481  Advances in Production Engineering & Management ISSN 1854 ‐6250 Volu me 15 | Number 4 | Decem ber 2020 | pp 4 81–492 Journal ho me: a p em‐journal.or g https://doi.org /10.14743/apem2020.4.380 Original s cientif i c paper     Due date optimization in multi‐objective scheduling of  flexible job shop production  Ojstersek, R. a,* , Tang, M. b , Buchmeister, B. a  a University of Maribor, Faculty of Mechanical Engineering, Maribor, Slovenia  b Beijing Jiaotong University, International Center for Informatics Research, Beijing, P.R. China      A B S T R A C T   A R T I C L E   I N F O The manuscript p resents the i mportance of i ntegrating m at hemati cal meth‐ ods for the d eterminatio n o f due date o ptim ization parameter fo r maturity optimizati on i n evoluti o nary c omputatio n ( EC) methods i n multi‐ objectiv e f l e x i b l e j o b s h o p s c h e d u l i n g p r o b l e m ( F J S S P ) . T h e u s e o f m a t h e m atical m ode l ‐ l i n g m e t h o d s o f d u e d a t e o p t i m i z a t i o n w i t h s l a c k ( S L K ) f o r l o w and total wor k content (TWK) for medium a nd h ig h dimensional problems w as p res ente d with the i nteg ration i n t o the m ulti‐ o bjectiv e h euristic K al man algorithm ( M O H K A ) . T h e m u l t i ‐ o b j e c t i v e o p t i m i z a t i o n r e s u l t s o f m a k e s p a n , machine utilizati o n and due date s cheduling wi th the M OHKA a lgorithm w e re c om‐ pared with two comparative multi‐ objective algorith ms. Th e high c apability a n d d o m i n a n c e o f t h e E C m e t h o d r e s u l t s i n s c h e d u l i n g j o b s f o r F JSSP p ro duc‐ tion w a s d e m on s t r a te d b y c om p a r ing the op t i m iz a t ion r e s u lt s w it h the results of s cheduling according to c on ventio nal priori ty r ules . The obt ained results o f r a n d o m l y g e n e r a t e d d a t a s e t s p r o v e d t h e h i g h l e v e l o f j o b s c h e d u ling i m‐ portance w ith respect to the i nterdependence o f the o ptimizat io n parameters. The ability to a pply the p resented m ethod to t he r eal‐world env iro n ment w as demonstrated b y using a real‐wor ld m anufacturing s ystem d a taset a p p l i e d i n Simio simulat i o n a nd s cheduling software. The optimizati on r esu lts prove the i m p o r t a n c e o f t h e d u e d a t e o p t i m i z a t i o n p a r a m e t e r i n h i g h l y d y n amic F JSSP w h e n it c om e s to a c h ie ving low nu m b e r s of ta rd y j ob s , s h or t j ob t ardiness and potentially low e r tardy jobs cost s in relation to s h ort makes p a n of orders with h i g h l y u t i l i z e d p r o d u c t i o n c a p a c i t i e s . T h e m a i n f i n d i n g s p r o v e that mult i‐ o b j e c t i v e o p t i m i z a t i o n o f F J S S P p l a n n i n g a n d s c h e d u l i n g , t a k i n g i nto account the o ptimizatio n parameter due date, is the k ey t o achieving a financially and timely sustaina b le production sy stem that is competiti ve in th e global market. © 2020 CPE, Uni versity of M a r ib or. All rights re s erve d.   Keywords: Flexib le job sho p scheduling prob‐ lem (F JSSP); Due date; Makespan; Capacities utilization; Multi‐object ive op timizati on; Evolutionary c omputation; Multi‐object ive heuris tic Kalman algorithm ; Simio simulat i o n and scheduling so ftware *Corresponding author: robert.ojstersek@um.si (Ojstersek, R.) Article history: Received 15 Ma y 2020 Revised 23 October 2020 Accepted 25 November 2020       1. Introduction   The product i on plannin g a nd s ched uling of f lexib l e job shop p ro duction (FJSSP) is e xtremely i m p o r t a n t i f a c o m p a n y w a n t s t o ensure g lobal competitiveness an d s u s t a i n a b l e b u s i n e s s [ 1 ] . Optimization p arameter s that d efine short mak e span o f orders a n d enable h igh utilization of production c a pacities a re m eanin g les s if the expected o rder d ue d a t e s a r e n o t g u a r a n t e e d . A d e ‐ q u a t e p l a n n i n g a n d s c h e d u l i n g o f d u e d a t e s , w h i c h a r e u s u a l l y v ery tight, e xpresses the need f or a det a iled d iscussion of t he s chedulin g orders i mportance fro m th e point of d u e d at es. Th e re‐ s e a r c h q u e s t i o n p r e s e n t e d i n t h e r e s e a r c h w o r k r e f e r s t o t h e i m portanc e o f math em