljenem krmnem obroku. Ker smo pri cenah upoštevali negativen predznak, je posledično namenska funkcija predmet maksimiranja. Druga enačba predstavlja prehranske normative, katerim mora biti zadoščeno, da model najde rešitev. S pomočjo dualnega programa lahko dobimo senčne cene (Xi) posameznih omejujočih omejitev. V primeijavi s klasičnim linearnim programom smo naš primarni LP model razširili s t.i. kalibracijskimi omejitvami (3). Z njimi model 'prisilimo', da raven izbrane i-tekrme (x,) ne preseže referenčne količine z-te krme, kateri je prišteta zelo majhna vrednost, t.i. perturbacija (e). Slednja je vpeljana v kalibracijsko omejitev z namenom, da preprečimo linearno odvisnost med klasičnimi omejitvami (prehranskimi) in kalibracijskimi omejitvami (Heckelei in Britz, 2000). Z dodanimi kalibracijskimi omejitvami pridemo do rešitve samo v primeru, da je referenčni obrok skladen z omejitvami modela. Na prvi pogled gre za povsem trivialno trditev, vendar se le-ta lahko izkaže kot problematična, če z modelom analiziramo sestavo podobnih krmnih obrokov, katerih sestavine imajo zaradi najrazličnejših vzrokov povsem različne hranilne A^ednosti. S pomočjo dualnega programa dobimo senčne cene kalibracijskih omejitev. V drugem koraku (5 in 6) na podlagi senčnih, lastnih in tržnih cen izračunamo parametre stroškovne funkcije. S pomočjo teorije povprečnih stroškov izpeljemo a, ki predstavlja presečišče stroškovne funkcije in parameter ß, ki predstavlja naklon stroškovne funkcije. V zadnji fazi kalibriranja uporabimo izračunane parametre stroškovne funkcije. Namenska funkcija (7) se zaradi kvadriranja (x/) spremeni v nelinearno, pri kateri zopet iščemo maksimum. Tako prilagojena in 'uravnotežena' namenska funkcija, ob upoštevanju prehranskih omejitev, nam brez kalibracijskih omejitev vrne sestavo referenčnega krmnega obroka. Na tako pripravljenem modelu lahko nato študiramo npr. vpliv sprememb cen in stroškov preteklega desetletnega obdobja. V našem primeru smo kot referenčni krmni obrok izbrali nekoliko prilagojen krmni obrok, predpostavljen v modelnih kalkulacijah (KIS, 2008). Prehranske potrebe bikov pitancev Seveda gre pri sestavljanju krmnih obrokov za številne dejavnike, ki vodijo kmeta pri njegovem odločanju. Poleg izbrane pasme, velikosti kmetijskega gospodarstva ter razmerja med ornimi in travnimi površinami, ki določajo potrebe po krmi ter razmerje med doma pridelano in kupljeno krmo, je pomembna tudi tehnologija pitanja. Za analizo smo izbrali tehnološke predpostavke analitične modelne kalkulacije (KIS, 2008). Predpostavili smo, da se pitanje začne pri telesni masi 120 kg in se konča pri telesni masi 550 kg. Povprečen dnevni prirast preko celotnega obdobja znaša 0,9 kg/dan, kar pomeni, da pitanje traja 478 krmnih dni. Ker se za potrebe modelnih kalkulacij uporablja starejši sistem škrobnih enot, smo prehranske potrebe pitancev ocenili s pomočjo simulacijskega modela za ocenjevanje prehranskih potreb prežvekovalcev, ki temelji na presnovni energiji. Simulacijski model je podrobneje opisan v Žgajnar in sod. (2007). Kupljena in doma pridelana krma Za analizo smo izbrali najpogostejši način pitanja v Sloveniji. Predpostavili smo, da kmetijsko gospodarstvo večji del krme pridela na lastnih zemljiščih, del močne krme pa dokupi na trgu po tržnih cenah. Ker voluminozne krme večinoma ni tržna dobrina, smo na podlagi izračunov modelnih kalkulacij ocenili skupne stroške pridelave posamezne krme in jih nadalje ovrednotili s polno lastno ceno (brez upoštevanja morebitnih subvencij). Za razliko od metode pokritja, kjer so zajeti zgolj spremenljivi stroški, modelne kalkulacije vključujejo vse stroške, ki so povezani s pridelavo, kamor prištevamo tudi stroške dela (Rednak, 1998). Ob tem je potrebno podariti, da smo upoštevali zgolj stroške, povezane s pridelavo glavnega pridelka oziroma pridelka, ki ga lahko vključimo v krmni obrok. Pri vrednotenju krme po polni lastni ceni ima ekonomija obsega ključno vlogo. Zato je potrebno izpostaviti, da kalkulacije temeljijo na predpostavki, daje velikost parcel 1 ha in so od kmetijskega gospodarstva oddaljene 1 km. Serijo osnovnih podatkov med leti 1998 in 2008 smo pridobili na spletni strani Kmetijskega inštituta, kjer imajo objavljene t.i. zbirnike podatkov na letni ravni (KIS, 2008). Prva dva modela (LP in WGP) lahko pri sestavljanju krmnega obroka izbirata med osmimi vrstami krme (slika 1). Na razpolago imata pet vrst močnih krmil (ječmen, koruza, pšenica, dopolnilna krmna mešanica K-18 in sojine tropine), ter tri vrste voluminozne krme (seno, koruzna silaža in travna silaža). Predpostavili smo, da rejci vsa močna krmila dokupijo po tržnih cenah. Na lastnih zemljiščih pa pridelajo seno, travno in koruzno silažo. Slednje lahko ovrednotimo po njihovi polm lastni ceni. Kot je razvidno s slike 1, seje v opazovanem obdobju vsa krma podražila. -Ječmen - Barley -Pšenica-Wheat Sojine tropine - Soya meal ■ Koruzna silaža (II os) - Maize silage (II axis) - Koruza - Maize • Seno - Hay ■K-18 - - Travna silaža (II os) - Grass silage (II axis) Slika 1: Gibanje tržnih cen močne krme ter polnih lastnih cen doma pridelane voluminozne krme v obdobju 1998 -2008 Figure 1: Changing market prices and total unit costs for feed and voluminous forage in the period 1998 - 2008 Izračunane polne lastne cene doma pridelane voluminozne krme so se vse od leta 1998 nenehno zviševale. S podrobnejšo analizo smo ugotovili, daje zviševanje cen voluminozne krme posledica predvsem vse dražjih strojnih storitev in vse višjih postavk domačega dela ter kapitala. Poleg tega so se v opazovanem obdobju tudi mineralna gnojila nenehno dražila, kar je bilo še posebej izrazito v zadnjih dveh letih. V letu 2008 so se denimo cene mineralnih gnojil zvišale sl(oraj za trikrat. Slednje je tudi ključni razlog, da so se lastne cene pridelkov v zadnjem letu tako povečale. Slika bi bila nekoliko drugačna, če bi pretežen del rastlinskih hranil rejci zagotovili z giojem domačih živali. S slike 1 je razvidno, da se je cena travne silaže v primerjavi s koruzno silažo relativno hitreje zviševala. Izrazit razkorak se kaže od leta 2002 dalje. Na prvi pogled nelogično dejstvo je moč pojasniti s količino pridelka na enako površino zemljišča. Pridelek travne silaže je bistveno manjši v primerjavi s sicer že tako ali tako cenejšo koruzno silažo, zato so stroški pridelave travne silaže na enoto pridelka večji. Nihanja so opazna tudi pri kupljeni močni krmi. Dvig cen je nedvomno posledica kompleksnih pojavov in vplivov, ki pa jih ni mogoče enoznačno opredeliti. S slike 1 je razvidno, da so energijska krmila (koruza, pšenica in ječmen) v primeijavi s pretežno beljakovinsko krmo (sojine tropine) in sestavljenim močnim krmilom K-18 bistveno cenejša. Koruzno zrnje je v vsem opazovanem obdobju dražje od pšenice in ječmena, ki se izraziteje podražita šele v zadnjih treh letih. Za pokrivanje potreb po rudninskih snoveh so v nabor krmil vključene tudi štiri rudninsko vitaminske mešanice. Sprememb njihovih cen v danem obdobju ne prikazujemo, saj zaradi manjše količinske zastopanosti v obroku ne vplivajo na našo analizo. Pri optimiranju sestave krmnega obroka sta, poleg ekonomskega vidika, ključnega pomena hranilna vrednost in kakovost krme. Obe sta odvisni od številnih dejavnikov kot so kakovost tal, klimatski dejavniki, količine padavin, tehnologije pridelave in tehnologije spravila. Iz tega sledi, da lahko kakovost krme med leti močno niha, kar lahko povzroči, da obroki s povsem enako sestavo ne pokrijejo vedno vseh potreb živali po hranljivih snoveh. V naši analizi smo ta vidik zanemarili; v izračunu smo upoštevali nekoliko nadpovprečno hranilno vrednost krme, ki je bila enaka v celotnem obdobju opazovanja. REZULTATI IN RAZPRAVA Rezultate modelov prikazujemo v enakem vrstnem redu, kot so opisani uporabljeni pristopi. Najprej pokažemo, kako bi se sestava obroka spreminjala, če bi bil rejec povsem prilagodljiv in bi bil njegov edini cilj minimiranje stroškov (rezultati LP). Sledijo krmni obroki, ki so sestavljeni s pomočjo tehtanega ciljnega programiranja. Nadaljujemo s predstavitvijo rezultatov post-optimalne analize in njihovega pomena. V zadnjem delu se osredotočimo na simulirane krmne obroke s pomočjo PMP modela. Vsi grafikoni, ki prikazujejo skupne stroške in strukturo krmnih obrokov, se nanašajo na celotno obdobje pitanja. V prvi model smo vključili 12 vrst krme, iz katerih smo sestavili najcenejši možni krmni obrok. S slike 2 je razvidno, da se sestava tega krmnega obroka med leti močno spreminja. Značilnost LP je namreč prekinjen (nezvezen) odziv na spremenjene zunanje razmere - v našem primeru tržne cene oziroma izračunane polne lastne cene. Posledično se dobljena rešitev izrazito spreminja med leti in kar je bolj problematično, iz dobljenih rezultatov se ne da izluščiti neke splošne zakonitosti, kaj se je v opazovanem obdobju dogajalo s sestavo krmnega obroka in napovedati, kakšna bodo gibanja v prihodnosti. To dejstvo je še zlasti izrazito pri vključevanju energijskih močnih krmil v obrok. — a "O D T3 W S C §1 iiS o I Vjo ra e t o 1.200 1.000 800 600 400 200 .o ® 8 O 5 h t % . ^ir -/i VTI". A ' M T / \\ \ \ / \ \ / \f * / W ' ! -^y ■A". / A A /\ ^ \ ■■ i'-g—T-^ "1 ■••^•'i'''« " 1 g 1 LUHj o o o o o o 11 Ii s C7> _ _ _ _ _ X- t- CJ CN CVJ N CN - Ječmen - Barley - Sojine tropine - Soya meal Koruzna silaža - Maize silage —a— Koruza - Maize -Cena - Cost (EUR) - - Travna silaža - Grass silage ■Pšenica-Wheat -K-18 —- Seno - Hay Slika 2: BCrmni obroki v obdobju 1998 do 2008, sestavljeni s pomočjo linearnega in tehtanega ciljnega programa Figure 2: Rations for the period 1998 to 2008, calculated with linear and weighted goal program S slike 2 je razvidno, da manjkajoče potrebe po energiji z izjemo leta 1999 in zadnjih dveh let, kjer v krmni obrok vstopa koruzna silaža, pokrijemo s pšenico in ječmenom, ki se v krmnem obroku linearnega modela pojavljata kot alternativi. Predvsem v zadnjem obdobju se zaradi vse dražje doma pridelane travne silaže količina sojinih tropin, kot vira beljakovin, v obroku povečuje. Zviševanje cen sojinih tropin je vse od leta 2005 dalje na enoto beljakovin manjše kot pri travni silaži. Drago koruzno zrnje ni vključeno v rešitev. Svoj delež k temu doprinese tudi povečana količina koruzne silaže v krmnem obroku. Kljub rahlemu povečanju količine koruzne silaže v obrokih, postaja zagotavljanje ustrezne strukture obroka (strukturna vlaknina iz voluminozne krme) ključen problem. Na to je pokazala tudi dodatna analiza senčnih cen, ki so pri omejitvi zagotavljanja najmanjšega deleža strukturne vlaknine v obroku najvišje. Nedvomno je to posledica dragega in kakovostnega sena. Izračunane senčne cene bi bile tako bistveno drugačne, če bi imeli v naboru voluminozne krme cenejše seno slabše hranilne vrednosti. Do nekoliko drugačnih zaključkov pridemo pri rešitvi WGP, ki po definiciji išče s prehranskega vidika bolj uravnotežen krmni obrok. Ker ima sama cena nekoliko manjši vpliv, je pričakovano, da je obrok v primerjavi z obrokom linearnega modela nekoliko dražji. Razvidno je, da se med leti sestava obroka spreminja predvsem na račun zmanjševanja količine travne silaže in povečevanja količine ječmena v obroku. To je tudi edini obrok, ki vključuje relativno drago krmno mešanico K-18, kar je nedvomno posledica manjšega pomena stroška krmnega obroka pri ciljnem programiranju. Zanimivo je, da koruzna silaža z izjemo zadnjih dveh let ni zastopana v nobeni rešitvi WGP. V vsem opazovanem obdobju je pri rezultatih obeh metod opazen izrazit trend podražitve krmnega obroka. S pomočjo dodatnih izračunov smo ugotovili, da se pri linearnem programu med leti stroški vsebovane močne krme praktično ne zvišujejo. V desetletnem obdobju vseskozi ostajajo na ravni 100 EUR, z izjemo zadnjih dveh let, ko se zvišajo za slabih 20 EUR na pitanca. To pomeni, da dvig cen vodi do vse večjega deleža voluminozne krme v skupnem strošku krmnega obroka. Precej drugačne zaključke lahko potegnemo iz rezultatov WGP. Do leta 2003 so namreč stroški močnih krmil predstavljali okrog 10 %, po tem letu pa zelo hitro narastejo na nekaj manj kot 20 % celotnih stroškov krmnega obroka. —X— Konjzna silaža - Maize silage T- T- C^J 7 6 S 5 o i' m 3 2 1 —X—Travna silaža - Grass silage CO a> o cn o> o 05 o> o _ ^ T- cg 0 (2) (3) (4) tors are mostly dependent on markets situation including CAP measures in place and of course also on the technology apphed. Technological coefficients {a.^ present the quantities of the zth nutrient in one unit of the jth feed. Second (WGP) sub-model: mm K inZ = £w,. /=1 dj+dt such that ž'/ (5) n ^V^j = Si for all z = 1 to r and g = O (6) ;=1 re OyXj +d: + d: = g. for all z = 1 to r and g; =}= O (7a) n ^ CjXj + d~ + d: = C for all / = 1 to r (7b) tt 2 a,pC. < b, for all / = 1 to m M d:,d;,Xj>o (8) (9) The meanings of the first and the second sub-model notations: Z and C - objective function; a., the quantity of the z'th nutrient in one unit of/th feed; X. the level ofjth feed; c. jthfeed cost; b. the amount of the žth resource available - right hand side (RHS); g. expected daily requirement of the zth nutrient (goal); w. weight expressing the relative importance of achieving the zth goal; d.^ d." - positive and negative deviation variables including over- and under achievement of the rth goal WGP sub-model could be formulated in mathematical terms as shown in equations (5) to (9). The objective function is defined as weighted sum of undes-ired deviation variables fi-om observed goals (5) and is subject of minimization. The relative importance of each goal is represented by weights (w) associated with the corresponding positive or negative deviations. Because of the normalization process, only goals that have nonzero target values (7a, 7b) could be relaxed with positive and negative deviations. In other case (6) we would face forbidden division by zero. The second sub-model is directly connected with the first one through cost function (7b). Obtained target value (Q from the first sub-model enters in the second sub-model as goal that should be met as close as possible. All the rest constraints that do not have defined target value or do not have priority attribute are considered in equation (8). One of the main assumptions of the linear programming is also non-negativity that is considered in equation (4) for the first sub-model and in equation (9) for the second one. Input data The primal aim of developed tool is to assist breeders in formulating a ration that is both firom nutritional and from economic viewpoint more efficient. It could be used also to assess the variable cost of feed used. In this paper we are going to present a hypothetical case. We presumed that beef fattening starts at 200 kg of live weight and stops at 650 kg. This fattening horizon has been divided into three periods with different average daily weight gains (Table 1). Nutritional requirements are presented in absolute values (Table 2) and have been assessed with the spreadsheet model for ruminants' nutritional requirements estimation (Zgajnar et al, 2007). It calculates requirements for metabolic energy (ME), metabolisable proteins (MP), dry matter consumption (DM), mineral elements (Ca, P, K, Na and Mg) and the minimal and maximal crude fibre (CF) for any breeding period investigated. Table 1 Assumptions concerning growth pattern for beef cattle fattening Indices Fattening period First Second Third Average daily weight 900 1100 1000 gain, g/day Starting live weight, kg 200 350 500 Finishing live weight, kg 350 500 650 Fattening duration, day 167 136 150 Table 2 Nutrition requirements divided into three breeding periods, presented as constraints (LP) and goals (WGP) with belonging weights Indices Fattening period Weights within scenario First Second Third LP WGP LP WGP LP WGP SI sn ME (MJ) >9.881 9 881 >11.003 11 003 >14.085 14 085 70 70 MP (g) >71.114 71 114 >71.335 71 335 >82.950 82 950 100 100 DM (kg) <1.036 1 036 <1.310 1 310 <1.467 1468 33 33 CFmin (kg) >186 >186 >236 >236 >264 >264 CFmax (kg) <269 <269 <341 <341 <381 <381 Price (eurocent) C1 C2 C3 1 100 Ca (g) >6.460 6 460 >6.582 6 582 >7.800 7 800 5 5 P (g) >3.735 3 735 >4.297 A 191 >4.950 4 950 5 5 Na (g) >836 836 >961 961 >1.275 1 275 5 5 Mg (g) >1.171 >1.171 >1.441 >1.441 >1.800 >1.800 K (g) >9.320 >9.320 >11.791 >11.791 >13.208 >13.208 Ca:P (%) (1.5-2):1 (1.5-2):1 (1.5-2):1 K:Na (%) (5.5-10):l (5.5-10):l (5.5-10):l Max hay (kg/day) 2 2 2 Min grass silage (kg/day) 5 5 5 The most important constraints for all three fattening periods are presented in Table 2. Basic set of constraints in both sub-models (LP and WGP) is more or less the same. Constraints presented in Table 2 differ only in mathematical sign when they are transformed into goals. The first sub-model (LP) claims only satisfaction of minimvim or maximum constraints. As stated earlier this might lead into xmrealistic solution. Linear sub-model is therefore included into the tool foremost to give rough estimate of the lowest possible cost for the animal diet that could be formulated with disposable feeds. In the process of ration formulation one should also consider other 'non-nutrition' constraints. For example this could be quantity of feed that must or might be included into the diet. In our hypothetical case study we assume quite frequent example that might be met on Slovene beef farms. Because of our climate characteristics, the fnst grass mowing is gathered in hay and all the rest are gathered in grass silage. This is why both models must take into consideration maximal constraint of 2 kg hay per day and at least 5 kg of grass silage per day (Table 2). Initial version of