ati c al m od‐ elling o f the due dates op timizati on objective in t h e m ulti‐obj ective F JSSP o ptimizati on problem. Ojstersek, Tang, Buchmeister    482  Advances in Production Engineering & Management 15(4) 2020 The importance o f sched u ling F JS S P f r o m t h e p o i n t o f t h e d u e d a tes has a significant impact on other opti mi zation par ameters t hat FJSSP deals with. A c c o r d i n g t o t h e l i t e r a t u r e , t h e p r o b l e m o f s c h e d u l i n g o r d e r s i n job shop p r o duction h a s long b e e n k n o w n , d e f i n e d a n d d i s c u s s e d i n d e t a i l . T h e i n i t i a l l y u s e d s c h e d u l i n g p r i o r i t y r u l e s [ 2 ] o n l y allowed the theoretical solution of s ingle‐obj e ctive optimizatio n p r o b l e m s , w h i c h t h e d e v e l o p e r s transferred to d yn amic j ob s hop pro d uction en vi ronments b y mean s o f s i m ulatio n modelling approaches [ 3]. Th e set o f m athematical methods for modelling due da t e pa ra me te r is e x t e n siv e [ 4 ] . T h e i r s u i t a b i l i t y f o r i n d i v i d u a l u s e i s d e m o n s t r a t e d b y t h e specificity of the o ptimizati o n problem and its complexity [ 5]. The c o mplexity o f scheduling i s r eflected i n sever a l supporting parameters that influence the correc t a ssessment of t he d ue d at e pa ra mete r f rom the a ve r ag e j o b t a r d i n e s s , t h e n u m b e r o f t a r dy j obs and the total tardy job s costs leading to t ime and finan‐ c i a l l o s s e s o f t h e c o m p a n y [ 6 ] . G i v e n t h e c o m p l e x i t y p r e s e n t e d , w h i c h i s d e f i n e d i n F J S S P a s N P ‐ hard, the use of e volutio n ary comput ation meth ods (EC) i s one o f the e f fective ways o f achievin g optimal opti mizati on r e sults [7, 8]. The opti mizat i on probl e m of s c h e d u l i n g d u e d a t e s i n f l e x i b l e m a n u f a c t u r e d s y s t e m s [ 9 ] h a s e n c o u n t e r e d m a n y l i m i t a t i o n s i n t h e res e arc h d ue to conflicting optimiz a tion g oals a nd th e u se o f diff ere n t ma thema tica l mode ll ing methods [10]. The r e search‐ e r s h a v e l i m i t e d i t t o o p t i m i z a t i o n p a r a m e t e r s t h a t d e f i n e t h e due date o f jobs [ 11], assuming independenc e f rom oth e r optimizati on paramet e rs [ 12], which sig nificantly i nfluenc e p roduc‐ tion flexibilit y [13]. Th e dynamic chan ge i n FJSSP p roduction d ue t o dynamic customer d emand and high‐mi x l ow‐volume producti on [14, 15] c i t es P areto‐b a sed optimi zation appr oaches a s s u i t a b l e o p t i m i z a t i o n a p p r o a c h e s [ 1 6 ] . T h e u s e o f f u z z y a p p r o a c hes [17], which satisfactoril y solve th e opt i mizati on pr oblem of F JSSP production, u sually t re ats the pr obl e m only on a single‐ level of p rimary o ptimization criteria and limits the m ulti‐lev el s tructure o f the FJSSP p roblem [18]. H e uristic meth ods [1 9, 2 0], w h ich allow a detailed d e v alu ati on of the o ptimization ap‐ proach a nd t he s atisfacto r y optimizati on meth od, are usually l im i t e d b y t h e t r a n s f e r o f t h e o p t i ‐ mization res u lts to a r eal‐world o r s i mulation e nvironment [21, 2 2 ] . T h e n e e d f o r a n e f f i c i e n t o p t i m i z a t i o n m e t h o d t h a t a l l o w s t h e p l a n n i n g a n d s c h e d u l i n g o f the FJSSP p roblem w ith the op ‐ timizati on p a rameter of d ue d ates i s the key to a chieving a c om prehensive o pti m ization ap‐ proach [ 23]. H owever, the research r esults m ust allow for the d evaluation o f both t est and real‐ istic datasets f or a pprop riate integration of th e p roposed met h ods into t he r eal‐world produc‐ tion environ m ent [24]. I n t h e p r e s e n t e d r e s e a r c h w o r k , w e w a n t t o p r e s e n t t h e i m p o r t a n ce of int egrati ng m a t h em at‐ i c a l m e t h o d s f o r d e t e r m i n i n g d u e d a t e s i n t o t h e e x i s t i n g E C m e t h o d . T h e r e s e a r c h w o r k t r i e s t o o v e r c o m e t h e e x i s t i n g l i m i t a t i o n s o f t h e F J S S P r e s e a r c h p r o b l e m , w h i c h d o e s n o t d e a l w i t h t h e optimiz a tion p aramet er o f planni n g a nd s cheduling orders w ith th e d u e d a t e p a r a m e t e r . T h e math ematical m odellin g w ith know n total w o rk c ontent (TW K ) and slack (SLK) methods and t h e i r i n t e g r a t i o n i n t o t h e p r o p o s e d E C a l g o r i t h m M O H K A a l l o w s t o evaluate t he i mpor tance of the FJSSP m ulti‐objective o ptimizati on with p arameters that e ns ure short makespan, high u tili‐ zation o f pro d uction cap a cities and th e achi e ve me nt o f tight du e dates. 2. Problem description   In t h e o pti m izati on pr oblem of p lannin g a nd s cheduling o f t he f lexibl e job shop p roduction (FJSSP), the t hree most fr e quent opti mizati on p a r a meters ar e sh own in Eq. 1, Eq. 2 and Eq. 3:  Mak e span = | 1 ,…, , (1)  Total workload of all mac h ine , 1 ,2 ,…, (2) and  Due date optimization in multi‐objective scheduling of flexible job shop production   Advances in Production Engineering & Management 15(4) 2020  483  The workload of the most loaded mac h ine , 1 ,2 ,…, (3) Fig. 1 Jobs arrival sequence with different due d ates Where th e C j is c ompletion time o f j o b j , n r epresents number o f jobs a nd m t h e n u m b e r o f machin es. These three o p timizati on param e ters r elate to t he t im e of j ob s completion and th e a c h i e v e m e n t o f t h e h i g h e s t p o s s i b l e u t i l i z a t i o n o f t h e m a c h i n e s . I n t h e h i g h l y d y n a m i c j o b s h o p production, a v er y imp o rtant p a ram e t er i s the du e date o f j o b s d j , which in m ost c a ses are very t i g h t . F i g . 1 s h o w s t h e j o b a r r i v a l s e q u e n c e o f f i v e j o b s , w h e r e e a c h j o b m u s t b e e x e c u t e d w i t h a d i f f e r e n t d u e d a t e i n t h e p r o d u c t i o n s y s t e m d e f i n e d a s F J S S P . T he o pti m iz ation o f t he j obs pro‐ cess sequence m ust be c arried o ut w ith regard to the multi‐obje ctive nature o f FJSSP, whereby three p a rameters must be mi n imized (MC, MW, d j ) and o n e p a rameter must b e maximi ze d (TW). In this case, each j ob j h a s a c e r t a i n n u m b e r o f o p e r a t i o n s O i , which must b e performed on the avail a ble ma chine m f ro m the gi ven set of m achi nes capabl e of p erformin g an i ndividu a l o p e r a ‐ tion. T he p r o cess time o f the op erati on p jk v aries in r elation t o the a ssign ed m achin e c apable o f performi ng t he individual operatio n O i . The opti miz a tion algorit h m must a rra n ge the job proce ss s e q u e n c e i n s u c h a w a y t h a t i t h a n d l e s a l l f o u r o p t i m i z a t i o n p a rameters a ccordingly. E xample: If the conv enti onal priority r ule Earli est Due Dat e ( EDD) w as u sed , the job process sequenc e would be J 2 , J 5 , J 1 , J 4 a n d J 3 . T h i s j o b p r o c e s s e x e c u t i o n s e q u e n c e d e a l s o n l y w i t h o n e o p t i m izati o n parameter d j , which is defined as follo ws: T h e due date of job j r epresents t h e esti mat e d dispatch date of job j ( dispatch d ate promised to the customer). Completion of j o b j a f t e r t h e d u e d a t e ( p r o m i s e d t o t h e c u s t o m e r ) i s a l l o w e d , b u t r e p r e s e n t s a n a d d i t i onal fi nancial p e nalty for th e compan y. W hen considering the opt i mizati on paramet e r d j , important related goals must b e specified. Th e priority ob jective is t o r e duce th e m axi m um late ness, which i s defined as i n Eq. 4: ,…, , (4) where th e lateness o f a n i n dividual jo b j defi n ed b y the Eq. 5 – (5) depends on t he co m pletio n time o f th e job j and the assumed delive ry ti m e of the jo b d j .  The ti med L max c a n b e m o r e e a s i l y d e f i n e d w i t h t h e p a r a m e t e r n u m b e r o f t a r d y jobs. This o p‐ timizati on p a rameter only d efine s w h e t h e r t h e i n d i v i d u a l j o b j m issed the estimated delivery time or not. Tardiness of job j is de fin e d as pres e n t ed by Eq. 6: – ,0 , (6) and the corr esponding target f un ction de f i ne d b y Eq . 