presented WGP model includes seven goals. Importance of each goal is defmed with weights ranging between 0 and 100. As the most important goal in our case is satisfaction of protein requirements. We vary importance of'cost goal' that manifests in two scenarios (Table 2). In the fnst scenario economics has rather low importance, while in the second scenario it has the highest possible weight. Satisfaction of energy requirement has in both scenarios the same weight. Much lower weight is foreseen for the dry matter intake that presents consumption capacity. At first glance it seems that all three mineral goals (Ca, P and Na) are, due to low weights, almost neglected. However this is not true. Developed model includes several safety nets that prevent mineral deficits as also their toxic concentrations in the ration. Nutritionists' doctrine says that it is more important to satisfy ratios between Ca and P and also between K and Na than to meet the estimated mineral requirements. In analyzed hypothetical case we assumed that both sub-models might choose between six different feed and four different rnineral-vitamin components (Table 3). Described feed characteristics are mostly dependent on soil structure, fertilization management and intensity of production. We assumed that hay, grass silage and maize silage are grown on the farm. Since these forages are usually not tradable, we estimate variable cost of their production. Fixed costs were not considered at all. All the rest forage on disposal could be purchased at market prices (Table 3). Results Presented tool for nutrition management is built as an open system, which means that any beef case could be analysed. A hypothetical case has been chosen to test developed approach. Fattening time has been divided into three periods with different daily weight gains (0.9 kg, 1.1 kg and 1.0 kg). The fnst period starts at 200 kg body weight and than in each period bull gains 150 kg on weight. Fattening stops at 650 kg body weight. Formulated rations for all three breeding periods are presented in Table 4. In the first period there is significant difference between formulated rations. Quantity of hay is the same in all three rations and achieves the highest allowed quantity (2 kg/day). Grain maize and rape seed cakes are included only in the second ration (WGP I) where the price is not of so high importance. From nutrition viewpoint this ration is the most suitable what manifests also in the lowest total deviation from nutrition requirements. The latest has been observed as one of those parameters that measures the 'quality' of obtained results. Total de- viation has been in WGP I solution almost two times lower than in LP solution and 1.3 times lower than in WGP n solution where priority of cost goal is the same as satisfaction of protein target value. The third solution is from nutrition viewpoint still satisfactory. It misses protein requirements for one percent and deviation from mineral requirements are sUghtly higher than in WGP I. It is only 2.7 % more expensive than the least-cost ration compared with 31.1% cost increase of WGP n solution. In all three formulated diets mineral requirements are covered only with limestone and salt. This is due to rich mineral content assumed in used feedstuff. The second fattening period has the highest average daily weight gain (1.1 kg/day) that result in the shortest fattening period. Linear program suggest very simple ration that is again the cheapest, but with 21.2 % energy surplus. Therefore protein-energy ratio is totally unbalanced. The second (WGP I) and the third daily ration (WGP II) differs from the parallel rations in the first period mostly in increased inclusion of grass and maize silage and decrease of soya meals and rape-seed cakes. From nutrition viewpoint most balanced ration (WGP I) in the second fattening period is 21.1 % more expensive than LP one, but total deviation is for 148 % reduced in comparison with LP and 51 % in comparison with WGP IL The latest ration is from nutrition viewpoint much better than LP solution, and for practice due to its simplification compared to WGP I and costs lowered by 18.6 % the recommended one. For the third fattening period our tool yields solutions with comparable facts already pointed out. Cost of the feed included into ration plays significant role in LP's and WGP II solutions. WGP II yields better ration for the same daily price as LP. In this period the highest difference between ration costs is noticed. Expenditure of WGP I ration is for 65.6 EUR higher than in the case of still balanced WGP II ration during the third period only, and for the whole fattening period examined even 120 EUR per animal higher. This dif- Table 3 Nutritive value of assumed feed Indices DM, ME, MP CF Ca P Mg Na K Price/VC, g/kg MJ/kg DM g/kg DM cent Feed on disposal Hay 860 7.52 64.33 200 4.31 2.65 1.51 0.26 13.81 8.02 Grass silage 350 2.93 19.1 800 1.85 1.08 0.68 0.11 6.56 4.04 Maize silage 320 3.03 12.67 600 1.99 1.69 0.54 0.03 3.03 2.55 Grain maize 880 10.39 64.28 0 0.18 3.17 0.97 0.18 2.9 30 Soya meal 880 10.21 166.5 0 2.64 6.07 2.02 0.88 15.49 46 Rapeseed cake 900 9.75 99 0 2.29 5.54 2.2 1.76 7.92 37 Mineral and vitamin components MVM 1* 930 0 0 0 171.86 57.2 0 110.53 0 58.08 MVM 2* 930 0 0 0 130.94 81.84 29.46 98.21 0 67.56 Salt 950 0 0 0 0 0 0 334.4 0 50 Limestone 950 0 0 0 818.4 0 0 0 0 16.4 ♦Commercial names of mineral- vitamin mixtures are Bovisal 1 and Bovisal2 ference is difficult to be outweighed by likely small increase of daily weight gains when WGPI solutions would be followed in practical feeding. Discussion The results showed that mathematical deterministic programming techniques can be successfully ap-phed in the ration formulation process. In the presented analysis an example has been solved for illustration that utiUsed approach partly mitigates the mentioned drawbacks of LP (single objective function), which can still be useful to estimate the lowest possible fodder cost. It is logical that daily ration costs are higher in both WGP solutions. Price increase is mostly dependent on weights set to cost function (1=1,11=100). In this paper we are presenting two extreme economic situations, while the solution to be followed in practice should be somewhere between both. Anyhow, economic weight is likely to be high, therefore close to 100. The structure of the rations would be much different if all feed would be produced on the farm. Significant discrepancy is expected especially in LP and WGP II solutions, where feed cost has high importance. Obtained rations are satisfactory, especially if we consider only foreseen nutrition requirements in initial version of the tool. But if we focus on micro elements and vitamins rations presented very likely do not meet animal requirements. This issue could be simple solved by setting new constraints for minimal incorporation of any (one) mineral-vitamin components (e.g. Bovisal 1 or Bovisal 2) into the ration. Their quantities are usually prescribed by producer. Conclusions Presented approach of combining linear programming with weighted goal programming enables to consider more than just one objective. This is becoming more important also in nutrition management and seems to be emphasised in line with general globaiiza- 3 e2 CS fi a> u « Ph Ü T3 § "O O) 9 S u a cn e 0 1 Ž" rt "O rs a ft -H a tf> OJ h TS o CN c> rt r--' 1—1 ö NO S (N S NO ® O O 2 O OJ TJ U ii, D .a SP I I ^ S g « « g öS« , -s .a - (D M C3 o Xfi TS ID ß M 5 [rt (u n ^ ft o O od s (N o NO o r- p; ^ 2 o s- o t-- NO ./S f-: (N On o NO ro ON C^ ^ ■ NO -f" ^ 2 CNl ro OO OO r-< • O O ^ cn t- _ m (N OO o ^ «cH w rt t« rt cn ^ ° :s ® p: i i-j g i I ^ I .9 B ^ pi a § I" 11 u u u 3 y .9 o" 'l-l fcH Ii i> P^ o. o. 0!i m IN (N CN CN lO O On m NO CN CN m ON NO m OO —: rt 00 OO ON 00 • cn \ o o ON Ö o rt NO 0^ lo m o On m cn * W P-, o S ^ I > cS -M O H lO o o ^ o o o o vo o r- o Jä ca ^H O • S a C N (X •o a ca ca bS Q Ph" S s c2 cn n D S •ia 1 = penalty function parameters defining first deviation interval of /th nutrient p < 1, < 1 = penalty function parameters defining second deviation interval of /th nutrient The second sub-model (WGP with PF) is formulated as shown in equations (2) to (7). The objective (achievement) function (2) expresses the aggregate unwanted deviations and is therefore subject to minimization. It is defined as the weighted sum of deviations. Since the PF is in place also, its coefficients (Sj and Sj) are considered. Preferences of defined goals are reflected by weights (w) associated with the corresponding positive or negative deviations. Tke scale of deviations is controlled through the defined penalty intervals {5a, 5b, 6a, 6b). Because of the normalization process, only goals that have nonzero target values (3a, 3b) could be relaxed; all the rest must be considered as fixed constraints (4). Tlie obtained target value (C) in the first sub-model (LP) enters into the second one (WGP with PF) as the cost goal (3b) that should be met as close as possible. This is also the only case where negative deviation is not penalised and also not restricted with intervals. The main assumption of the linear programming is the non-negativity that is considered for the first sub-model {X > 0) as for the second one in equation (7). Input data The presented tool has been tested on a simple ration formulation example for a 650 kg dairy cow in the 150'^* day of lactation (total milk yield envisaged is 7 000 kg) with a daily milk yield of 25 kg and nutritional requirements for the 90th day of pregnancy. The most important constraints and goals for the analysed case are presented in Table 1. A basic set of constraints (LP and WGP supported by PF) is more or less the same in both models. Nutritional constraints presented in Table 2 differ only in mathematical sign when nutrient requirements are transformed into goals. In the case when least-cost criterion is considered (LP), only the most important (non-conflicting) minimum or maximum constraints must be met. This might manifest in an 'unrealistic' diet. Nevertheless, this simplification has been made due to the fact that the LP module is needed foremost to give a rough estimation of the lowest possible diet cost. Undisputedly, an unbalanced ration is cheaper, and on one hand, this assures a feasible solution that is necessary, but on the other hand, the WGP with PF is encouraged to draw the price close to the one that might be achieved in practice. In the everyday ration formulation process, one also has to consider constraints concerning quantities of feed, which must be included into the ration. In this case study, we assumed that the ration should include at least 3 kg of hay, but its quantity should not exceed 5 kg. Both sub-models should also not exceed the maximum quantity of grass and maize silage (Table 1). Table 1. Daily nutrition requirements for dairy cow with 25 kg milk yield and requirements for 90th day of pregnancy, presented as constraints (LP) and set of goals in WGP Daily requirements summer/winter Penalty function interval 1 (%) interval 2 I LP WGP I / II sl- sl + s2- s2+ NE L (MJ) > 122.4 122.4 0.5 0.5 5 5 100 MP (g) > 1 471.3 1 471.3 0.5 0.5 5 5 100 DM (kg) < 18.5 18.5 5 0 10 0 33 CF min (kg) > 3.3 CP max (kg) < 4.8 Ca (g) > 104.1 104.1 2 5 20 20 5 P (g) > 67.7 67.7 2 5 20 20 5 Ca: P (%) (1.5-2) : 1 K: Na (%) (5.5-10) : 1 Price (cent) CI 00 10 8 20 5/95 Min hay (kg/day) 3 CO Max hay (kg/day) 5 Max Grass silage (kg/day) 30 Max Maize silage (kg/day) 30 Max Salt (g/day) 30 Max Bovisal winter (g/day) 240 Max Bovisal summer (g/day) 200 Since the tool has been used to formulate both the winter and summer diet separately, there are also different quantities of the allowed mineral vitamin mixtures included (declared by the producer). The initial version of the WGP model involves six goals supported by the PF (Table 1). The relative importance of each goal is defined with weights ranging between 0 and 100. As the most important goals to be met in our case, there are regarded the satisfaction of energy (NEL) and protein (MP) requirements (100), in both cases the deviation intervals are very restricted, since only 0.5% positive and negative deviations are allowed in the first stage and 5% in the second one. A much lower weight is foreseen for the dry matter intake that presents the consumption capacity. In this case, the deviation intervals are defined only for the underachievement of the goal, while for the practical reasons (consumption capacity), overachievement is not allowed. Besides that, an additional constraint is included to ensure that the proportion of dry matter derived from voluminous forage does not exceed 14 kg of DM. Since the nutritionists' doctrine ensures that it is more important to satisfy the ratio between Ca and P and also between K and Na than to meet the estimated mineral requirements, we consider rela- tively low weights for mineral (Ca, P) goals. All the remaining minerals are controlled through several safety measures, which prevent deficits as well as toxic concentrations. With the applied approach we have tested how the 'optimal' ration would change due to different preferences concerning the cost goal. This analysis manifests in two scenarios. In the first scenario, the cost of the obtained ration (WGP I) was of minor importance (w = 5), while in the second scenario (WGP II), its importance was increased {w - 95). In both scenarios, the deviation intervals remain the same (+10% and +20%). The ingredients assumed to be available for formulating the rations and their characteristics are given in Table 2. The described feed characteristics are mostly dependent on soil structure, application of fertilizers, and intensity of production. Consequently, high variability in nutrition quality might arise in practice. Due to this fact, a chemical analysis for each feed used (when analysing the practical case) should be performed to prevent errors in the formulated ration. We assumed that all voluminous forage (hay, maize silage, grass silage, and grass) is produced on the farm. Of course grass might be included only in summer Table 2. Nutritive value of feed on disposal DM NEL MP*" CF Ca P Mg Na K Price or TC* (g/kg) (MJ/kg DM) (g/kg DM) (cent/kg) Feed on disposal Hay 860 5.90 85.00 270 5.70 3.50 2.00 0.35 18.25 15.30 Maize silage 320 6.50 45.00 200 7.06 6.00 1.91 0.12 10.76 3.70 Grass silage 350 5.60 62.00 260 6.00 3.51 2.20 0.35 21.30 6.14 Grass 160 7.10 121.00 205 6.00 2.60 2.00 0.10 10.50 1.50 Maize 880 8.50 83.00 0.23 4.09 1.25 0.23 3.75 30.00 Wheat 880 8.60 88.00 0.57 3.86 1.59 0.45 5.00 32.00 Rapeseed cake 900 7.50 125.00 2.89 7.00 2.78 2.22 10.00 37.00 Soya meal 880 8.20 215.00 3.41 7.84 2.61 1.14 20.00 46.00 K-18"" 880 7.61 136.74 10.23 5.68 2.84 3.98 10.23 27.67 K-19"* 880 7.61 146.51 10.23 5.68 2.84 5.11 10.23 30.00 Mineral and vitamin components Limestone 950 400.00 16.40 MVMl""* 930 160.00 100.00 36.00 120.00 67.56 MVM2""*" 930 210.00 70.00 135.00 58.08 Salt 950 400.00 50.00 "Total cost approach, '"The lowest value of metabolisable protein is considered, ""Commercial names of dairy cows' feed containing different % of metabolisable proteins, "'"Commercial name of mineral-vitamin mixtures are Bovisal summer and Bovisal winter rations. Since these forages are usually not tradable, we estimate the total cost of their production on the basis üf model calculations' prepared by the Agricultural Institute of Slovenia (KIS 2007). All other forage and mineral-vitamin components on disposal could be purchased at market prices (Table 2). The question raised might be what should be grown on the farm to improve profitability, but this issue is very complex and is beyond the scope of the paper. EESULTS AND DISCUSSION The tool has been tested on a simple everyday example (650 kg dairy COw with a milk yield of 25 kg/day and day of pregnancy). It was run four times. two times for the winter period and two times for the summer period, where grass was also at the cows' disposal. The formulated daily rations for both periods are presented in Table 3, including LP solutions. The latter serve only to estimate the diet least-cost and might not be really applicable since they are simplified. There is a significant difference between the compositions of winter and summer rations, as well as the rations within each season (Table 3). The first difference is self-explanatory - there is grass available in the summer season - while the second difference manifests itself through different preferential weights and a PF in place. In winter rations (WGP I and WGP II), protein requirements are mainly covered with grass silage and Table 3. Obtained daily rations formulated with LP and WGP with cost penalty function scenarios Daily ration winter summer LP WGP I WGP II LP WGP I WGP II Feed used (kg/day) Hay 5.00 5.00 5.00 4.56 3.00 5.00 Maize silage 25.16 10.33 15.18 17.22 Grass silage 6.14 23.84 16.57 5.80 0.16 Grass 69.23 34.58 32.08 Wheat 1.98 5.00 2.19 Maize 1.18 1.50 1.50 1.95 1.50 1.50 Soya meal 2.30 K-18 3.56 3.08 K-19 0.17 1.56 Mineral components used (g/day) Limestone 24.2 13.0 30.4 37.0 Bovisal Summer 104.6 56.8 50.2 Bovisal Winter 61.1 34.8 Salt 30.0 30.0 28.1 30.0 30.0 Price (EUR/day) 3.87 4.34 3.87 2.66 2.93 2.91 Price deviation (%) 0.0 12.2 0.0 0.0 10.2 9.3 Requirements deviations (%) NHL 0.0 -1.7 -2.2 0.0 -0.5 -0.5 MP 0.0 0.0 0.0 39.0 0,0 0.0 Total deviation* 56.3 10.1 37.0 69.6 27.2 30.7 Physical ration attribute CF (%) 18 18 18 19 19 19 DM (kg/day) 18.5 18.5 18.5 17.8 18.0 17.9 "Total sum of deviations (including mineral deviations