7 . (7) D u e t o t h e s h o r t c o m i n g s o f t h e a b o v e o p t i m i z a t i o n f u n c t i o n , w h i ch r efers to s om e v e ry t ardy j o b s , i t i s u s e f u l t o d e t e r m i n e t h e i m p o r t a n c e w e i g h t s o f j o b s j b y w j . T h e h i g h e r t h e w e i g h t , t h e more i mport a nt th e jo b is . Ojstersek, Tang, Buchmeister    484  Advances in Production Engineering & Management 15(4) 2020 T h e a s s u m p t i o n i n t h e p r e s e n t r e s e a r c h w o r k r e f e r s t o : t h e g i v e n wei g ht w j refers o nly to the importanc e o f an i ndivid ual job j , wh ich can be w eighted directly b y t h e p l a n n i n g t e a m o f t h e manufacturing system. However, t h e i mportance of t he m u l ti‐obje ctive decision making b e‐ tween t he f our optimi zation p a rameters (MC, TW , MW a n d d j ) d o e s n o t d e t e r m i n e t h e i m ‐ portance o f the correlation b etween t hem, s ince t his is p erform ed w ith th e evoluti o n a ry c ompu‐ tation method M OHKA, which present s s olutions o f the optimi zati on problem with Pareto opti‐ mal solutions. 3. Due date modelling  T o m o d e l d u e d a t e s o f j o b s , a r a n d o m d a t a s e t i s g e n e r a t e d ( a c c o r d i n g t o t h e F J S S P c h a r a c t e r i s ‐ tics) and divided into thr e e gr o ups wit h regard to t heir compl e xity dimensions:  Low dimensional opti miz a tion pro b lem, in the present manusc ript t h e d a t a s e t J 5 , M 11 , O 66 has been c onfigur e d to e valuate MOH K A capabilities i n relation t o t h e o p t i m i z a t i o n r e s u l t s of co n ventio nal priority rules.  Middle dimensional opti mizati on pro b lems a re r epresented b y two d a t a s e t s , a t h e o r e t i c a l dataset J 10 , M 11 , O 12 2 a n d a r e a l ‐ w o r l d d a t a s e t J 15 , M 10 , O 84 , whi c h was used i n the FJSSP c ase study section.  High d ime n s i onal optimi zation p robl ems are repr esented by d atas ets J 15 , M 11 , O 17 6 a n d J 20 , M 11 , O 24 0 , res p ectively. Due date o p t imizati on p a rameter modelling is performed with T WK ( Total WorK c ontent) method by t h e E q . 8. ,, ∈ (8) The ti ghtn ess coefficie n t of t he o rder d ue d ate K x ( allowance factor) determines the tightness o f t h e d e l i v e r y t i m e s . I n t h e c u r r e n t l i t e r a t u r e [ 7 ] f o r t h e T W K method a nd d etermin a ti on o f t h e tightness co effici ent o f t he p er missible deviati on of t h e d elive r y t i m e f o r t h e E C m e t h o d , v a l u e s i n t h e r a n g e o f 3 ≤ K x ≤ 5 a r e g i v e n . T h e s m a l l e r t h e value of t he t ightness coefficie n t , t h e n a r ‐ rower the due date o f th e order j i s . T h e e x p e r i m e n t s i n t h e m a n u s c r i p t u s e t h e v a l u e o f t h e c o e f‐ ficient K x = 3 . T h e due date m odelled accor d i n g t o t h e T W K m e t h o d d e p e n d s on the a rriv a l time o f t h e o r d e r j (at j ), t otal t ime of p ro cessing o f all operations (p ijk ) and the described tightness c o e f f i c i e n t . T h e M O H K A a l g o r i t h m s c h e d u l e s t h e j o b o r d e r s a c c o r ding to four o ptimization crite‐ r i a , i n c l u d i n g t h e d u e d a t e d j . The adequac y c omparison of th e p roposed MOHKA met hod i s per‐ formed w ith two compar ison al gori thms: Multi‐objective particle s w a r m o p t i m i z a t i o n ( M O P S O ) [ 2 5 ] a n d B a r e ‐ b o n e s m u l t i ‐ o b j e c t ive particle s warm o ptimization (BBMO PSO) [26]. These two algorith ms d o not u se a n integr ated m athematical decision mo del to termin ate orders a c c ording to the d ue d ate criterion, this cr iterion is c alculated numeric ally i n the experiment a t the end of the optimization results. A s stated i n the initial research q ues t i o n , t h e d u e d a t e p a r a m e t e r i n t h e FJSSP o ptimization pr oblem is not w ell researc h ed, especially w hen it c omes t o using th e EC method t o o b tain o pti m al s olutions. All algorithms i n the exper iment us e th e same i nitialization parameter: p opulation size (N s = 3 0 0 ) , m a x i m u m n u m b e r o f a r c h i v e d n o n d o m i n a t e d s o l u t i o n s (N a = 1 00), and maxi mu m nu mb er o f algorithm it erations (MaxIter = 3 0 0 ). The optimiz a tion p a rameter for scheduling j obs by d ue d ate is a nalys e d using three criteria: numb er o f ta rdy jobs, ave r age j o b tard iness and tar d y jobs c ost . The tardy jobs c osts is modelled a s s h o w n i n E q . 