not presented in the table) purchased fodder K-19 (WGP I) and K-18 (WGP II). It is obvious that prices play a significant role since more restricted cost conditions (WGP II) have a significant impact on the inclusion of (expensive) grass silage. This is even more obvious in the summer season, where the main source of protein is much cheaper grass (WGP I) and some negligible quantity of grass silage (WGP II). Grass is therefore the crucial trigger for the difference between summer and winter rations composition. As already stated, the second difference is caused by preferential weights and the penalty system in place. The penalty system enables one to control the deviations from the set target values (goals). The more severe cost penalty system (through higher relative importance w = 95) in the second scenario has a significant impact in both seasons from the nutrition quality aspect. Even though the WGP II rations are more balanced, in the summer season they are by 9.3% more expensive, while in the winter season, there is no difference in estimated cost at all. At a first glance, the least cost ration seems better, since the energy and protein requirements are fully met. Anyhow, if one considers also the sum of the total deviation as a measure of the 'quality' of obtained results, it is obvious that the WGP II ration is better than the LP's one, since the LP neglects some nutrition objectives. This fact is even more powerfully manifested in the first scenario (WGP I), where the importance of the cost goal is reduced (w = 5). As a result, prices increase in comparison to the second scenario for 0.9 to 12.2%, but total deviations (as a quality parameter) improve from 3.5 up to 26.9%, respectively. This could be explained as the competition between nutrition quality and economics. However, when rations are not balanced - even if the individual parameter requirements are fulfilled - one cannot expect to achieve the anticipated daily yields. This is especially true when very high (> 35 kg) daily milk yields are analysed. CONCLUSIONS The aim of this paper was to present a simple spreadsheet tool that can support daily management tasks - the dairy cow ration formulation. The applied approach - a combination of the LP paradigm and the WGP with PF - proves to be a useful 'engine' in an end-user application. It enables one to formulate close to least-cost ration, not taking a too high a risk of worsening the ration's nutritive value, which is the main common drawback of the LP. Rations might be additionally improved with fine-tuning enabled through the PF that differs between the deviation sizes for each goal separately. This significantly reflects in the obtained rations, especially in the summer season. This can be illustrated with the case presented in this paper, where the formulation of a daily ration only by the least cost criterion resulted in a 39% surplus of proteins in the summer ration, which might seriously affect the animals' health. In spite of a slightly higher price, cost efficiency can be improved through numerous factors. On one hand, surpluses cost money and have a negative impact on production (daily milk yields). On the other hand, they also increase greenhouse gas emissions (Brink et al. 2001). General efficiency is becoming more and more important in nutrition management and this seems to be emphasised in line with the general globalization impacts (input price rise, price volatility, and environmental as well as climate change aspects). The developed tool might be useful also for the assessment of impact consequences by preparing calculations for different situations and technology types. It may also be useful in assessing variable costs of feed used or to provide an answer on different sector questions such as how market changes are affecting the 'optimal' animal diets through longer periods. Acknowledgements Thanks are due to Lecturer Ajda Kermauner Kavčič and Asist. Prof. Andrej Lavrenčič for their support in evaluation of obtained rations. REFERENCES Brink C., Kroeze C., Klimont Z. (2001): Ammonia abatement and its impact on emissions of nitrous oxide and methane in Europe - Part 1: method. Atmospheric Environment, 35 (36): 6299-6312. Castrodeza C., Lara P., Pena T. (2005): Multicriteria fractional model for feed formulation: economic, nutritional and environmental criteria. Agricultural Systems, 86 (1): 76-96. Ferguson E.L., Darmon N., Fahmida U., Fitriyanti S., Harper T.B., Premachandra I.M. (2006): Design of optimal food-based complementary feeding recommendations and identification of key "Problem Nutrients" using goal programming. The Journal of Nutrition, J36 (9): 2399-2404. Gass S. (1987): The setting of weights in linear goal-programming problems. Computers and Operations Research, J4 (3): 227-229. KIS (2007): Model calculations (unpublished). Agricultural institute of Slovenia, Ljubljana. Lira P. (1993): Multiple objective fractional programming and livestock ration formulation: A case study for dairy cow diets in Spain. Agricultural Systems, 41 (3): 321-334. Lara P., Romero C. (1994): Relaxation of nutrient requirements on livestock rations through interactive multigoal programming. Agricultural Systems, 45 (4): 443-453. Rehman T., Romero C. (1984): Multiple-criteria deci-sion-making techniques and their role in livestock ration formulation. Agricultural Systems, IS (1): 23-49. Rehman T., Romero C. (1987): Goal Programming with penalty functions and livestock ration formulation. Agricultural Systems, 23 (2): 117-132. Rehman T., Romero C. (1993): The application of the MCDM paradigm o the management of agricultural systems: Some basic considerations. Agricultural Systems, 41 (2): 239-255. Romero C., Rehman T. (2003): Multiple criteria analysis for agricultural decisions. 2nd ed. Elsevir, Amsterdam. Tamiz M., Jones D., Romero C. (1998): Goal programming for decision making: An overview of the current state-of-the-art. European Journal of Operational Research, 111 (6): 569-581. Waugh F.V. (1951): The minimum-cost dairy feed. Journal of Farm Economics, 33 (3): 299-310. Zgajnar J., Kermauner A., Kavcic S. (2007): Estimation of ruminants' nutritional requirements and livestock ration optimization (in Slovene). In: Slovensko kmetijstvo in podeželje v Evropi, ki se siri in spreminja. 4. konferenca DAES. Kavcic S. (ed). Ljubljana, Društvo agrarnih ekonomistov Slovenije, Domžale, pp. 279-288. Arrived on 27"^ November 2008 Contact address: Jaka Žgajnar, BSc, University of Ljubljana, Biotechnical Faculty, Zootechnical Department, Chair for Agricultural Economics, Policy and Law, Groblje 3, SI-1230 Domžale, Slovenia e-mail: jaka.zgajnar@bfro.uni-lj.si Žgijnar, J./ Kermauner, A./ Kavčič, S. Model za ocenjevanje prehranskih potreb prežvekovalcev in optimiranje laiuiih obrokov. In: Slovensko kmetijstvo in podeželje v Evropi, ki se širi in spreminja, 4. konferenca DAES, ^Moravske toplice, 2007-11-08/09 (ed.: Kavčič, S.). Ljubljana, Društvo agrarnih ekonomistov Slovenije, Domžale, 2007, 278-288 MODEL ZA OCENJEVANJE PREHRANSKIH POTREB PREŽVEKOVALCEV IN OPTIMIRANJE KRMNIH OBROKOV Jaka Žgajnar*, Ajda Kermauner in Stane Kavčič Globalne spremembe močno vplivajo na upravljavsice procese v ionetijstvu, id so zato vse bolj pcdobni procesom ostalih gospodarskih sektorjev. Znotraj kmetijskega sektorja se nakazujejo pcstopne struiiturne spremembe tudi z vidika bioenergetike. To v kmetijskem seidorju ustvarja dodatno povpraševanje, Id v pogojih zdrave konkurence vodi do višjih cen. Ce pri trendu cen npoštevamo tudi šoke, povzročene z vse pogostejšimi naravnimi nesrečami, ugotovimo, da je posledično cenovno-stroškovno razmerje v živinoreji zelo nestabilno. Zato postaja pri slednji ključnega pomena dobro, natančno in hkrati hitro definiranje krmnega obroka, kar predpostavlja ustrezno določanje krmnih potreb in čim boljšo oceno hranilne vrednosti razpoložljive krme. Presežki in primanjkljaji posameznih hranljivih snovi rejcu namreč predstavljajo neposredno gospodarsko škodo, ki se z rastjo cen krme le še povečuje. V prispevku je predstavljen simulacijski model za izračunavanje Icrmnih potreb različnih kategorij živali pri različnih intenzivnostih reje in simulacijski model za vrednotenje hranilne vrednosti io-me za prežvekovalce. Izračunane vrednosti simulacijskih modelov'bomo uporabili kot tehnološke koeficiente pri optimiranju icrmnega obroka in pri dopolnitvi že razvitega linearnega modela za optimiranje proizvodnih odločitev na kmetijskih gospodarstvih. Ključne besede: prehrana živali, prežvekovalci, optimiranje obrokov, linearno programiranje, ciljno programiranje *Biotehmška fakulteta Univerze v Ljubljani, Oddelek za zootehniko, 1230 Domžale, Groblje 3, iaka.zgainar@bfro.uni-li.si ESTIMATION OF RUMINANTS' NUTRITIONAL REQUIREMENTS AND LIVESTOCK RATION OPTIMISATION Global changes are having large impact on agricultural decision making process. Consequently it becomes similar to decision making in other business sectors. Within agriculture progressive structural changes are being indicated also from bio-energy point of view. As result additional demand in agricultural sector has been formed reflecting in upward price trends. If shocks caused by natural disasters, beside positive price trends, are taken into consideration, one can find out that price-costs relations in livestock sector are very unstable. For this reason good, precise and at the same time fast rations formulation in competitive livestock production is going to be of increasing importance, which means definition of corresponding nutrition needs and assessment of nutritional value offeeds available. Surplus or shortage of individual nutrients causes direct economic loss for breeder, what is especially emphasized when input prices are increasing. The paper presents a simulation model for assessment nutrient needs of different animal categories at different breeding intensities and simulation model for assessment nutritional value of different feeds for ruminants. Results obtained with these models are going to be used as technological coefficients in ration optimization and in completing of already developed linear model for production plans' optimization on agricultural holdings. Keywords: animal nutrition, ruminants, ration optimization, linear programming, goal programming Uvod Profesionalizacija kmetijstva z deregulacijo trgov, rastočimi okoljskimi in družbenimi zahtevami ter posledicami klimatskih sprememb vodi v vedno večja tržna nihanja, od Žgajnar, J./ Kermauner, A./ Kavčič, S. Model za ocenjevanje prehranskih potreb prežvekovalcev in optimiranje krmnih obrokov. In: Slovensko kmetijstvo in podeželje v Evropi, ki se širi in spreminja, 4. konferenca DAES, Moravske toplice, 2007-11-08/09 (ed.: Kavčič, S.). Ljubljana, Društvo agrarnih ekonomistov Slovenije, Domžale, 2007, 278-288 gospodarskih subjektov pa zahteva temeljitejše obvladovanje tveganj ter učinkovitejše načrtovanje gospodarjenja. Poleg tega se v celotni verigi kmetijskega sektoija kažejo strukturne spremembe. Evropska Strategija bio-goriv (Commission of the European Communities, 2006), Izvedbeni plan biomase (Commission of the European Communities, 2005) in sprejetje Direktive o bio-gorivih (Directive 2003/30/EC) s strani Komisije dajejo jasen signal, da EU želi podpreti bio-energetsko industrijo. Dautzenberg in sod. (2007) ugotavljajo, daje skupna kmetijska politika vse bolj naklonjena zmanjševanju pridelave hrane na račun povečevanja ne-prehranske pridelave. Zeller in Hiring (2007) omenjata posledičen pozitiven vpliv dodatnega povpraševanja na zvišanje cen in s tem na ekonomsko situacijo poljedelcev. Z vidika živinoreje pa takšen trend nedvomno pomeni resen problem. Na podlagi Kataloga kalkulacij (Jerič, 2001) z revaloriziranimi cenami na leto 2006 smo izračunali delež spremenljivih stroškov krmnega obroka od skupnih spremenljivih stroškov pri različnih rejah. Ugotovili smo, da se deleži pri govedu gibljejo med 41 % in 71 %. To potrjuje našo hipotezo, da bo v prihodnje za dosego čim boljšega finančnega rezultata na živinorejskih, kmetijah čedalje bolj pomembna cenovna optimizacija krmnega obroka in posredno tudi optimizacija primarne pridelave na obdelovalnih površinah. S tem kmetijski sektor postopno prevzema značilnosti ostalih gospodarskih sektoijev, kjer ekonomske zakonitosti predstavljajo osnovno vodilo nadaljnjega razvoja. Vodenje kmetijskega gospodarstva je tako vse bolj kompleksno in od upravljavca zahteva povezovanje znanja naravoslovnih in družboslovnih ved. Za podporo pri odločanju na ravni kmetijskih gospodarstev v Sloveniji je bil že razvit deterministični statični linearni program (Žgajnar, 2006). Optimizacija je izvedena po načelu maksimiranja skupnega doseženega pokritja na ravni kmetije, ki jo opredelimo preko vnosa precej obširnega nabora podatkov in izklapljanja tistih aktivnosti, ki na konkretnem gospodarstvu niso realna alternativa. Model je namenjen predvsem živinorejsko usmeijenim kmetijskim gospodarstvom, ki se ukvaijajo z rejo prežvekovalcev. Pri testiranju modela seje izkazalo, daje optimizacija proizvodnje z vnaprej izbranim krmnim obrokom precej okrnjena (Žgajnar in sod., 2007). Optimizacija krmnega obroka je eden izmed ključnih dejavnikov, ki širi manevrski prostor za izboljšanje ekonomskega položaja. Da bi rejci prežvekovalcev laže ocenili potrebe svojih živali, smo v Excelovem okolju pripravili simulacijski model za ocenjevanje dnevnih in letnih potreb po hranljivih snoveh v odvisnosti od intenzivnosti prireje. Nepoznavanje dnevnih potreb in krmne vrednosti obroka namreč lahko vodi v preskromno ali pa prekomerno prehrano, oboje pa rejcu predstavlja gospodarsko škodo. Z metodami matematičnega programiranja lahko pripravimo orodje, ki omogoča optimizacijo krmnega obroka na podlagi minimiziranja stroškov ob hkratnem povečevanju učinkovitosti izkoriščanja krme. Tovrstni izračuni so lahko v pomoč rejcu pri izračunu potrebnih količin, vrste in kakovosti doma pridelane krme za vriaprej predvideno intenzivnost reje. V prispevku podajamo pregled uporabe metod linearnega programiranja za reševanje prehranskih problemov in predstavljamo Vmesni' model za izračuna dnevnih in letnih potreb posameznih kategorij domačih živali pri različnih intenzivnostih prireje. Rezultati vmesnega modela, ki bodo za posamezna kmetijska gospodarstva precej različni, bodo predstavljali vhodne podatke pri ekonomski optimizaciji letnega krmnega obroka, primerni pa bodo tudi za večstopenjsko reševanje klasičnih prehranskih problemov s pomočjo nadgrajenega linearnega programa v ciljni program. Pregled literature Tehnike linearnega programiranja za načrtovanje prehrane 2gajnar, J./ Kermauner, A./ Kavčič, S. Model za ocenjevanje preliranskih potreb prežvekovalcev in optimiranje irmnih obrokov. In: Slovensko kmetijstvo in podeželje v Evropi, ki se širi in spreminja, 4. konferenca DAES, Moravske toplice, 2007-11-08/09 (ed.: Kavčič, S.). Ljubljana, Društvo agrarnih ekonomistov Slovenije, Domžale, 2007, 278-288 Orodje linearnega programiranja je klasično orodje za reševanje najrazličnejših prehranskih problemov tako na področju humane prehrane kot pri uravnavanja krmnih obrokov vseh vrst domačih živali (Darmon in sod., 2002). Pri humani prehrani se linearno programiranje iiporablja za reševanje najrazličnejših problemov, od iskanja najokusnejšega obroka (Smith "VE, 1995; Fletcher in sod., 1994), definiranja diete za individualnega pacienta v bolnišnicah, reševanja lakote v državah tretjega sveta, iskanja najcenejše prehrane za brezdomce (Holcomb in DePorter, 1990) in vse do iskanja najcenejšega obroka (Rozman in sod., 2002). Darmon in sod. (2002) ugotavljajo, da se linearni program lahko uporabi tudi za iskanje prehranskih predlogov in omejujočih hranil, pa tudi za oceno, ali je primemo prehransko dieto mogoče doseči z lokalno dosegljivo hrano v različnih sezonah. Kombinacijo linearnega programa z nelinearnim programom so uporabili za analizo pomena (izraženo z Langrangovimi multiplikatoiji) posameznih tudi nelinearnih omejitev. Optimizacij ski model je definiran z namensko funkcijo, ki je odvisna od nabora vključenih spremenljivk in omejena z različnimi omejitvami. Cilj optimiranja je poiskati nabor spremenljivk, ki dajo optimalno vrednost namenske funkcije in hkrati zadostijo vsem predpostavljenim omejitvam. V literaturi zasledimo številne prehranske modele, ki optimirajo hodisi dieto ali krmni obrok s številnih vidikov. Najpogostejši so modeli iskanja najcenejšega krmnega obroka, zasledimo pa tudi modele, ki ocenjujejo vrednost krme na podlagi razpoložljive energije za rastoče živali (Magowan in O'Callaghan, 1986), minimizirajo čas krmljenja pri divjadi (Nolet in sod., 1995), minimizirajo koHčino zaužite energije (Darmon in sod., 2002) ali pa minimizirajo absolutno razliko (MOTAD) med povprečnim obrokom določene socio-ekonomske skupine in sestavljeno dieto na podlagi prehranskih priporočil (Darmon in sod., 2006). Pri reševanju prehranskih problemov s pomočjo klasičnega linearnega programa pogosto naletimo na problem kontradiktomih ciljev. Rezultat slednjih je, da model ne najde možne rešitve ali pa je teh neskončno mnogo. V takšnem primeru je problem rešljiv le, če arbitrarno spremenimo omejitve (Ferguson in sod., 2006). Model je zato zelo fleksibilen in v določenih primerih lahko pripelje do nerealne rešitve (Rehman in Romero, 1984). Da bi zaobšli to pomanjkljivost klasičnega hneamega programa, ga je v nekaterih primerih smiselno nadgraditi v večkriterijalni - ciljni program (Rehman in Romero, 1984, 1987; Pablo, 1993; Ferguson in sod., 2006). V tem primeru nam izbrani nivoji hranil predstavljajo cilje in ne več omejitve, kot so to v klasičnem lineamem programu za iskanje najcenejšega krmnega obroka. Poleg tega lahko dodamo tudi druge cilje, s katerimi poizkušamo rešitev približati realnosti. Castrodeza in sod. (2005) pri načrtovanju krmnega obroka poleg minimalnih stroškov poizkušajo zagotoviti tudi čim boljšo učinkovitost krmnega obroka, ob hkratnem minimiziranju negativnih vplivov na okolje. V živinoreji je to lahko na primer tudi osnovanje krmnega obroka na pretežno doma pridelani krmi. Dobljena optimalna rešitev nam pri večkritetjalnem programiranju tako predstavlja kompromis med kontradiktomimi cilji. Opredeljeni so s pomočjo pozitivnih in negativnih odstopanj od zastavljenih ciljev. Njihov relativen pomen je definiran s pomočjo uteži k pripadajočemu pozitivnemu oziroma negativnemu odstopanju. Tehtana vsota odstopanj nam definira namensko funkcijo, ki je predmet minimizacije. Tako nadgrajen klasičen lineami program omogoča večjo fleksibilnost in v večini primerov pripelje do realnejše rešitve. S ciljnim programiranjem torej minimiziramo neželeno odstopanje od zastavljenih ciljev in ne minimiziramo oziroma maksimiramo ciljev samih (Ferguson in sod., 2006). Kvaliteta modela je tako v največji meri odvisna od definiranja zastavljenih ciljev. Zato je pri takšnem modeliranju nujno sodelovanje strokovnjakov z vpletenih področij ali celo uporaba druge metode za čim manjšo pristranskost pri definiranju uteži (Gass, 1987). Linearnost in nelinearnost pri reševanju prehranskih problemov Žgajnar, J./ Kennauner, A./ Kavčič, S. Model za ocenjevanje prehranskih potreb prežvekovalcev in optimiranje krmnih obrokov. In: Slovensko kmetijstvo in podeželje v Evropi, ki se širi in spreminja, 4. konferenca DAES, Moravske toplice, 2007-11-08/09 (ed.: Kavčič, S.). Ljubljana, Društvo agrarnih ekonomistov Slovenije, Domžale, 2007, 278-288 Pri reševanju prehranskih problemov se pogosto srečamo z nehneamimi omejitvami. Eden takšnih primerov je omejitev, izražena kot razmerja hranil oziroma mineralov (Darmon in sod., 2002). Da zadostimo pogojem linearnosti, moramo s pomočjo ustreznih matematičnih transformacij takšno razmeije prevesti v linearno omejitev. Model je namreč linearen le, če so vse omejitve, znotraj katerih iščemo rešitev, linearne, in je nelinearen, če je ena ali več omejitev nelinearnih. Tudi v primeru neekonomske, a hkrati linearne optimizacije krmnega obroka se lahko srečamo z nelinearno ciljno funkcijo. Takšen primer je minimiziranje absolutnega odstopanja pri večstopenjskem pristopu sestavljanja krmnih obrokov. Material in metode Opis zasnove simulacijskega modela Simulacijski model je namenjen izračunavanju prehranskih potreb za različne kategorije goveda in drobnice. Izračunane vrednosti bodo služile kot vhodni podatki pri optimizacijskem modelu. Govedo smo zajeli s kategorijami krav molznic, krav dojilj, telic, telet ter treh pasem govejih pitancev, ki se najpogosteje pojavljajo na slovenskih kmetijah. Drobnico pa zastopajo mlečna in mesna usmeritev reje ovac. Pri izračunu krmnih potreb smo se omejili na oceno konzumacijske sposobnosti in na potrebe po energiji, beljakovinah ter minimalni in maksimalni strukturni surovi vlaknini. Za ocenjevanje energijske vrednosti krme in za ocenjevanje oskrbljenosti prežvekovalcev z energijo se je v preteklosti uporabljal sistem škrobnih enot (Žgajnar, 1990). Zaradi nekaterih pomanjkljivosti tega sistema se sedaj v Sloveniji uporablja nemški sistem, ki za krave molznice izračunava potrebe v neto energiji za laktacijo (NEL), za plemensko govedo, govedo v pitanju in za ovce pa v presnovljivi energiji (Verbič in Babnik, 1999). Prehranski model izračunava energijske potrebe na podlagi enačb in normativov za posamezno obdobje reje (Verbič in Babnik, 1999). Potrebe po beljakovinah pri prežvekovalcih ocenjujemo na podlagi presnovljivih beljakovin. Normative in enačbe za izračunavanje potreb prežvekovalcev v različnih obdobjih proizvodnega cikla smo prav tako povzeli po priporočilih Verbiča in Babnika (1998). Osnovno izhodišče za izračun krmnega obroka in za učinkovito vodenje prehrane je definiranje količine krme, ki jo žival lahko poje. Na podlagi obsežnih raziskav v svetu in pri nas lahko danes dokaj točno napovemo konzumacijsko sposobnost živali (Orešnik, 1996). Odvisna je predvsem od pasme, obdobja proizvodnega cikla živali, obsega prireje in telesne mase. Za krave molznice in krave dojilje jo izračunamo na podlagi Forbesovih formul, ki so bile v slovenskih razmerah že preveijene (Orešnik, 1994). Pri teletih in govejih pitancih sposobnost za zauživanje suhe snovi ocenimo na podlagi telesne mase (Žgajnar, 1990). Podobne zakonitosti veljajo tudi pri prehrani drobnice, le da je razmeije med teoretično sposobnostjo za zauživanje krme in telesno maso nekoliko širše (Kermauner, 1996). Da bi se kar najbolj približali izračunani sposobnosti za zauživanje suhe snovi, je potrebno zagotoviti ustrezno kakovost krme, ki nenazadnje vpliva tudi na končen rezultat prireje. Razvit prehranski model zajema le ključna dejavnika kakovosti voluminozne krme in sicer dovoljeno najvišjo in zahtevano najnižjo vsebnost surove strukturne vlaknine. S tem po eni strani zagotovimo ustrezno kakovost, po drugi strani pa normalno delovanje predželodcev in vseh bioloških procesov, ki so s tem povezani. Minimalne in maksimalne vrednosti smo za govedo povzeli po Žgajnaiju (1990), za drobnico pa po Kermauner (1996). Potrebe po hranljivih snoveh so navadno podane za posamezna obdobja reje (Verbič in Babnik, 1999; Verbič in Babnik, 1998; Kennauner, 1996; Orešnik, 1996; Žgajnar 1990), kar pomeni, da je za pridobitev vrednosti za enoletno ali drugo ustrezno časovno obdobje Žgajnar, J./ Kermauner, A./ Kavčič, S. Model za ocenjevanje prehranskih potreb prežvekovalcev in optimiranje krmnih obrokov. In: Slovensko kmetijstvo in podeželje v Evropi, ki se širi in spreminja, 4. konferenca DAES, Moravske toplice, 2007-11-08/09 (ed.: Kavčič, S.). Ljubljana, Društvo agrarnih ekonomistov Slovenije, Domžale, 2007,278-288 potrebno izračune združevati in v nekaterih primerih tudi nekoliko korigirati. Dodaten tehnični izziv predstavlja izračunavanje potreb po energiji in presnovljivih beljakovinah. Potrebe se namreč računajo ločeno za vzdrževanje, brejost, mlečnost, prirast, hujšanje, nalaganje telesnih rezerv in pri drobnici tudi za rast volne. Pri pitancih se denimo zaradi rasti, ki je odvisna od dnevnega prirasta, potrebe za vzdrževanje nenehno povečujejo. To povečevanje pa ni nujno enakomerno, saj se v obdobju pitanja spreminja dnevni prirast, posledično pa se telesna masa ne povečuje linearno. Do podobnih navzkrižnih odvisnosti pridemo pri vzreji plemenskih živali. Pri mlečnih rejah prihaja do razlik predvsem v nalaganju in sproščanju telesnih rezerv ter v dobi med telitvama, v obeh primerih tudi kot posledica količine prirejenega mleka. Hkrati se količina prirejenega mleka s trajanjem laktacije spreminja. Da čim bolje zajamemo opisano kompleksnost v modelu, je potrebno izračunavati dnevne potrebe znotraj celotnega (največkrat enoletnega) obdobja in jih nato sešteti. Simulacijski prehranski model za izračunavanje krmnih potreb je izdelan tako, da omogoča izračunavanje povprečnih dnevnih potreb, potreb na točno določen dan znotraj proizvodne dobe, potreb v definiranem obdobju sezone, potreb v celotnem obdobju pitanja ali vzreje oziroma v enem letu glede na vnaprej definirane proizvodne lastnosti. Na podlagi slednjih model izračuna tudi predvideno dobo vzreje plemenskih živali in živali v pitanju. S takšnim pristopom je omogočeno obravnavanje različnih tehnologij reje in vzreje, s katerimi se v praksi srečujemo. Posebna pestrost tehnologij je prisotna pri govejih pitancih, pri katerih se ta odraža poleg pestre pasemske strukture predvsem v različnih začetnih masah pitanja in intenzivnosti pitanja. Slednja se odraža tako v povprečnem dnevnem prirastu, dobi pitanja, kot tudi v klavno zreli telesni masi. Samo robusten in uporabnikom prijazen vmesnik omogoča hitro in enostavno nastavitev modelov za izračunavanje želenih spremenljivk. To smo dosegli z združitvijo najpomembnejših parametrov na posebnem listu, ti parametri pa se v naslednji stopnji vključujejo v posamezne podrobnejše izračune. Tak vmesnik od potencialnih uporabnikov ne zahteva podrobnega poznavanja uporabljenih fiinkcijskih pristopov, pač pa le nekatere bistvene zakonitosti živinoreje. Npr. pri večjih prirastih so pitanci prej klavno zreli in zato je tudi pričakovana končna telesna masa nekoliko nižja kot bi bila pri nekoliko manjših dnevnih prirastih. V simulacijskem modelu zajete proizvodne parametre, ki jih lahko spreminjamo in vplivajo na izračune prehranskih potreb, prikazujemo v preglednici 1. Nabor vhodnih podatkov med kategorijami se seveda razlikuje. Žgajnar, J./ Kermauner, A./ Kavčič, S. Model za ocenjevanje prehranskih potreb prežvekovalcev in optimiranje krmnih obrokov. In: Slovensko kmetijstvo in podeželje v Evropi, ki se širi in spreminja, 4. konferenca DAES, Moravske toplice, 2007-11-08/09 (ed.: Kavčič, S.). Ljubljana, Društvo agrarnih ekonomistov Slovenije, Domžale, 2007, 278-288 Preglednica 1: Vhodni podatki simulacijskega prehranskega modela 0) o 'c Jsl o E ^ "O 0 > C(3 S m 0 0 Ü Ü C (C o 0 N 0 Ü > O 0 č' CD 07 'E' ■ ns Vhodni podatki Kategorija živali Telesna masa ✓ Začetna telesna rnasa ✓ ✓ Končna telesna masa Sproščanje in nalaganje telesnih rezerv Obdobje sproščanja in nalaganja telesnih rezerv ■/ Obdobje brejosti ✓ Laktacijska doba Doba med telitvama ✓ Povprečen dnevni prirast 1 Povprečen dnevni prirast II v' Skupna mlečnost v/ Sestava mleka (% maščob in beljakovin) Št. telet/jagnjet Rojstna masa telet/jagnjet Pasma Sestavljanje krmnih obrokov Pri vodenju prehrane različnih kategorij domačih živali se v praksi srečujemo z različnimi sistemi krmljenja. Bistvena razlika med njimi je v ciljih reje oziroma prireje, velikosti kmetijskih gospodarstev, možnostih za pridelavo voluminozne in močne krme in nenazadnje tudi od ukrepov kmetijske politike, ki posredno ali neposredno favorizirajo določen tip gospodarjenja (Žgajnar in sod., 2007). Ti dejavniki so toliko izrazitejši, ko gre za ekonomsko optimizacijo gospodarjenja na kmetijskih gospodarstvih. Razvit simulacijski model poleg krmnih potreb živali izračunava tudi krmno vrednost različnih vrst krme, ki jo bodisi pridelamo na kmetijskih površinah, bodisi kupimo. Ocena hranilne vrednosti krme za prežvekovalce je v večjem delu povzeta po Verbiču in Babniku (1998). V nekaterih primerih je razpoložljiva energija krme izražena le v neto energiji za laktacijo. Zaradi manjkajočih podatkov je pogosto ni možno preračunati v metabolno energijo, s katero operiramo pri (ostalih) prežvekovalcih, ki prvenstv^eno niso namenjeni prireji mleka. Manjkajoče podatke za izračune smo povzeli po nemških prehranskih tabelah (DLG, 1997). Simulacijski model skupno zajema 92 ocen vrednosti različnih vrst krme za prežvekovalce, ki jo kmet lahko pridela na lastnih površinah ali dokupi. Dobljeni podatki zadostujejo za neekonomsko optimizacijo krmnega obroka, kar pomeni, da ne spremljamo stroškovnega vidika. Potrebno je le definirati razpoložljive vrste krme in njihove količine ter obdobje in način spravila. Uporabljena tehnika matematičnega programiranja je odvisna od narave problema in pristopa k njegovemu reševanju. Pri pregledu literature smo ugotovili, da sta najpogosteje uporabljena deterministično statično linearno programiranje in večkriterijalno oziroma ciljno programiranje. Dejstvo, da je ekonomska uspešnost živinoreje v največji meri odvisna od spremenljivih stroškov krme, narekuje stroškovno optimizacijo krmnega obroka. Torej je za opazovane parametre (NEL, ME, suha snov, minimalna in maksimalna vsebnost strukturne surove Žgajnar, J./ Kemiauner, A./ Kavčič, S. Model za ocenjevanje prehranskih potreb prežvekovalcev in optimiranje kmmih obrokov. In: Slovensko kmetijstvo in podeželje v Evropi, ki se širi in spreminja, 4. konferenca DAES, Noravske toplice, 2007-11-08/09 (ed.: Kavčič, S.). Ljubljana, Društvo agrarnih ekonomistov Slovenije, Domžale, 2007, 278-288 vlaknine) potrebno izračunati spremenljive stroške za vsako vrsto krme posebej. Ta korak zahteva pripravo podrobnih kalkulacij, na podlagi katerih je mogoče oceniti stroške za kilogram posamezne krme pri različnih tehnologijah in intenzivnostih pridelave. Tako ovrednotene hranilne vrednosti posamezne krme bodo omogočale ekonomsko optimizacijo kminega obroka. Naša naslednja naloga je torej pripraviti takšen optimizacij ski program, ki bo minimiziral stroške krmnega obroka. Linearni program za optimiranje proizvodnih odločitev na ravni kmetijskih gospodarstev (Žgajnar, 2006) bomo v prehranskem delu nadgradili z razvitim simulacijskim modelom (slika 1). S tem bomo nadomestili vnaprej definirane potrebe po posamezni vrsti krme s potrebami po posameznih hranljivih snoveh. Model bo omogočal sestavljanje krmnih obrokov na ravni cele kmetije. To bo razmeroma enostavno v primeru, ko gre za specializirano kmetijo (postopek 1), za katero bo model sestavil krmni obrok le za dotično kategorijo domačih živali. Precej zahtevnejši postopek pa bo potrebno ubrati pri živinorejsko mešanem tipu kmetij (postopek 2), na katerih krmnega obroka posamezne kategorije živali ne bo možno vnaprej definirati. Hkrati se pojavi problem pri močni krmi, ki je namenjena le določeni kategoriji domačih živali. Problema se bomo lotili z dvostopenjsko optimizacijo. V prvi fazi bomo optimirali krmni obrok za posamezno kategorijo domačih živali izven optimizacijskega modela. Na podlagi vhodnih podatkov kmetije bomo definirali aktivnosti pridelave krme, ki so v danem primeru realno možne. Na osnovi predvidenih pridelkov in načina spravila bomo poleg hranilne vrednosti iz baze kalkulacij dobili tudi oceno o spremenljivih stroških na enoto proizvodnje. Za vsako kategorijo domačih živali bomo tako razvili samostojen optimizacijski model, ki bo iskal najcenejši krmni obrok. Dobljene rešitve bomo upoštevali v drugi fazi iskanja optimalne rešitve, v kateri bomo s pomočjo že razvitega linearnega programa (Žgajnar, 2006) optimirali proizvodnjo na ravni cele kmetije. Žgajnar, J./ Kermauner, A./ Kavčič, S. Model za ocenjevanje prehranskih potreb prežvekovalcev in optimiranje krmnih obrokov. In: Slovensko kmetijstvo in podeželje v Evropi, ki se širi in spreminja, 4. konferenca DAES, Moravske toplice, 2007-11-08/09 (ed.: Kavčič, S.). Ljubljana, Društvo agrarnih ekonomistov Slovenije, Domžale, 2007, 278-288 SMI I U IIS! 1 \ioni I /A (K 1:N11 \ M rikinii "T" I T" J- I Vhodni podatki za LP j Linearni model za optimiranje proizvodnje na ravni KMG ' 1. Specializacija 2. Živinorejsko mešan tip KMG Model za optimiranje krmnega obroka za posamezno kategorijo živali Obrok za molznice Obrok za pitance Obrok za ... Legenda: 1 1 r - — "1 — J 1 2 Simulacijski model, predstavljen v tem prispevku OptimizacijsM model za sestavljanje krmnih obrokov (v pripravi) Linearni model za optimiranje proizvodnje na ravni KMG (Žgajnar, 2006) Povezave med modeli Izračun krmnega obroka za specializiran [1] oziroma živinorejsko mešan [2] tip kmetije Slika 1: Shema povezave simulacijskega modela z linearnim modelom za optimiranje proizvodnih usmeritev na ravni kmetijskih gospodarstev in postopek dvostopenjske optimizacije krmnega obroka Da bi ugotovili, kako se s takšnim pristopom spremeni dobljena optimalna rešitev na konkretnem kmetijskem gospodarstvu, bo potrebna dodatna analiza. Če se bo izkazalo, da je takšen pristop optimizacije preveč pristranski in nas hkrati ne bo zanimala sestava krmnega obroka, bomo v drugi fazi optimiranja upoštevali le hranilne vrednosti in cene za krmne mešanice, ki z že omenjenega vidika predstavljajo problem. V prehranskem delu razšiijen in natančnejši model bo omogočal dodatne analize s področja ekonomike prehrane. S ponovnim definiranjem namenske funkcije bomo naredili primeijalno analizo med optimalno rešitvijo, ki jo dobimo pri maksimiranju pokritja in med optimalno rešitvijo, če namenska funkcija predstavlja minimiziranje krmnih stroškov. Pričakujemo, da bo ob istih omejitvah korekcija med dobljenimi rešitvami zelo visoka. Sklep Menimo, da bi moralo biti iskanje najcenejšega krmnega obroka, ki hkrati pokrije vse potrebe živali, temeljno vodilo vsakega sodobnega živinorejca. Temu v prid govori dejstvo, da stroški krmnega obroka pogosto presegajo polovico, ob visokih cenah krmnih žit pa pri nekaterih kategorijah goved celo dve tretjini skupnih spremenljivih stroškov. Le enostaven, a hkrati dovolj natančen program za izračunavanje krmnih potreb bo rejce prepričal v smiselnost pogostejšega izračunavanja potreb njihovih živali. S primernim optimizacijskim programom 2gajnar, J./ Kemiauner, A./ Kavčič, S. Model za ocenjevanje prehranskih potreb prežvekovalcev in optimii'anje krmnih obrokov. In: Slovensko kmetijstvo in podeželje v Evropi, ki se širi in spreminja, 4. konferenca DAES, Moravske toplice, 2007-11-08/09 (ed.: Kavčič, S.). Ljubljana, Društvo agrarnih ekonomistov Slovenije, Domžale, 2007, 278-288 Tjodo lahko sestavljali cenejše krmne obroke, ki bodo v danih ekonomskih in tržnih pogojih za njihovo rejo ekonomsko najugodnejši. Rejec bi s pomočjo takšnega programa dosegel tudi večjo alokacijsko učinkovitost, saj bi lahko vnaprej načrtoval, katere kulture so zanj v danih pogojih najbolj donosne, in bi svoje proizvodne vire lahko razporedil tako, da bi kar najbolje pokril potrebe svojih živali. Prav alokacijska učinkovitost pa je poleg tehnične učinkovitosti ključen element ekonomske učinkovitosti (Farrell, 1957). 