9 , w h e r e t h e i n i t i a l j o b c o s t (J cost ) are multiplied b y the constant v alue o f three, divided by t he v alue c onstant K s , and multiplied b y subtr a cting the comp letion ti me C j and the due date d j . 3 (9) A constant v alue o f thr e e determines t hree ti mes t he cost o f t ar d y j o b s c o m p a r e d t o t h e c o s t o f i n ‐ t i m e c o m p l e t e d j o b s . T h e v a l u e c o n s t a n t K S i s a u t o m a t i c a l l y d e t e r m i n e d b y t h e o r d e r s Due date optimization in multi‐objective scheduling of flexible job shop production   Advances in Production Engineering & Management 15(4) 2020  485 mak e span. The paramet e r J cost is d etermined numerically a ccording to the c haracteristic s o f t he machines performing an ind ividual job oper ation. The mod e lling of t h e du e dates and t h e achi ev em ent o f t h e ot h er t h r e e o p t i m i z a t i o n p a r a m e ‐ t e r s w e r e c a r r i e d o u t u s i n g c o n v e n t i o n a l m e t h o d s ( p r i o r i t y r u l e s ) a n d t h e h e u r i s t i c G S B R m e t h ‐ o d , w i t h t h e a i m o f e v a l u a t i n g t h e e f f i c i e n c y o f t h e c o n v e n t i o n al s cheduling methods c o mpared t o t h e p r o p o s e d M O H K A E C m e t h o d . T h e c o m p a r i s o n i s p e r f o r m e d i n t he s oftwar e envi ronment Lekin. A s th e Leki n soft ware e nviro n ment onl y allows t he o ptimi zati on of d at asets o f up to one hundred operations i n th e FJSSP o pti m izati on pro b lem, th e e valu ation is p erformed w i t h a r a n‐ domly deter m ined d atas et classified a s low dimensional optimiza ti on pro b lem J 5 , M 11 , O 66 . A ran‐ domly gen e rated dat a set does not c o n tain d at a wh ere two or m ore o per a tions are per f or med on the sa me m a c hine within a sing l e order, limitation of Lekin. I n c o n t r a s t t o l a r g e r d a t a s e t s , w h e r e i n t h e T W K m e t h o d i s u s e d t o model due dates, t he S LK (slack) meth od [4] is recommended for smaller da ta se t s, wh ich ca n m o de l due dates by the Eq. 10 . , , ∈ (10) The ti me r eserve c onst a nt K y d eter mines th e lo oseness‐tigh tness of d u e d ates, in t h e S LK method t he d etermin a ti on of t he t ime reserve co nstant o f th e du e date i s give n by t he l iterature v a l u e s 4 ≤ K y ≤ 16. I n the presented re search w ork the valu e K y = 8 i s u s e d . T h e K y m u s t b e c a l c u ‐ lated individ u ally for the spe cific optimization problem. 3.1 Performance testing  T o t e s t t h e p e r f o r m a n c e o f t h e M O H K A a l g o r i t h m f o r d u e d a t e j o b s cheduling, f our randomly generat e d benchmark datasets a nd one r eal‐world d ataset a ll of w h i c h d e s c r i b e a m u l t i ‐ objective FJS S P optimiz a t ion problem were u s e d. T he d atasets wer e c r e a t e d u s i n g t h e i n t e r d e ‐ pendency f u n ction b e tw een d iffer e n t p aram eter s describing t he o pti m ization problem. W e di‐ vided these bench m ark datasets i nto three group s a ccording to th e c o m p l e x i t y o f t h e o p t i m i z a ‐ tion probl e m.  3.2 Using TWK and SLK methods  The division of the d atasets used i n different g roups according t o their complexity provided the basis for testing two different due date m od elling m eth o ds. TWK m ethod for middle and high dimension a l optimiz a tio n p roblem s and SLK method for low dimens io nal opti mization prob‐ l e m s . T h e u s e o f T W K a n d S L K m e t h o d s f o r d i f f e r e n t d a t a s e t s i s supported b y th e m a th ematical formul ation of t he i ndivi d ual meth ods. W ith the presented class ification approach, the complexi‐ ty o f the opt i mizati on pr oblems c an b e evaluated more p recisely i n o r d e r t o d e t e r m i n e t h e a d ‐ vantages a nd l imitations o f the due d a te m ethods c apabilities. Th e propos ed M OHKA a lgorithm performed the optimi zat i on of d atas ets with f ou r parameter s o f a flexible production system: mak e span (MC ), total w orkload of a l l m achines (TW) , m a x i m u m w o r k l o a d o f a n i n d i v i d u a l m a ‐ chine (MW) and added d u e date (d j ) parameter. T he o btained op timization results w e re c om‐ p a r e d w i t h t w o m u l t i ‐ o b j e c t i v e p a r t i c l e s w a r m b a s e d o p t i m i z a t i o n a l g o r i t h m s M O P S O a n d BBMOPSO. The