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V: Proceedings of 16th International Farm Management Association Congress. A Vibrant Rural Economy - The Challenge for Žgajnar, J./ Kermauner, A./ Kavčič, S. Model za ocenjevanje prehranskih potreb prežvekovalcev in optimiranje krmnih obrokov. In: Slovensko kmetijstvo in podeželje v Evropi, ki se širi in spreminja, 4. konferenca DAES, Moravske toplice, 2007-11-08/09 (ed.; Kavčič, S.). Ljubljana, Društvo agrarnih ekonomistov Slovenije, Domžale, 2007, 278-288 Balance, Cork, 15-20 July 2007. O'Reilly S., Keane M., Enright P. (eds.). New Zealand, International Farm Management Association: 199-208 ^üa agriculturae Slovenica, suplemet 2 (september 2008) Napaka! Zaznamek ni definiran.. ^ ://aas. bf. uni-!j. si 2 .Agris category codes: Q03 COBiSS Code 1.01 3 SPREADSHEET TOOL FOR LEAST-COST AND NUTRITION BALANCED BEEF RATION 4 FORMULATION 5 Jaka ŽGAJNAR and Stane KAVČIČ 6 XJiiv. of Ljubljana, Biotechnical Fac., Dept. of Animal Science, Groblje 3, SI-I230 Domžale, Slovenia, e-mail: 7 iika.zgainar@:bfro.uni-li .si. 8 ABSTRACT 9 TMs paper points out some facts that might improve economic outcome of livestock production 10 in the sense of diet formulation. A spreadsheet tool from two linked modules based on MS Excel 11 platform was constructed, merging different mathematical deterministic programming 12 techniques. The first module utilizes linear program for least-cost ration formulation, aiming to 13 obtain rough estimate what magnitude of the costs might be expected. Resulting value is then 14 considered as target value of cost goal in the second module. It is based on weighted goal 15 programming with penalty function. Obtained results confirm benefits of applied approach. It 16 enables formulation of least-cost ration not taking to much risk of worsening the ration's 17 nutritive value and balance between nutrients. This is especially important when improved 18 economic and nutritive efficiency is the primal and common aim of optimization tool. 19 Key words: cattle / bulls / spreadsheet tools / beef economics / beef ration optimization / linear programming / 20 weighted goal programming / penalty function 21 ORODJE ZA NAČRTOVANJE NAJCENEJŠIH IN PREHRANSKO IZRAVNANIH 22 OBROKOV ZA PITANCE 23 IZVLEČEK 24 Prispevek izpostavlja nekatere dejavnike, ki z vidika sestavljanja krmnih obrokov lahko 25 izboljšajo ekonomiko živinoreje. V Excelovem okolju je bilo v obliki elektronskih preglednic 26 razvito modularno orodje, ki združuje različne tehnike determinističnega matematičnega 27 modeliranja. Prvi modul vključuje tehniko linearnega programiranja in služi za oceno 28 najcenejšega možnega krmnega obroka. Dobljeni rezultat kot ciljna vrednost vstopa v drugi 29 modul, ki temelji na tehtanem ciljnem programiranju, nadgrajenem s kazensko funkcijo. 30 Pridobljeni rezultati potijujejo prednosti uporabljenega pristopa, ki omogoča sestavljanje 31 najcenejših krmnih obrokov, ne da bi ob tem tvegali močnejše poslabšanje hranilne vrednosti in 32 razmeija hranil. To je posebej pomembno, ko je izboljšanje ekonomske in prehranske 33 učinkovitosti temeljni cilj optimizacijskega orodja. 34 Ključne besede: govedo / biki / pitanje / elektronsko orodje / ekonomika / optimiranje prehrane / linearno 35 programiranje / tehtano ciljno programiranje / kazenska funkcija 36 INTRODUCTION 37 Due to changing economic and political environment, the beef sector is becoming one of the most 38 sensible agricultural sectors in the European Union. Its economic position is mostly dependent on the 39 efficiency of each agricultural holding production structure, with the crucial role playing the economy of 40 scale. However, at the moment poor economics position of beef sector could be significantly imposed 41 with progressive abolition of previous Common Agricultural Policy (CAP) production coupled support 42 and increasing environmental and other public demands - in addition to World Trade Organization 43 (WTO) pressures, which have led to rapid market fluctuations. Together with direct consequences on the 1 beef market, there are indirect influences that ai-e going to present an increasing economic challenge for 2 beef farmers, especially through higher input prices. Since ration costs might present 40 to 70 % of total 3 variable costs, it follows that livestock ration formulation is becoming an increasingly important task also 4 in management of beef sector. It is the fundamental lever in technological improvement that manifests in 5 economic as also ecological terms. In order to help breeders to deal with these challenges many tools 6 have been developed. 7 The most frequent technique applied is deterministic linear programming (LP). It is a classical 8 approach to formulate animal diets and also appropriate tool to optimize human nutrition (Darmon et al, 9 2002). When focusing only on livestock diets, one can find out that the most frequent manner of utilizing 10 LP technique is least-cost ration formulation, for the first time used by Waugh (1951). As any 11 optimisation technique also LP has some drawbacks. 12 Common to all LP problems is single objective function as its basic concept. It means that one try to 13 get the optimal solution in minimizing or maximizing desired objective within set of constraints imposed. 14 From this point of view LP could be deficient method for ration formulation, since it exclusively relies on 15 one objective (cost flmction) as the only and the most important decision criteria (Rehman and Romero, 16 1984; 1987). Lara and Romero (1994) are stressing that in practice decision maker never formulates 17 ration only on the basis of a single objective, but rather on the basis of several different objectives, where 18 economic issue is only one of many. 19 Another drawback of pure LP is also mathematical rigidity of constraints (right hand side - RHS), 20 which usually results in fact that set of equations does not have a feasible solution (Rehman and Romero, 21 1984). This means that no constraints' (e.g. given nutrition requirements) violence is allowed at all, 22 irrespective of deviation level. However, relatively small deviations in RHS would not seriously affect 23 animal welfare, but would result in a feasible solution (Lara and Romero, 1994). 24 The most appropriate and commonly used method that partly overcomes listed problems of LP 25 paradigm is weighted goal programming (WGP) (Tamiz et al., 1998). It is a pragmatic and flexible 26 methodology for resolving multiple criteria decision making problems what ration formulation definitely 27 is. Its advantage is also in familiarity with LP, since simplex algorithm is utilized to find the solution 28 (Rehman and Romero, 1993). 29 The aim of this paper is to present developed spreadsheet tool, utilizing mathematical modelling 30 techniques. In the first part a brief overview of WGP and penalty function is given. It is followed by a 31 short description of the optimization tool. Then, the basic characteristics of the analysed case are 32 presented, followed by the results and discussion. Brief conclusions are given in the last section. 3 3 MATERIAL AND METHODS 34 Weighted goal programming with penalty function 35 Weighted goal programming's formulation is expressed as mathematical model with a single objective 36 (achievement) function (weighted sum of the deviations variables). Hence, the objective fianction in WGP 37 model minimizes the undesirable deviations from the target goal levels and does not minimize or 38 maximize goals themselves (Ferguson et al., 2006). In most cases obtained solution is compromise 39 between contradictory goals, enabled with positive and negative deviation variables. Negative deviation 40 variables are included in the objective fimction for goals that are of type "more is better" and positive 41 deviations variables are included in the objective function for goals of type "less is better". Since any 42 deviation is undesired, the relative importance of each deviation variable is determined by belongiag 43 weights. 44 Since the goals are measured in different units and have different numerical values, the deviations are 45 scaled with normalisation techniques (Tamiz et al, 1998). With this process incommensurability is 46 prevented and all deviations are expressed as ratio difference (i.e. (desired - actual)/desired) = 47 (deviation)/desired)). 48 Rehman and Romero (1987) are pointing on the main drawback of WGP that is concerning the 49 marginal changes. Namely, the method does not distinct between marginal changes within one observed 50 goal; all changes (deviations) are of equal importance. This addresses another new issue in ration 51 formulation example. Namely, in some situations too big deviation might lead to fail animal's Žjajnar and Kavčič Spreadsheet tool for least-cost and nutrition balanced beef ration formulation. 3 1 xe([uirements within nutrition desirable limits, and obtained solution is useless. To keep deviations within 2 desired limits and to distinguish between different levels of deviations, penalty function (PF) might be 3 dniroduced into the WGP model (Rehman and Romero, 1984). 4 Our approach enables one to define allowed positive and negative deviation intervals in more stages 5 for each goal separately. Dependant on goal's characteristics (nature and importance of 100 % matching) 6 these intervals might be different. Sensitivity is dependant on number and size of defined intervals and the 7 penalty scale utilised (s,-; for i=l to n). Penalty system is coupled with achievement ftmction (WGP) 8 through penalty coefficients. 9 Toll for two-phase beef ration formulation 10 11 12 13 14 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 The aim of the paper is to present a simple optimization tool for beef ration formulation, developed in MS Excel framework. It is designed as two phase approach (modules) based on mathematical programming techniques (LP and WGP with PF). < o z MODULE 1 LP RATION (LP) MODULE 2 WGP with PF Optimization: tool Figure 1: Scheme of the optimization tool The first module (Figure 1) is based on LP paradigm and is an example of least-cost ration formulation. On the basis of the most important non-competitive constraints it searches for the roughly balanced ration at the least possible cost. On the solution obtained an estimate of cost magnitude expected might be made. Therefore the first module (LP) is as simple as possible (on constraints side), intended just to get crude cost estimation. Through cost function it is linked to the second module based on weighted goal program (WGP) with PF. 21 Mathematical formulation of the first and the second module The first module (LP) is formulated as shown in equations (1), (4) and (7). It mostly relays on economic (cost) function (C) and satisfies only the most important nutrition requirements coefficients (b,), known also as right hand side (RHS). In the first optimization phase one is searching for the ration at the lowest possible cost. Except minimum requirements (i,) that should be met, prices (cj) are the most important factor that dictates the level ofy'th feed (Xj) included into the ration. mm y=i such that mm 1=1 g/ /=1 ^ ayXj + J;, + d 12 - - dti = Si y=i 7=1 dn^gi-pfSi such that for all / = 1 to r and gj 0 for all /=1 to m for all z=l tor for all i=\ to r for all i=\ to r (1) (2) (3) (4) (5a) (5b) (6a) 1 ^/Xz^/'r^z-g/ foralh=ldor (6b) 2 (7) 3 The second module (WGP with PF) is formulated as shown in equations (2) to (7). The achievement 4 function (Z), expressed in equation (2) is defined as weighted sum of undesired deviation variables (d.j^ 5 dii, dy'^, d/i") fi:om observed goals (g), multipUed with belonging penalty coefficients (sj and S2). 6 Obtained sum-product is subject of mirdindzation (2). The relative importance of each goal is represented 7 by weights (w,) associated with the corresponding positive or negative deviations. To control deviations 8 (5a, 5b, 6a, 6b) for each goal in WGP, penalty intervals (p,/""", Pii"'", Pia""", Pi2"""') are in place. Because of 9 the normalization process, only goals that have nonzero target values (3) could be relaxed with positive 10 and negative deviations. 11 Obtained target value (Q in the first module enters into the second module (WGP with PF) as cost 12 goal (3) that should be met as close as possible. This is also the only case where negative deviation is not 13 penalised and also not restricted with intervals. All other constraints that do not have defined target value 14 or do not have priority attribute are considered in equation (4). One of the main assumptions of the LP 15 paradigm is also non-negativity that is considered for both models in equation (7). 16 Case analysis 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 The tool has been tested on a hypothetical case. It was presumed that beef fattening starts at 200 kg of live weight and stops at 600 kg. For the reason of more precise ration formulation, whole fattening period has been split into four breeding periods (100 kg weight gains) with different average daily gains. In the first period bulls gained 0.9 kg per day, while in the second and the third period the average daily weight gain is the same (1.1 kg). The last quarter last 100 day which means that average daily weight gain was 1 kg. Table 1: Nutrition requirements divided into four breeding periods, presented as constraints (LP) and set of Fattening period 200-300 kg 300-400 kg 400-500 kg 500-600 kg LP WGPI/II LP WGPI/II LP WGPI/II LP WGPI/n ME (MJ) >6,311 6,311 >6,574 6,574 >7,547 7,547 >9,105 9,105 MP (g) >46,880 46,880 >45,228 45,228 >48,114 48,114 >54,260 54,260 DM (kg) <632 632 <718 718 <920 920 <936 936 CP min (kg) >114 >129 >166 >168 CFmax (kg) <164 <187 <239 <243 Ca (g) >4,152 4,152 >4,368 4,368 >4,462 4,462 >5,200 5,200 P (g) >2,358 2,358 >2,596 2,596 >2,958 2,958 >3,300 3,300 Price (cent) CI C2 C3 C4 Hay (kg/day) <2 <2 <2 <2 LP - constraints for the first module (both scenarios) WGP I/11- constraints for the second module (both scenarios) All nutritional requirements have been assessed with the spreadsheet model for ruminants' nutritional requirements estimation (Žgajnar et al, 2007). The most important constraints and goals are presented in Table 1. Basic set of constraints in both modules (LP and WGP with PF) is more or less the same; they differ only in mathematical sign when they are transformed into goals. In the process of ration formulation one should also consider other 'non-nutrition' constraints. In our hypothetical case study we assume quite frequent example that might be met on Slovene beef farms. Because of our climate characteristics, the first or second grass mowing is usually conserved as hay and from rest the grass silages are prepared. This is why the amount of hay in the diet is restricted and in all four periods maximal amount of hay is set to 2 kg per day (Table 1). Initial version of WGP model involves six goals (Table 2). Importance of each goal is defined with weights (wi) ranging between 0 and 100. For energy and protein requirements deviation intervals are very restricted, while for the rest of the goals deviations are more relaxed. For the dry matter intake that ^iajnar and Kavčič Spreadsheet tool for least-cost and nutrition balanced beef ration formulation. 5 1 presents consumption capacity deviation intervals are defined only for underachievement of the goal, 2 Avkile overachievement is for practical reasons (consxomption capacity) not allowed. 3 Table 2: Weights of defined goals and penalty function intervals for two scenarios_ Penalty function intervals_ Goal weights "a 3 .8 I Hi tu J3 g I i -O 0^ d o ■g A "o M O o ^ o o CN u CS V u Vi ti s .a S -o a « "o o a I/} J TS 15! "M s o a _o 'S !-c .-I' C« -a T3 n 73 O) ■O -w XI O 3 a H P-, O 00 ^ Pi O o M Ph O ^ ^ o >-H O. si o ^ (N ^ o\ ro OO W-) NO 1 (O -d (D M 0 u s g „ 1 s J o .h o ca ^ J m 00 "tS CN MD ro VO o r-^ p P rt; p p d d c-i od p ^ p p o d d ^ (N CT\ p p d d r-^ o ^ -< m -«a- ä? C u S -pT8i for ali/=1 tor (5a) dj, + dj, < g, - for all 2=1 to r (5b) dti ž pTgi - gi for all /=1 to r (6a) d:,+dt,0 (7) The second sub-model (WGP with a PF) is formulated as shown in equations (2) to (7). The achievement function (Z), expressed in equation (2), is defmed as the weighted sum of the undesired deviation variables (^v^ d u, d a') from observed goals (g,), multiplied by belonging penalty coefficients {si and s2) that measure the slope of the penalty function. The obtained sum-product is the subject of minimization (2). The relative importance of each goal is represented by weights (w,) associated with the corresponding positive or negative deviations. Penalty intervals (pu""", pu""", p 12""", P12""^) are in place to prevent uncontrolled deviations (5 a to 6b) within each goal. Because of the normalization process, only goals that have nonzero target values (3) could be relaxed with positive and negative deviations. The obtained target value (C) in the first sub-model enters into the second one (WGP with PF) through "cost goal" (g,- = Q. This is also the only case where negative deviation is not penalized and also not restricted to intervals. All other constraints that do not have defmed target values or do not have priority attributes are considered in the equation (4a). All upper bounds for ratios are transformed into linear equations with equation (4b), and the same holds for lower bounds, which should be multiplied by -1. Non-negativity condition for both models is considered in equation (7). Analyzed example To illustrate the use of the tool, we chose a hypothetical case of pig production. We considered that the tool should formulate the complete ration/feed-mix in relation to the nutritional requirements. Due to significant changes in nutritional requirements throughout a pig's life, the fattening period (40 kg - 100 kg) has been split into three periods with a 20 kg weight gain in each. In each period, the average daily weight gains were different. In the first period, the pigs gained 740 g/day; in the second period, they gained 800 g/day; in the last period, they gained 750 g/day. Table 1: Assumed daily requirements for three fattening periods Fattening period 40-60 kg 60-80 kg 80-100 kg Average daily weight gain (g/day) 740 800 750 Metabolisable energy (ME) MJ 25.5 31.4 34.8 Crude protein (CP) g/day 330 370 340 Lysine (Lys) g/day 17.2 19.5 18.8 Methionine + Cystine (Met + Cys) g/day 10.3 11.7 11.3 Methionine (Met) g/day 5.2 5.9 5.6 Threonine (Thr) g/day 10.3 11.7 11.3 Tryptophan (Trp) g/day 3.4 3.9 3.8 All nutrition requirements are taken from DLG (1991). The most important are presented in Table 1. Besides those, the tool also considers the mineral requirements (Ca, P, and Na). The formulated ration should also have the appropriate crude fibre content, which is assured through minimal and maximal ratio as well as protein digestibility. In order to prevent a solution that has too much of one feed in the diet, we considered recommendations for maximal feed inclusion (Futtermittelspecifische ..., 2006). Table 2: Importance ofgoals with corresponding penalty function intervals Penalty function intervals Together Weight Pi + 1 Pif Pi2 + Pi2 Pi^ Pi' Goal Unit (/day) (Wi) % % ME MJ 80 1 0 2 0 3 0 CP g 65 1 0 2 0 3 0 Lys g 75 2 1 3 3 5 4 Met + Cys, Met, Thr g 65 3 2 5 4 8 6 and Trp Pdigest g 20 5 5 10 10 15 15 Cost Cent 20/90 5 00 20 oo 25 Weights indicate the decision maker's preferences with respect to each goal. The tool offers the option to switch between goals and constraints, depending on the needs of the decision maker. In the analyzed case, we chose nine goals (Table 2) that should be met as accurately as possible. The importance of each goal is defined by weights (w,) ranging between 0 and 100. For each goal, deviation intervals are defined separately. They are measured in percentage deviation from the desired level. The most rigorous and short intervals are anticipated by energy, protein, and amino acids goals. Specifically, reducing the unbalanced protein fraction by increasing protein quality (fulfilling the amino acids ratios in relation to the energy) reduces nitrogen excretion and pollution. The tool also includes "the library" of feeds and their nutrition values. It is organized in such a way that it is possible to change the quality parameters, as well as add new ones. The initial tool version includes 35 feeds and vitamin-mineral mixtures. In the process of ration formulation, one can select only those that are at one's disposal to enter into the formulated ration. Results The application of the tool is presented through a simple example that might be applicable to larger agricultural holdings. This means that rations primarily consist of feed-mixes prepared at the farm gate. We have presumed that the decision maker prepares three different feed-mixes for growing pigs, in two different scenarios. In the first scenario, the most important element is quality of the ration {Wcosr=20\ while in the second scenario, cost is more important {Wcost=9G). The results obtained are presented in Figures 2 and 3. Figure 2 illustrates the structure of two different ration sets differentiated by their cost importance. Within each set, formulated rations are dependent on the energy concentration of animal rations. The range of the energy content of the ration was set between 12.3 and 13.7 MJ ME. Figure 3 illustrates the level of ration costs for different fattening periods over the same range of ME content. 500 400 X £ ■g 300 o D) 200 100 CO-^ lOCON-eOOJO-r-; cNcscsicNicsicvicsicoco CO -Ij; iq CD CO CO CO CO tri -«-r-« I « I y^-m-r-^ CO tj in CD t-- CO CJ) cJ eg Cvi cj C\i CM' CN ME (MJ)/kg ME(MJ CM CO -a- in CD CO CO CO CO CO i/kg • Maize (0.12€/kg) prim • Soya meal, decorticated fried (0.30 €/kg) prim ■ Molasses (0.18 €/kg) sec ■ Sunflower meal, decorticated (0.14 €/kg) sec Maize gluten, 60% CP (0.70 €/kg) sec ■ Ruecana (0.87 €/kg) sec -Wheat(0.14 €/kg) prim - Wheat flour (0.11 €/kg) sec -+— Soya proteins, isolat (0.55 €/kg) sec -tv- Maize gluten meal, 23% (0.13 €/kg) sec Limestone (0.04 €/kg) sec ■it«- L-Lys*HCI (1.65 €/kg) sec Figure 2: Formulated feed-mix for the second fattening period at low (W=20) and high importance (W=90) of ration cost (prim = primary axis; sec ~ secondary axis) One of the main parameters that defines how much a pig is going to eat is the energy content of the feed-mix. If the feed-mix is more concentrated, an animal is going to eat less, and vice versa. Figure 2 presents formulated rations for the second fattening period. It is obvious that the energy content of the ration strongly influences selection of the feed. With increasing energy content, the quantity of maize increases and the quantity of wheat decreases. From Figure 2, it is apparent that cheap wheat flour reduces costs, since it enters into the solution only at high W values. The same holds for sunflower meal. From Figure 2, one can also observe the phenomena of energy-low rations, demonstrated by high limestone content. ° 30 , , 1-45 S 1-40 <§ 1.35 Wcost^90 o C g E 'TO Q 1.30 1.25 1.20 1.15 Wcosf=20 __________________1 _ _ ^ 1—it—A—■> / 3-Q-G 1 I Wcost=90 c^CNicNcvicNicsicvicocococococococo co^LOcor^ooo^o-^-cgco-^jncor-. (NcJcvicvicsicvicNicococococococrJco (MJ/kg) (MJ/kg) -A-1. Fattening period (40-60 kg) II. Fattening period (60-80 kg) II. Fattening period (80-100 kg) Figure 3: Daily ration costs dependent on energy content of the feed-mix by low (left side) and high (right side) ration cost importance The importance of finding the "optimal" energy content of the feed-mix, which further influences its structure and the profitability of pork production, is illustrated in Figure 3. It is logical that pressure on economics reduces rations' cost. The difference ranges between a few tenths of a cent up to several cents per day, and increases with animal growth. Of course, the difference for one pig per day is no big deal, but if one considers a facility with 50,000 animals, this becomes an important issue. It is an interesting coincidence that optimal rations in all three fattening periods shift to the left if the cost is of higher importance. Even though the difference is only 0.1 MJ, this demonstrates that it is cheaper to formulate feed-mixes with lower energy content. From Figure 3 it is also apparent that in spite of lower daily ration cost in earlier fattening periods, such rations are more expensive per MJ of ME. With animal growth, the optimal energy content shifts to higher concentrations. From Figure 3, we can see that in the third fattening period, the tool finds solution only from 13.2 MJ onwards. Deviations from set goals are too big and the tool does not find solutions at lower energy. Tlie difference in ration costs between different energy concentrations is obvious. It ranges 2.4 up to 4.5 cents per daily ration. In any case, it should be an important issue to find the "optimal" energy concentration in the daily management of pork production. Conclusions The results of this study show that the three phase optimization approach, supported by mathematical programming (LP and WGP with PF), can be applied efficiently to the ration formulation for growing pigs. Through using this tool, more efficient diets might be formulated, since the model enables the decision maker to find the optimal energy content of the diet for various economic circumstances. The tool could be utilized in medium and large-scale agricultural holdings, which are usually the major pollutants of the environment, and where such tasks are an important part of daily management. Specifically, precisely balanced rations prevents over-feeding as well as under-feeding, both of which are expensive and burden the environment. References Bailleul P.J., Rivest J.,Dubeau F., Pomar C. 2001. Reducing nitrogen excretion in pigs by modifying the traditional least-cost formulation algorithm. Livestock Production Science. 72: 199-211 Black J.R. and Hlubik J. 1980. Symposium: Computer programs for dairy cattle feeding and management - past, present, and future. Journal of Dairy Science. 63: 1366-1378 Buysse J., Huylenbroeck G.V., Lauwers L. 2007. Normative, positive and econometric mathematical programming as tools for incorporation of multifiinctionality in agricultural policy modelling. Agriculture, Ecosystems & Environment, 120: 70-81. Castrodeza C., Lara P., Pena T. 2005. Multicriteria fractional model for feed formulation: economic, nutritional and environmental criteria. Agricultural Systems. 86:76-96 DLG. 1991. DLG-Futterwerttabellen - Schweine. 6. Auflage. DLG-Veriag, Frankfurt, 58-59 Futtermittelspecifische Restriktionen. Rinder, Schafe, Ziegen, Pferde, Kaninchen, Schweine, Geflügel. 2006, 40 p Lara, P. and Romero, C. 1994. Relaxation of Nutrient Requirements on Livestock Rations through Interactive Multigoal Programming. Agricultural Systems 45: 443-453 Rehman, T. and Romero, C. 1984. Multiple-criteria decision-making techniques and their role in livestock ration formulation. Agricultural Systems 15: 23-49 Rehman, T. and Romero, C. 1987. Goal Programming with penalty ftmctions and livestock ration formulation. Agricultural Systems 23: 117-132 Tamiz, M., Jones, D. and Romero, C. 1998. Goal programming for decision making: An overview of the current state-of-the-art. European Journal of Operational Research 111: 569-581 Weintraub A., Romero C., Bjomdal T. and Lane D.E. 2001. Operational research Models and the Management of Renewable Nature Resources: A Review. Working paper No. 11/01. Centre for Fisheries Economics, Discussion paper No 2/2001: 1-32 Waugh, F.V. 1951. The minimum-cost dairy feed. Journal of Farm Economics 33: 299-310 Agronomy Research 7(Special issue II), 775-782, 2009 Multi-goal pig ration formulation; mathematical optimization approach N/ 1 2 J. Zgajnar and S. Kavčič 'University of Ljubljana, Biotechnical Faculty, Deptartment of Animal Science, Groblje 3, SI-1230 Domžale, Slovenia; e-mail: jaka.zgajnar@bfro.uni-lj.si ^The same address as' Abstract. Organically produced pork is characterized by high production costs, within the main part goes to ration cost. Forage must be produced under strict conditions, reflecting in high prime costs. The main challenge for fanners is how to formulate economically efficient, nutrition balanced and politically acceptable rations at the least-cost to be competitive. This challenging task demands handy tool that merges all three viewpoints. In this paper an example of such a tool, based on three step approach, is presented. In the first step, a common linear program is utilized to formulate least-cost ration. In the second step, a sub-model, based on weighted goal programming and supported by a system of penalty functions, is used to formulate a nutritionally balanced and economically acceptable ration that also fulfils conditions demanded by organic farming. The most 'efficient' energy content of the ration is searched in the last step. The obtained results confirm the benefits of the applied approach. Key words: mathematical programming, ration costs, organic farming, pork INTRODUCTION Organic farming is globally characterized by higher production costs that are affected by strict organic production policy constraints; however profits are very diverse and are highly related to the market strategy in place. Because the farmer's main objective is to maximize profits, costs must be minimized. This may be accomplished through improved technical or economical efficiency. Due to high expense of ration costs and the possibility of negative externalities that might occur, it is obvious that ration formulation is a crucial task in daily pig breeding management-even more if the organic farming practice is in place. Comparing to the conventional production the majority of fodder is usually produced at the farm gate or less common, purchased (maximum 20%) from another organic producer in the same region at the relatively high price. In this case, changes in world (cereal) markets could rapidly affect the economic outcome. However, even if the majority of the feed is produced at the farm gate, there are opportunity costs that require the decision maker to make efficient decisions in relation to breeding practices. This may allow for improved productivity, or at least may keep profitability at an acceptable level. Organic fattening confronts also with the lack of availabihty of pure amino acids that results in more unbalanced protein composition, increased feed cost and what is unlike with organic philosophy, increased load of excessive nitrogen from manure on the environment (Blair, 2007). In order to help breeders to deal with these challenges, many tools based on mathematical programming (MP) paradigm have been developed. The first problem of this kind has been conducted by Waugh (1951), who applied the linear programming (LP) paradigm in order to formulate rations on a least-cost basis. This approach has been very popular in the past, especially after the rapid development of personal computers. In the 1960s, it became a classical approach to formulate animal diets as well as feed-mixes (Black & Hlubik, 1980). More recently, Castrodeza et al. (2005) stressed that the daily routine of ration formulation is one of the fields in which LP is most widely used. Common to all LP problems is the concept of constraint optimization, which means that one tries to find the optimum of a single objective function. However, exclusive reliance just on one objective (cost function) as the only and the most important decision criteria is one of the reasons why the LP paradigm may be a deficient method in the process of ration formulation (Rehman & Romero, 1984; 1987). Lara & Romero (1994) stress that in practice decision makers never formulate rations exclusively on the basis of a single objective, but rather on the basis of several different objectives, where economic issues are only one of many concerns. In common LP models for pig ration formulation, animal amino acid requirements are usually expressed in terms of minimal concentrations. Such models do not consider the total exceeded amount of protein or its quality as long as the minimal amounts of essential amino acids are satisfied (Bailleul et al., 2001). The same authors stress that 'economical optimal' diets are often too rich in protein, which directly burdens the environment and does not improve animal grovrth. This problem could partly be solved by adding additional upper or lower constraints. However, it might rapidly lead into over-constraint model that has no feasible solution. This problem is also related to the next LP drawback-rigidity of constraints (right hand side-RHS) (Rehman & Romero, 1984). This means that no constraint (e.g. given nutrition requirements) violation is allowed at all. However, relatively small deviations in RHS would not seriously affect animal welfare, but would result in a feasible solution (Lara & Romero, 1994). Numerous methodological developments in the field of MP have eased these problems of LP paradigm (Buysse et al, 2007). For instance in the field of animal nutrition, Rehman & Romero (1984) introduced goal programming (GP) and its improvement with a system of penalty function (PF), as well as multi-objective programming (MOP) as a way to incorporate more than one objective function; Lara & Romero (1994) applied interactive methodologies where the optimal ration is achieved through 'computer dialog'; Castrodeza et al. (2005) addressed a multicriteria fractional model. The purpose of this paper is to present a spreadsheet tool for organic pig ration formulation, designed as a three-phase optimization approach that merges two normative MP techniques. The first part of the paper provides a brief overview of weighted goal programming (WGP) and the penalty function. This is followed by a short description of the optimization tool that also involves LP in order to calculate least-cost ration formulation. Finally, the characteristics of the analysed case are presented, followed by the results and discussion. MATERIALS AND METHODS Weighted goal programming supported by a system of penalty functions Common to all MP problems is the concept of constraint optimization, which means that one tries to find the optimum of a single objective function within set of constraints. Based on the approaches reported in the literature and the primary aim of the tool presented in this paper, we decided to apply the WGP approach. This was in the context of ration formulation introduced by Rehman & Romero (1984). WGP formulation is expressed as a mathematical model with a single objective (achievement) function (the weighted sum of the deviations variables). The optimal compromise solution is found through the philosophy of 'distance measure' that measures the discrepancy between the desired goal and the performance level of a goal. To consider all goals simultaneously normalization techniques should be applied (Tamiz et al, 1998). Rehman & Romero (1984) introduced PF paradigm into the WGP to keep deviations within desired limits and to distinguish between different levels of deviations. This system is coupled with the achdevement fiinction (WGP) through penalty coefficients and with additional