experiments were p erformed on a personal c o mputer w i t h I n t e l i 7 p r o c e s s o r and 1 6 GB in ternal m e m o r y. 3.3 Results for the TWK method  T h e r e s u l t s i n T a b l e 1 s h o w t h e h i g h r e l i a b i l i t y o f s c h e d u l i n g jobs w ith the TWK meth od, taking i n t o a c c o u n t d u e d a t e s w i t h t h e M O H K A o p t i m i z a t i o n a l g o r i t h m . I t s s u c c e s s i n s c h e d u l i n g j o b s w i t h t i g h t d u e d a t e s , l o w a v e r a g e j o b t a r d i n e s s p o t e n t i a l l y l o w t a r d y j o b s c o s t a n d s h o r t o r d e r s mak e span. T h e middle dimensional dataset J 10 , M 11 , O 12 2 c aused no pr obl e ms f or a ll t hree evoluti onary computation algorithms in scheduling o rders for tight due d a tes o f th e TWK method w ith the tightness coeffici ent of K x = 3. N o job has missed the scheduled due date, which in turn di d not result i n ad ditional tard y jobs c osts i n the manufacturing s y st em. Since only th e referen tial MOHKA opti mizati on algorithm t a kes into a ccount the math ematica l architecture o f the TWK Ojstersek, Tang, Buchmeister    486  Advances in Production Engineering & Management 15(4) 2020 method, we s ee that t he r esults o f the multi‐objective optimi za tion h a ve a p ositive effect on the achiev em ent of t he m ini m um o rders makesp an. Mak e span i s the shor t e s t i n t h e M O H K A a l g o ‐ rithm with u p to 1 88 h , i n c ontr a st t o MOPSO and BBMOPSO, where t h e m a k e s p a n i s 2 2 7 h a n d 20 6 h, respe ctively. W h e n t h e d i m e n s i o n o f d a t a s e t s i n c r e a s e s f r o m m i d d l e d i m e n s i o n a l to high dimensio nal op‐ timizati on problems, the difference between the optimization r esults of c omparison and refer‐ ence a lgorit hms is m ore pronounc ed, presented on Fi g. 2 . In d at aset J 15 , M 11 , O 17 6 , the MOHKA algorith m t e rminat es o r d ers in s uch a w a y th at t hree orders a re l ate for t h e e x pect ed d ue d ate w i t h a n a v e r a g e j o b t a r d i n e s s o f 1 9 h , r e s u l t i n g i n a t a r d y j o b s costs of 2 272.2 E UR. The MOPS O algorithm terminates o rders so that only two o rders miss the exp e c t e d d u e d a t e , b u t w i t h h i g h e r a v e r a g e j o b t a r d i n e s s o f 4 5 . 5 h , w h i c h m e a n s a 1 3 9 % h i g h e r a v e r age job tardiness than the MOHKA a l g o rithm. A longe r a ve ra ge job ta rdine ss le a ds to highe r ta rdy jobs costs, which a mount t o E U R 2 9 6 6 . 5 i n t h e M O P S O a l g o r i t h m . T h e B B M O P S O a l g o r i t h m h a d t h e m o s t d i f f i c u l t i e s i n scheduling t he J 15 , M 11 , O 17 6 d a t a s e t b e c a u s e u p t o o n e ‐ t h i r d o f t h e o r d e r s h a v e m i s s e d t h e sched‐ u l e d d u e d a t e , w i t h a n a v e r a g e j o b t a r d i n e s s o f 2 0 . 6 h a n d h i g h tardy j obs costs of 3 558. 5 EUR. This c orresponds to a n increase o f 5 6.6% i n the costs of tardy j o b s c o m p a r e d t o t h e M O H K A a l ‐ g o r i t h m . T h e r e s u l t s s h o w t h a t t h e M O H K A a l g o r i t h m i s a l s o m o s t s ucc e ssful w ith t he order m a k e s p a n p a r a m e t e r o f 2 8 9 h , w h i c h i s 2 . 8 % s h o r t e r t h a n t h e B B M OPSO a lgorith m a nd 1 7% shorter than the M OPSO a lgorith m . Based on the optimiz a tion r esu l t s d e s c r i b e d a b o v e , w e c a n a s s u m e h o w i m p o r t a n t t h e s c h e d u l i n g o f t h e d y n a m i c F J S S P w i t h t h e p a r a m e t e r o f d u e d a t e i s , especially if the complexity of th e opti mizati on problem i n crea se s . The hypothesis is confirmed fo r the high‐dimensional datas e t J 20 , M 11 , O 24 0 , i n w h i c h t h e r e f e r ‐ e n c e M O H K A a l g o r i t h m d o m i n a t e s o v e r t h e r e s u l t s o f t h e t w o c o m p arison algorith ms p resented o f F i g . 3 . T h e l o w e s t n u m b e r o f t a r d y j o b s w i t h a n a v e r a g e j o b tardiness of 31.1 h compared t o 4 4 . 4 h a n d 4 6 . 8 h f o r M O P S O a n d B B M O P S O , c o r r e s p o n d i n g t o 4 2 . 