constraints defining deviation intervals. Such approach enables one to define allowable positive and negative deviation intervals separately for each goal. Depending on the goal's characteristics (nature and importance of 100% matching), these intervals might be different. Sensitivity is dependent on the number and size of defined intervals and the penalty scale utilized (si; fori=lton). Tool for three phase pig ration formulation Presented optimization tool for organic pig ration formulation was developed in MS Excel as an add-in application. This tool is capable of formulating least-cost, nutritionally balanced, and environmental acceptable rations for 'organically' growing pigs in different production periods. It also gives information about which feed-mix provides the optimal energy content. The tool is organized as a three phase approach that merges two sub-models based on MP techniques. The first sub-model is an example of a common least-cost ration formulation, based on the LP paradigm. The purpose of including this into the tool is to get an approximate estimate of expected ration cost. In this manner, the tool calculates the target economic goal, which is one of the goals in the second sub-model. The first sub-model is therefore, from the perspective of constraints, as simple as possible and is intended to exclusively measure the 'rough' cost estimation. Through cost function, this is linked to the second sub-model. The latter is based on WGP and is supported by a system of six sided PF. In this approach, the desired nutrition levels and ration costs are modelled as goals instead of as constraints. Besides in the second sub-model, additional constraints with indirect influence on the environment are added. Consequentially, the model is much more complex, and it finally yields a better solution. For more detailed mathematical description of the model one can refer to Žgajnar & Kavčič (2008), where the similar approach has been applied. Due to the importance of energy concentration of the feed-mix and its influence on the ration structure and cost, the tool also includes a third phase. In this phase, a macro loop is added that runs the first and the second sub-models for n-times, and consequently it yields n-formulated rations. The number of iterations in the third phase depends on the starting/ending energy content of the feed-mix and on the energy rise in each iteration step (e.g. 0,1 MJ kg"'). From the n-obtained solutions, the tool selects the cheapest option and marks it as the 'optimal' feed-mix structure for this given example. Analyzed example The tool has been applied for hypothetic organic pork production, with an average genotype for less intensive fattening. In this paper we present just the fattening period between 50 and 100 kg with an average daily gain of 700 g. We considered that the tool should formulate the complete ration/feed-mix in relation to the nutritional requirements. It is presumed that most of the fodder is produced at the farm under organic conditions and is evaluated with the full cost approach. The rest feed (less than 20%) that cannot be produced at the farm is accounted for at market price. However no synthetic substances (e.g. amino acids supplement) could be added, since they are baimed by law. The nutrition requirements (Metabolizable energy (35.2 MJ day"'). Crude protein (399 g day'), Amino acids (Lys-19.7 g day"'; Met+Cys-11.3 g day"'; Thr-13 g day"'; Trp-3.6 g day"') and Minerals (Ca-12.88 g day"'; P-11.59 g day'; Pavaiiabie-4.89 g day" '; Na-2.58 g day"')) are taken from Blair (2007). In order to prevent unrealistic solution that has too much of one feed in the diet, we considered recommendations for maximal feed inclusion (Blair, 2007) and (Futtermittelspecifische ..., 2006), namely through additional upper-bound constraints (Table 1). In the process of ration formulation the tool could choose between twelve different feeds (Table 1) that might be produced at the farm (except: alfalfa-dehydrated, yeast-brewer's dried, potato protein concentrate that might be purchased at market price), and four mineral components (limestone, salt, monocalcium phosphate and dicalcium phosphate) that could be purchased at market price. Table 1. Prices and nutritive values of available feed and their suggested maximal share of the ration._ Met+ Price* ME DM CP Lys Cys Ihr Tip Max** Feed on disposal (Cent kg-') MJ kg-' S :kg-' % Maize 18 14.1 880 85 2.5 3.5 3.0 0.8 0.6 Wheat 21 13.8 880 120 3.4 4.5 3.5 1.5 0.7 Barley 21 12.6 880 106 3.8 3.7 3.7 1.4 - Oats 26 11.2 880 108 4.3 4.1 3.7 1.4 0.25 Wheat flour 17 12.5 880 167 7.3 5.6 6.5 2.0 0.15 Wheat bran 14 8.3 880 141 6.2 5.0 5.5 2.5 0.25 Alfalfa, dehydrated 33 6.1 910 180 8.7 4.5 7.8 2.9 - Yeast, brewer's dried 71 13.2 900 452 32.1 11.7 21.8 5.1 0.05 Potato protein concentrate 132 15.7 930 780 56.9 20.1 45.3 10.6 0.15 Lupinseed meal 58 14.1 890 349 15.4 7.8 12.0 2.6 0.15 Faba beans 42 12.7 870 254 16.2 5.2 8.9 2.2 0.2 Pea - field 38 13.4 890 228 15.0 5.2 7.8 1.9 0.3 *Prices are estimated with model calculations - own source ' Suggested maximum inclusion of feedstujfs in pig diets Table 2. Importance of goals with corresponding penalty function intervals. Penalty function intervals Together Goal Unit (day"') Weight (Wi) Pi/ Pil' Pi2^ % Pi2" Pi"" Pi" % ME MJ 75 1 0 2 0 3 0 CP g 60 1 0 2 D 3 0 Lys g 80 5 1 5 3 10 4 Met + Cys g 60 5 1 5 3 10 4 Thi and Tip g 60 5 1 10 3 15 4 ^available g 40 3 1 5 3 8 4 Ca and Na g 30 3 1 5 3 8 4 Cost cent 5/90 10 20 oo 30 Pii^- Pii> p 12 penalty intervals at the first and the second stage The tool offers the option to switch between goals and constraints, depending on the needs and preferences of the decision maker. In the analyzed case, we chose ten goals (Table 2) that should be met as accurately as possible. The importance of each goal is defined by weights (w,) ranging between 0 and 100. Relatively high values are set for amino acids, since reduction of unbalanced protein fraction by increased protein quality (fulfilling the amino acids ratios in relation to the energy) reduces nitrogen excretion and pollution. For each goal, deviation intervals are defined separately (Table 2). They are measured in percentage deviation from the desired level. The cost goal is the only one that is not penalized for negative deviation and simultaneously the negative interval is unlimited. RESULTS AND DISCUSSION The main objective of the tool presented in this paper is to assist organic producers in formulating diets that are balanced and at the same time as cheap as possible. On a simple example we present how the tool could be applied and what might be the benefits. Namely, for organic producers this task is due to numerous limitations and constraints very complex. We have presumed that the decision maker prepares a feed-mix for growing pigs, looking from two different viewpoints (scenarios). In the first scenario, the most important element is quality of the ration (^cosi=-5), while in the second one, cost is more important (Wcosi=90). The results obtained are presented in Figs land 2. Fig. 1 illustrates the structure of the diet for the situation when economics is preferred to the quality (Scenario II). Fig. 2 illustrates the level of ration costs dependent on the energy concentration of the diet. The range of the energy content of the ration was set between 12.3 and 13.7 MJ of metabolizable energy (ME). 250 200 150 X E 100 t 50 ME (MJ/kg) - Maize (0.18€/kg) prim - Wlneat (0.21€/kg) prim - Oats (0.26€/kg) prim ■ Wheat bran (0.14€/kg) sec ■ Limestone (0.04€/kg) sec Lupinseed meal (0.58€/kg)sec Wheat flour (0.17€/kg) sec - Faba beans (0.42€/kg) sec ■ Pea - field (0.38€/kg) sec Fig. 1. Formulated feed-mix under scenario of high (W=90) ration cost importance (prim = primary axis; sec = secondary axis). One of the factors that defme how much a pig is going to eat is the energy content of the feed-mix. If the feed-mix is more concentrated, an animal is going to eat less, and vice versa (Blair, 2007). Fig. 1 presents formulated rations for the analysed fattening period. It is obvious that the energy content of the ration strongly influences selection of the feed. With increasing energy content, the quantity of maize increases and the quantity of oats decreases. From Fig. 1, it is apparent that in spite of expensive faba-beans, it enters into the solution, which is due to its favourable amino acids structure. The same holds for pea. Both are important substitutes for banned synthetic amino acid supplements. ~1-T" COrJ-LOCDN-COOiCOT-OJCO-^LOCOr^ ME (MJ/kg) Fig. 2. Daily ration costs dependent on the feed-mix energy content. The difference in daily ration costs between different energy concentrations is obvious. It ranges from 59.61 cents up to 70.43 / 69.42 cents per day per pig (scenario I/II). In any case, it should be an important issue to find the 'optimal' energy concentration of feed-mix in the daily management of organic pork production. In the Fig. 2 daily ration costs are presented for both scenarios. It is apparent that for analysed case importance of diet cost (Scenario II) has major influence only in the range of lower energy concentrations of feed-mixes (12.8 MJ kg"' backwards), while from 12.9 MJ kg"' onwards the trend of cost is the same. This is due to the fact that a feed-mix with lower energy content is harder to formulate especially more balanced one, which highly increases the costs. Consequently the minimal cost is achieved at relatively high energy concentration of feed-mix (Fig. 2), which is not usual in organic practise that is general less intensive. One could have legitimate scruples about the discrepancy between these results and practice, which is mainly due to poor quality of organically produced cereals in the sense of high nutritive value variability. CONCLUSIONS The results of this study show that the three phase optimization approach, supported by mathematical programming (LP and WGP with PF), can be efficiently applied to the diet formulation for organic pork production. The tool enables formulation of efficient diets, since it supports the farmer to find the optimal ration' energy content under various economic circumstances. With application of this tool problems like unbalanced protein composition, increased feed cost, increased burdening of the environment etc. might be mitigated. In this way the discrepancy between the aim of organic farming and practice could be reduced. REFERENCES Bailleul, P.J., Rivest, J., Dubeau, F. & Pomar, C. 200L Reducing nitrogen excretion in pigs by modifying the traditional least-cost formulation algorithm. Livest Prod Sei. 72, 199—211. Black, J.R. & Hlubik, J. 1980. Symposium: Computer programs for dairy cattle feeding and management-past, present, and future. JDS. 63, 1366—1378. Blair, R. 2007. Nutrition and Feeding of Organic pigs. CABI. Wallingford. 322 pp. Buysse, J., Huylenbroeck, G.V. & Lauwers, L. 2007. Normative, positive and econometric mathematical programming as tools for incorporation of multifunctionality in agricultural policy modelling. Agriculture, Ecosystems & Environment 120, 70—81. Castrodeza, C., Lara, P. & Pena, T. 2005. Multicriteria fractional model for feed formulation: economic, nutritional and environmental criteria. Agricultural Systems 86, 76-96. Futtermittelspecifische Restriktionen. Rinder, Schafe, Ziegen, Pferde, Kaninchen, Schweine, Geflügel. 2006. 40 pp. (in German). Lara, P. & Romero, C. 1994. Relaxation of Nutrient Requirements on Livestock Rations through Interactive Multigoal Programming. Agricultural Systems 45, 443-453. Rehman, T. & Romero, C. 1984. Multiple-criteria decision-making techniques and their role in livestock ration formulation. Agricultural Systems 15, 23—49. Rehman, T. & Romero, C. 1987. Goal Programming with penalty fimctions and livestock ration formulation. Agricultural Systems 23, 117-132. Tamiz, M., Jones, D. & Romero, C. 1998. Goal programming for decision making: An overview of the current state-of-the-art. EJOR. Ill, 569—581. Waugh, F.V. 1951. The minimum—cost dairy feed. Journal of Farm Economics 33,299-310. Žgajnar, J., & Kavčič, S. 2008. Spreadsheet tool for least-cost and nutrition balanced beef ration formulation. In Dovč, P., Petrič, N. (eds): Sustainable Farm Animal Breeding. 16"" International Symposium Animal Science Days. Biotechnical Faculty, Stranjan Slovenia, pp. 187-194. Linear and weighted goal programming in livestock production: an example of organic pig farming Jaka ŽGAJTNAR' and Stane KAVČIČ^ 'University of Ljubljana, Biotechnical Faculty, Department of Animal Science, Groblje 3, SI-1230 Domžale, Slovenia, e-mail: iaka.zgainar@bfro.uni-li.si ^The same address as' e-mail: stane.kavcic@,bfro.uni-li .si The paper presents an optimization approach that merges linear programming and weighted goal programming. It is applied in a spreadsheet tool for organic pig ration formulation. The formulation process is based on a three-stage procedure: hi the first step, common least-cost rations with different energy contents are formulated, hi the second stage, a sub-model based on weighted goal programming supported by a system of penalty functions formulate nutritionally balanced and economically acceptable rations that also fulfil conditions demanded by organic farming. In the third phase, the ration formulation procedure stops when the most efficient ration is selected. The results obtained for a hypothetical farm confirmed the applicability of the implemented approach. KejAVords: linear programming, weighted goal programming, ration costs, organic farming, pork production 1. INTRODUCTION Nowadays, livestock production demands precise management that leads to economically efficient and publicly acceptable production. This is possible through a very diverse range of measures. Due to the high share of ration cost within total production costs, ration formulation (optimization) is becoming a crucial task, especially in organic farming, which is globally characterized by higher production costs and affected by strict organic production policy constraints. However, pork production is also a livestock activity where unbalanced rations have significant negative impacts on the environment, especially if economics are taken as the most important criterion. Therefore, it is necessary to treat these kinds of problems as multiple criteria decision problems. Specifically, organic fattening that is confronted with the lack of availability of pure amino acids that results in a more unbalanced protein composition, increased feed cost, and, contrary to organic philosophy, an increased load of excessive nitrogen from manure on the environment [3]. hi order to help breeders to deal with these challenges, numerous tools based on mathematical programming (MP) paradigms have been developed. The first approach of this kind was conducted by [11], who applied the linear programming (LP) paradigm in order to formulate rations on a least-cost basis. This method was very popular in the past, especially after the rapid developments in personal computers. In the 1960s, it became a classical approach for the formulation of animal diets as well as feed mixes [2]. More recently, [5] stressed that the daily routine of ration formulation is one of the fields in which LP is most widely used. Common to all LP problems is the concept of constraint optimization, which means that one tries to find the optimum of a single objective fiinction. However, the exclusive reliance on just one objective (cost function) as the most important decision criteria is one of the reasons why the LP paradigm may be a deficient method in the process of ration formulation [8] and [9]. [7] stressed that, in practice, decision makers never formulate rations exclusively on the basis of a single objective, but rather on the basis of several different objectives, of which economic issues are only one of many concerns. In common LP models for pig ration formulation, animal amino acid requirements are usually expressed in terms of minimal concentrations. Such models do not consider the total exceeded amount of protein or its quality, as long as the minimal amounts of essential amino acids are satisfied [1], Furthermore, the same authors stressed that 'economically optimal' diets are often too rich in protein, which directly burdens the environment and does not improve animal growth. This problem could partly be solved by adding additional upper or lower constraints. However, this addition might rapidly lead into an over-constraint model that has no feasible solution. This problem is also related to the next LP drawback: the rigidity of constraints (right hand side (RHS)) [8]. This means that no constraint (e.g., the given nutrition requirements) violation is allowed at all. However, relatively small deviations in the RHS would not seriously affect animal welfare, but would result in a feasible solution [7]. Numerous methodological developments in the field of MP have eased these problems of the LP paradigm [4], For instance, in the field of animal nutrition, [8] introduced goal programming (GP) and its improvement with a system of penalty fianction (PF), as well as multi-objective programming (MOP) as ways to incorporate more than one objective function. Similarly, [7] applied interactive methodologies where the optimal ration is achieved through 'computer dialog', and [5] addressed a multi-criteria fractional model. The purpose of this paper is to present a spreadsheet tool for organic pig ration formulation, designed as a three-phase optimization approach that merges two normative MP techniques. The first part of the paper provides a brief overview of weighted goal programming (WGP) and the penalty function as the main method. This is followed by a short description of the optimization tool. Finally, the characteristics of the analysed case are presented, followed by the results and discussion. 