8 % a nd 50.5% h i g he r number o f t a r d y j o b s . G i v e n t h e h i g h e r n u m b e r o f t a r d y j o b s a n d t h e l o n g e r a v e r a g e j o b t a r d i n e s s , t h e costs of t ardy j obs is a lso high er f or t he t wo c omp a rison al gori t h m s t h a n f o r t h e r e f e r e n c e M O H ‐ K A a l g o r i t h m , w h i c h a m o u n t s t o 7 , 3 1 8 . 1 E U R . W i t h t h e M O P S O a l g o r i t h m , t h e t a r d y j o b s c o s t s a m o u n t t o 1 3 , 5 8 5 . 6 E U R , w h i l e w i t h B B M O P S O t h e y a m o u n t t o 3 3 , 0 7 0.1 E U R, w hich r e p resents an i ncreas e of 8 5.6% a n d 351.9%, respectively, in t he c osts o f tardy jobs that have e xceeded their scheduled due date. The prese n ted results prove the high import ance o f mat h em atical modelling w ith the parameter of d ue d ate optimi zation, a s th ey have a d ecisive influence on the m a ke s p a n an d f i na n c i a l ju s t i f i c a t i o n of a h i g h ly d yn a m i c m an uf a c t u r i n g . A s u i t a b l e ma t he m at i c a l m o d e l o f t h e m u l t i ‐ o b j e c t i v e o p t i m i z a t i o n p r o b l e m i s a l s o r e f l e cted i n th e achiev em en t of s h o rt order makespan. For the high d imensional dataset J 20 , M 11 , O 24 0 the r eferenc e M OHKA a lgorith m achiev ed a m akespa n of 3 41 h and the two compari s on algorith ms 38 9 h a n d 397 h. App ropriate multi‐objective decision making a llows f or a n evenly b alanced operation o f th e m a nu facturin g system r egarding to the makespan , machine util ization and achie v e m e nt o f ti ght order due dates.   Fig. 2 Optimiza t ion res ults J 15 , M 11 , O 17 6 : (a) av erage jo b tardi n ess, (b ) tardy jo bs co sts and ( c) o r der s mak esp an    Due date optimization in multi‐objective scheduling of flexible job shop production   Advances in Production Engineering & Management 15(4) 2020  487 Table 1 Algorit hms optimizati on results Algorithm D ataset Number of tardy job Average job tardiness (h) Tardy jobs costs (EUR) Orders makespan (h) MOHKA J 10 , M 11 , O 12 2 0 0 0 1 8 8 J 15 , M 11 , O 17 6 3 1 9 2 ,272.2 2 89 J 20 , M 11 , O 24 0 7 3 1.1 7 ,318.1 3 41 MOPSO J 10 , M 11 , O 12 2 0 0 0 2 2 7 J 15 , M 11 , O 17 6 2 4 5.5 2 ,966.5 3 39 J 20 , M 11 , O 24 0 1 0 44.4 13,585.6 3 89 BBMOPSO J 10 , M 11 , O 12 2 0 0 0 2 0 6 J 15 , M 11 , O 17 6 5 2 0.6 3 ,558.5 2 97 J 20 , M 11 , O 24 0 1 8 46.8 33,070.1 3 97   Fig. 3 Optimiza t ion res ults J 20 , M 11 , O 24 0 : (a) av erage job tardiness, (b ) tardy jobs costs, and (c ) orde rs makespan 3.4 Results for the SLK method  With t he a im t o compare the solutions o f the MOH K A algorithm an d the so lutions o f co nventi on‐ a l p r i o r i t y r u l e s , a c o m p a r i s o n o f t h e r e s u l t s o f t h e M O H K A o p t i m i z a t i o n w i t h t h e r e s u l t s o f j o b scheduling i n the Lekin softwar e e n v ironment was performed for the low d i mensional optimiza‐ tion probl e m of J 5 , M 11 , O 66 . Table 2 shows the optimization re sul ts of a randomly generated J 5 , M 11 , O 66 da t a s e t of f i ve jobs w i t h a t o t a l o f s i x t y ‐ s i x o p e r a t io ns p erform ed o n eleven m ac hin es. The o p timizati on was per‐ formed w ith the MOHKA optimizatio n a l g o r i t h m i n t h e s o f t w a r e e n viron m e n t MA TL AB a nd s ev‐ en o pti m iz at ion approac hes i n the softwar e e nvi r onment Lekin. O f th e s e ven opti mi zation a p‐ proaches, six are conventional priority r ules a nd one is a heur istic algorithm named General Shifting B ott l eneck Routi n e (GSBR). For the optimizati on of d ue d a t e s t h e S L K m e t h o d w i t h a time r eserve constant o f K y = 8 w as us e d. The results show a h igh reliabil ity of production jobs s cheduli ng b y the optimization a lgo ‐ rithm MOHK A. I n th e co nsidered d ataset M OHK A termin a tes jobs s o that two orders m iss the scheduled due dates with a n avera g e j o b t a r d i n e s s o f 9 . 5 h a n d a tardy job s c osts o f 2,6 51 EUR. W i t h t h e s i x p r i o r i t y r u l e s w e s e e t h a t t h e f i v e p r i o r i t y r u l e s , w i t h t h e e x c e p t i o n o f t h e S P T p r i o r ‐ ity rule, terminate orders in such a w ay that all five o rders m iss the scheduled tight due date. The av erage job tardines s is h igher t h an 3 0 9 .5% for the CR p rior i t y r u l e t o 5 0 5 . 