2. MATERIALS AND METHODS 2.1. Weighted goal programming supported by a system of penalty functions Based on the approaches reported in the literature and taking into accovint the primary aim of the tool presented in this paper, we decided to apply the WGP approach. In the context of ration formulation, the approach was introduced by [8]. WGP formulation is expressed as a mathematical model with a single objective (achievement) function (the weighted sum of the deviations variables). The optimal compromise solution is found through the philosophy of 'distance measure' that measures the discrepancy between the desired goal and the performance level of a goal. To consider all goals simultaneously, normalization techniques should be applied [10]. [8] introduced the PF paradigm into the WGP to keep deviations within desired limits and to distinguish between different levels of deviations. This system is coupled with the achievement function (WGP) through penalty coefficients and with additional constraints defining deviation intervals. Such an approach enables one to define allowable positive and negative deviation intervals separately for each goal. Depending on the goal's characteristics (nature and importance of 100% matching), these intervals mi^t be different. Sensitivity is dependent on the number and size of defined intervals and the penalty scale utilized (s,-; for i = 1 to n). 2.2. Tool for three-phase ration formulation The presented optimization tool for organic pig ration formulation was developed in Microsoft Excel as an add-in application. This tool is capable of formulating least-cost, nutritionally balanced and environmentally acceptable rations for 'organically' growing pigs in different production periods. In addition, it provides information about which feed mix provides the optimal energy content. The tool is organized as a three-phase approach (Figure 1) that merges two sub-models based on MP techniques. The first sub-model is an example of a common least-cost ration formulation, based on the LP paradigm. The purpose of including this sub-model into the tool is to obtain an approximate estimate of expected ration cost. In this manner, the tool calculates the target economic goal, which is one of the goals in the second sub-model. Therefore, the first sub-model is, from the perspective of constraints, as simple as possible and is intended to exclusively measure the 'rough' cost estimation. Through cost function, it is linked to the second sub-model. The latter is based on WGP and is supported by a system of a six-sided PF. In this approach, the desired nutrition levels and ration costs are modelled as goals instead of constraints. Moreover, in the second sub-model, additional constraints are added that have an indirect influence on the environment. Consequentially, the model is much more complex and ultimately yields a better solution. Figure 1: The scheme of the tool for three-phase organic pig ration formulation Due to the importance of the feed mix's energy concentration and its influence on the ration structure and cost, the tool also includes a third phase (Figure 1). In this phase, a macro loop is added that runs the first and the second sub-models for n-times, and consequently it yields n-formulated rations. The number of iterations in the third phase depends on the starting/ending energy content of the feed mix and on the energy rise in each iteration step (e.g., 0.1 MJ/kg). From the n-obtained solutions, the tool selects the cheapest option and marks it as the 'optimal' feed mix structure for this given example. 2.3. Mathematical formulation of the first and the second sub-model The first sub-model (LP) is formulated as shown in equation (1), equation (4a) and equation (7). It mostly relies on the economic (ration cost) function, C, and satisfies only the most important nutrition requirements coefficients, bi, also known as RHS. In the first optimization phase, the desired element is the ration at the lowest possible cost (C). rmnC=Y^Cj*Xj SUch that (1) y=i k ■ J- , j+ k + = + suchthat (2) M Si g i forall/= Itorandgi^^O (3) J=i n Y/a^i - for all z=l to m (4a) y=i ^(ay J < 0 for all i=\ to m and i-^k (4b) dl n O n PI on o ri PI —y-o-• -------- A A J. 1 4 co-^iocor-coo>coT-csico CNiosicNcviiNoicvi'^cococo rj-CO lo 122,4 122,4 0,5% 0,5% 5% 5% 100 ME/MP (g) >1.471,3 1.471,3 0,5% 0,5% 5% 5% 100 SS/DM (kg) <18,5 18,5 5% 0% 10% 0% 33 SV/CFmin (kg) >3,3 SV/CFmax (kg) <4,8 Ca (g) >104,1 104,1 2% 5% 20% 20% 5 P (g) >67,7 67,7 2% 5% 20% 20% 5 Ca:P (%) (1,5-2):1 K:Na (%) (5,5-10): 1 Strošek /Cost (cent) CI oo 10% oo 20% 5/95 Min Seno/hay (kg/day) 3 Max Seno/hay Max Travna silaža/ (kg/day) 5 Grass silage Max Koruzna silaža/ (kg/day) 30 Maize silage Max Sol/ (kg/day) 30 Salt Max Bovisal zimski/ (g/day) 30 winter Max Bovisal letni/ (g/day) 240 summer (g/day) 200 Osnovni nabor omejitev je podoben pri obeh pod-modelih. Prehranske omejitve se razlikujejo le v matematičnem 'predznaku' (<, >, ==) saj so pri tehtanem ciljnem programu zahteve po hranilnih snoveh transformirane v cilje (=). V primera LP modela so upoštevane le najpomembnejše omejitve tipa maksimum (<) ali minimum (>), ki si niso nasprotujoče. To se seveda odrazi tudi v izračunanem obroku, ki ni vedno primeren za prakso. Vseeno pa smo v orodje vgradili to poenostavitev, saj LP model služi le grobi oceni najnižjih možnih stroškov dnevnega obroka. Nesporno je dobljen neizravnan obrok cenejši, takšna poenostavitev pa po eni strani omogoča potrebno rešitev in po dragi strani 'spodbuja' tehtani ciljni program z vgrajeno kazensko fiinkcijo k iskanju rešitve, ki po ceni čim manj odstopa od dosegljive v praksi. Pri vsakodnevnem sestavljanju obrokov za živali moramo upoštevati tudi razpoložljive količine krme, ki jih lahko vključimo v dnevni obrok. V analiziranem primera smo predvideli, da naj obrok vsebuje najmanj 3 kg mrve, ne sme pa preseči 5 kg le-te. Oba pod-modela tudi ne smeta preseči maksimalne količine korazne in travne silaže, v analizi postavljene na 30 kg. Ker z orodjem lahko sestavljamo tako poletne kot zimske obroke, so predvidene različne količine radninsko-vitaminskih mešanic (skladno z navodili proizvajalca). Prvotna verzija WGP vsebuje šest ciljev, podprtih s kazenskimi funkcijami (pregl. 1). ielativen pomen posameznega cilja je določen z utežjo (w), katere vrednost se lahko giba med O in 100. Kot najpomembnejša cilja smo v našem primeru predvideli zadostitev potreb po energiji (NEL) in beljakovinah (presnovljive beljakovine), obema smo pripisali utež 100 in določili zelo interval odstopanja (0,5 % v prvi in 5 % v drugi stopnji). Veliko nižjo težo smo pripisali zauživanju suhe snovi, s katero ocenjujemo konzumacijsko sposobnost živali. Pri njem smo interval odstopanja določili le za negativno odstopanje od cilja, medtem ko zaradi praktičnih razlogov (konzumacijske sposobnosti) presežkov nismo dovolili. Poleg omenjenih smo uvedli dodatno omejitev, ki postavlja zgornjo mejo zauživanja suhe snovi iz voluminozne krme na 14 kg. Ker je s prehranskega vidika pomembneje zagotoviti ustrezno razmerje med Ca in P ter med K in Na kot doseči določene količine posameznih med njimi, smo za rudnine (Ca in P) predpostavili razmeroma nizke teže. Ostale rudnine so v izračun vključene preko več varnostnih zank, H preprečujejo pomanjkanje ali pa njihove toksične koncentracije. Z razvitim orodjem smo testirali, kako se spremeni 'optimalen' dnevni obrok, če cilju za minimiranje stroškov damo različen pomen (pripišemo različno težo). Analizo prikazujeta dva scenarija. Pri prvem (WGP I) je strošek obroka manj pomemben (relativna teža je samo 5), medtem ko je pri drugem (WGP II) njegov pomen povečan (w=95). V obeh scenarijih ostajajo intervali odstopanja enaki (+10 in + 20 %). Razpoložljive sestavine obroka in njihove hranilne vrednosti so prikazane v pregl. 2. Seveda lahko v praksi hranilne vrednosti močno odstopajo od predpostavljenih, kar je predvsem pri voluminozni krmi odvisno zlasti od tehnologije, intenzivnosti pridelave kot tudi od drugi zunanjih dejavnikov (npr. količina padavin). Zato je pred sestavljanjem obrokov seveda vedno smiselno upoštevati hranilno vrednost dejansko razpoložljive kraie, bodisi na podlagi kemijske analize ali vsaj organoleptične ocene. Pregl. 2: Hranilna vrednost razpoložljive (predpostavljene) krme Table 2: Nutritive value of feed on disposal SS/ PB/ SV/ Cena ali LC/ DM NEL MP** CF Ca P Mg Na K Price or TC* (MJ/kg SS)/ (g/kgSS)/ (g/kg) (MJ/kg DM) (g/kg DM) (cent/kg) Razpoložljiva krma Feed on disposal Seno/Hay 860 5,90 85,00 270 5,70 3,50 2,00 0,35 18,25 15,30 Koruzna silaža/ Maize silage 320 6,50 45,00 200 7,06 6,00 1,91 0,12 10,76 3,70 Travna silaža/ Grass silage 350 5,60 62,00 260 6,00 3,51 2,20 0,35 21,30 6,14 Trava - paša/ Grass - pasture 160 7,10 121,00 205 6,00 2,60 2,00 0,10 10,50 1,50 Koruza/ Maize 880 8,50 83,00 0,23 4,09 1,25 0,23 3,75 30,00 Pšenica/ Wheat 880 8,60 88,00 0,57 3,86 1,59 0,45 5,00 32,00 Repičine pogače/ Rapeseed cake 900 7,50 125,00 2,89 7,00 2,78 2,22 10,00 37,00 Sojine tropine/ Soya meal 880 8,20 215,00 3,41 7,84 2,61 1,14 20,00 46,00 K-18*** 880 7,61 136,74 10,23 5,68 2,84 3,98 10,23 27,67 K-19*** 880 7,61 146,51 10,23 5,68 2,84 5,11 10,23 30,00 Mineralne in vitaminske komponente Mineral and vitamin components Apnenec/ Limestone 950 400,00 16,40 MVMI**** 930 160,00 100,00 36,00 120,00 67,56 MVM2**** 930 210,00 70,00 135,00 58,08 Sol/Salt 950 400,00 50,00 * Izračun na podlagi lastne cene / Total cost approach ** Upoštevana je najnižja vrednost presnovljivih beljakovin / The lowest value of metabolisable protein is considered *** Komercialna imena krme za krave molznice z različnimi vsebnostmi (%) presnovljivih beljakovin / Commercial names of dairy cows' feed containing different % of metabolisable proteins **** Komercialni imeni za mineralno-vitaminske mešanice so 'Bovisal letni' in 'Bovisal zimski' /Commercial name of mineral-vitamin mixtures are Bovisal summer and Bovisal winter V simulaciji smo predvideli, da vso voluminozno krmo (mrvo, koruzno in travno silažo, pašo) pridelamo na kmetiji. Ker ta krma praviloma ni predmet trgovanja, smo stroške njihove pridelave povzeli po modelnih kalkulacijah Kmetijskega inštituta Slovenije (KIS, 2009). Vso ostalo krmo in rudninsko-vitaminske mešanice smo obračunali po tržnih cenah (pregl. 2). Logično vprašanje, ki se poraja, je, kaj naj pridelujemo sami in kaj naj kupimo, da bi izboljšali ekonomski rezultat kmetovanja, vendar pa ta vidik ni predmet obravnave v tem prispevku. 3. REZULTATI IN RAZPRAVA Orodje smo testirali na primeru, ki ga v vsakodnevni praksi pogosto srečamo (telesna masa krav 650 kg, dnevna mlečnost 25 kg, 90. dan brejosti). Opravili smo 4 simulacije, dve za zimsko in dve za poletno obdobje - pri slednjem smo v nabor razpoložljive krme vključili tudi pašo. Sestava dnevnih obrokov je prikazana v pregl. 3, vključno z rezultati LP modela. Ti služijo le za oceno najnižjih možnih stroškov, zaradi že opisanih poenostavitev pa sestave teh obrokov niso vedno primerne za prakso. Pregl. 3: Izračunani dnevni obroki s pomočjo LP (prvi pod-model) in WGP (drugi pod-nodel) (pri slednjem za dve različici pomena stroškov - scenarija) Table 3: Obtained daily rations formulated with LP (first sub-model) and WGP (second sub-model) (for the last one with two different cost importance - scenarios) Dnevni obrok / Daily ration Zimski / Winter Poletni / Summer LP WGP I WGP II LP WGP I WGP II ICrma vključena v obrok (kg/dan) Feed used (kg/day) Seno / Hay 5,00 5,00 5,00 4,56 3,00 5,00 Koruzna silaža / Maize silage 25,16 10,33 15,18 17,22 Travna silaža / Grass silage 6,14 23,84 16,57 5,80 0,16 Paša / Pasture 69,23 34,58 32,08 Pšenica / Wheat 1,98 5,00 2,19 Koruza / Maize 1,18 1,50 1,50 1,95 1,50 1,50 Sojine tropine / Soya meal 2,30 K-18 3,56 3,08 K-19 0,17 1,56 Uporabljeni mineralni dodatki (g/dan) Mineral components used (g/day) Apnenec / Limestone 24,2 13,0 30,4 37,0 Bovisal Letni / Summer 104,6 56,8 50,2 Bovisal Zimski / Winter 61,1 34,8 Sol / Salt 30,0 30,0 28,1 30,0 30,0 Strošek (€/dan) / Cost (€/day) 3,87 4,34 3,87 2,66 2,93 2,91 Stroškovno odstopanje/ Cost deviation (%) 0,0 12,2 0,0 0,0 10,2 9,3 Odstopanje od normativov/ Requirements deviations (%) NEL 0,0 -1,7 -2,2 0,0 -0,5 -0,5 PB/MP 0,0 0,0 0,0 39,0 0,0 0,0 Skupno odstopanje/ Total deviation* 56,3 10,1 37,0 69,6 27,2 30,7 Fizikalne značilnosti obroka/ Physical ration attribute SV / CF (%) 18 18 18 19 19 19 SS (kg/dan) / DM (kg/day) 18,5 18,5 18,5 17,8 18,0 17,9 *Skupna vsota odstopanj (vključno z odstopanji od normativov za minerale, ki niso predstavljeni v preglednici) / Total sum of deviations (including mineral deviations not presented in the table) Med sestavo krmnih obrokov v poletnem in zimskem obdobju je po pričakovanju velika razlika, se pa ta pojavi tudi znotraj posameznega obdobja med obema scenarijema (pregl. 3). Prva je predvsem posledica razpoložljive paše v poletnem obdobju, ki je z vidika zagotavljanja hranilnih snovi najcenejša krma, druga bistvena razlika pa nastopi predvsem zaradi različne ekonomske teže (stroški obroka) vgrajene kazenske funkcije. Pri zimskih obrokih (WGP I in WGP II) so potrebe po beljakovinah pokrite predvsem s travno silažo in kupljeno krmno mešanico K-19 (WGP I) oziroma K-18 (WGP II). Očitno je, da cene krme igrajo odločilno vlogo pri sestavi obroka, saj večji poudarek na stroškovni strani prehrane (WGP II) pomembno zniža količino (drage) travne silaže v obroku. Še bolj je to očitno pri poletnih obrokih, pri katerih je glavni vir beljakovin paša, travna silaža pa je posebej pri obroku z večjim poudarkom na cenenosti (WGP II) praktično v celoti izpodrinjena. Vgrajena kazenska funkcija nam omogoča nadzor nad odstopanjem od postavljenih ciljnih vrednosti. Bolj rigorozno postavljene kazni (v našem primeru višji relativni pomen stroškov; w = 95) v drugem scenariju imajo v obeh sezonah opazen učinek tudi z vidika kakovosti obroka. Čeprav so WGP obroki bolje izravnam, ti cenovno vedno ne odstopajo od LP rešitve (WGP II v zimski sezoni). Na splošno pa lahko pričakujemo dražje obroke pri uporabi WGP (tudi pri močnejšem vplivu kazenske funkcije - scenarij WGP II) kot pri LP in najbrž se nam zdi, da so LP obroki povsem v redu, saj pokrijejo tako potrebe po energiji kot po beljakovinah (so pa slednje pri poletnem obroku v velikem presežku). Ob upoštevanju ostalih odstopanj kot merilom prehranske kakovosti obroka (merjenih s skupno vsoto odstopanj) opazimo očitno razliko, saj smo pri LP zanemarili nekatere prehranske cilje. Še bolj očitno je to pri scenariju WGP I, ko stroški obroka ne igrajo tolikšne vloge (w = 5). Stroški obroka so v naši simulaciji višji za 1 do 12 % (v primeijavi z WGP II), skupno odstopanje pa je nižje za 3 do 27 %. Torej lahko govorimo o iskanju kompromisa med kakovostjo in ekonomičnostjo obroka. Ob tem pa se moramo zavedati, da neizravnani obroki - četudi so posamezne potrebe pokrite - ne bodo dali pričakovane (teoretično izračunane) prireje. To postane toliko bolj problematično, kolikor večje zahteve oz. pričakovanja imamo do svojih živali (npr. dnevna mlečnost nad 30 kg). 4. ZAKLJUČKI Namen tega prispevka je prikaz enostavnega orodja v obliki elektronske preglednice, ki lahko nudi podporo vsakodnevnim odločitvam na kmetijskem gospodarstvu, v prikazanem primeru pri sestavljanju dnevnih obrokov za krave molznice. Uporabljen pristop, ki temelji na kombinaciji linearnega in tehtanega ciljnega programiranja, podprtega s kazenskimi funkcijami, se je izkazal za uporabnega tudi v aplikaciji za končnega uporabnika. Orodje omogoča posamezniku, da oblikuje ekonomsko učinkovit obrok, ki ne odstopa bistveno od najcenejšega možnega, hkrati pa zmanjšuje tveganje, da ta ne bo izravnan, kar je velika pomanjkljivost praktične uporabe LP pristopa. Z zgrajenim orodjem lahko obroke dodatno izboljšamo z nastavljanjem parametrov vgrajene kazenske funkcije za posamezne elemente krmnega obroka. V analiziranem primeru seje to posebej izkazalo pri poletnem obroku, pri katerem je LP rešitev vsebovala kar 39 % presežek beljakovin, kar lahko pomembno poslabša zdravstveni z njim pa tudi proizvodni status živali. Čeprav so rešitve tehtanega ciljnega programa praviloma nekoliko dražje kot tiste dobljene s pomočjo klasičnega LP, pa lahko stroškovno učinkovitost sestavljenih obrokov izboljšamo na več načinov. Presežki v obrokih, dobljeni z LP, prav gotovo niso zastonj in imajo vpliv na prirejo (dnevno mlečnost), po drugi strani vplivajo tudi na dobrobit živali (njihovo dodatno obremenitev), zaradi dodatnega izločanja odvečnih hranil in povečanja izločanja toplogrednih vplivov pa imajo tudi negativen učinek na okolje (Brink s sod., 2001). Gre pa za področja, ki še niso dovolj raziskana in je te učinke težko kvantitativno ovrednotiti. Vse to kliče po nadaljnjem delu na tem področju, ki lahko pripelje do novega pogleda na družbeno najbolj sprejemljiv sistem prireje mleka, saj danes praviloma konkurenčnost v prireji mleka določajo le zasebni ekonomski učinki, družbeni pa so v pretežni meri še vedno zanemarjeni. 5. ZAHVALA ^vtorja se zahvaljujeva predavateljici Ajdi Kermauner Kavčič in profesorju Andreju Lavrenčič za njuno pomoč pri komentiranju izračunanih obrokov. 6. LITERATURA Brink C., l&oeze C. in Klimont Z. 2001. 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