3 % f o r t h e L P T p r i o r i t y r u l e t h a n f o r t h e M O H K A a l g o r i t h m . T h e r e a r e a l s o s i g n ificantl y higher tardy j obs costs. The only algorithm th at h as p artially a pproxi m at ed t he r es ults o f t h e M O H K A a l g o r i t h m i s t h e h e u r i s t i c G S B R a l g o r i t h m , w h e r e f o u r o r d e r s a r e t a r d y w i t h a n a verage j ob tardin e ss of 9 .4 h . Due to tw o a dditional delayed jobs, th e tardy job c o st a re 3 9.8% h i g h e r t h a n i n t h e M O H K A a l g o ‐ r i t h m . T h e r e i s a l s o a s i g n i f i c a n t d i f f e r e n c e i n a c h i e v i n g a s h or t makesp an o f orders, where the MOHKA algo rithm termi n ates w ork j o bs s o that t hey are co m p leted i n a m a k e s p a n o f 9 9 h , a n d all other algorithms terminate o rders with makespan between 208 h (GSBR ) and 2 5 6 h ( CR). The p resented o ptimization resu lts prove the high a bility t o t erminate p roduction or ders w i t h t h e M O H K A a l g o r i t h m a n d t o a c h i e v e t i g h t d u e d a t e s f r o m l o w dimension a l optimizati on cases (with SLK method ) to m iddle and high d imensional o ptimiza tion cases (with TWK meth‐ od) comp ared to opti miz a tion s o lu tions according to MOSPO, BBMO PSO and priority rules. Ojstersek, Tang, Buchmeister    488  Advances in Production Engineering & Management 15(4) 2020 Table 2 MOHKA vs. priority ru le s o p ti mi zati on results A lgorithm M OHK A E DD M S FC FS LPT S PT C R GS B R Number of tardy job 2 5 5 5 5 4 5 4 Average job tardiness (h) 9. 5 34.8 47.6 41.6 4 8 32.4 29.4 9.4 Tardy jobs costs (EUR ) 2 ,651 11,325.1 14,682.2 13,320 14,436.1 10,5 70.1 8,905 3,706.2 Orders makespan (h) 99 211 211 215 217 233 256 208 3.5 Real‐world case study  W i t h t h e p r o p o s e d m e t h o d f o r m o d e l l i n g t h e d u e d a t e f o r F J S S P , which was tested on randomly generat e d benchmark d a tasets, we p r o v e d t h e h i g h a b i l i t y t o s o l ve m ulti‐objective o pt imizati on problems. The initial experiment, w h ich was conducted on random ly g e n erat ed d atasets, w as ext e nded to a re al‐world c ase st udy for the FJSS P manufacturing s ystem to e valuat e MOHKA efficiency in determ ining due dates. The fo urth s ection pres ents t he a bilit y t o sol v e a multi‐object i v e opti miz a t i on probl e m of a real‐world m an uf acturing s yste m (the d ataset f rom a re al‐world environment is c alled RW_PS). T h e f i r s t p a r t o f t h e s e c t i o n p r e s e n t s t h e i n p u t d a t a o f t h e m a nufacturing system that has been p r e p a r e d t o d e s c r i b e F J S S P . W o r k i n g w i t h t h e c o m p a n y t o p r e p a r e r elevant and credible input data o ffers t h e opport un ity to a chie v e r eliable op timizati on r esults by t es ting t he proposed EC s c h e d u l i n g m e t h o d s . T h e R W _ P S d a t a s e t c o n s i s t s o f f i f t e e n j o b o rders that a re e xecuted on ten machin es w ith eighty‐ f ou r operations. The optimiz a tion results obtained w i t h the MOHKA algo‐ rithm were c ompared w i th the o pt imizati on res u lts of th e M OPSO and BBMOPSO a l g orithms. The prop osed i ntegrati o n a pproach o f transferri ng t h e o ptimizat ion r e sults to t he c on ventio nal simulation environment was used t o transfer the o ptimization re sults, t he o rder o f the due dates of th e jo b se quence, t o th e simu l a tion model o f th e real‐world manufacturing system. Manufacturing system input data S e l e c t e d d a t a w e r e o b t a i n e d f r o m a C e n t r a l E u r o p e a n m e d i u m ‐ s i z e d co mpan y that m an uf ac‐ tures individual o rders for different c ustomers. Orders r eceived i n t h e c o m p a n y b y t h e c u s t o m e r m u s t b e p e r f o r m e d o n s p e c i f i c , a v a i l a b l e m a c h i n e w i t h i n t h e m a n ufacturing s ystem c o ncerning four o ptimization parameters MC, TW, MW a n d d j ( F J S S P p r o b l e m ) . T h e o r d e r s c o n s i s t o f t w o t y p e s o f p r o d u c t s w i t h d i f f e r e n t p r o c e s s t i m e s , m a c h i n e o p e r a t i ng c osts (O c ) , m a c h i n e i d l e c o s t s (I c ) and fix l o cation of m achine i s k n own by x a n d y l ocation. I nput d ata are given in T able 3 . Compar ed t o the t e st r an dom gen erated datasets d escribed in s ec tion 3, t h e addition al c omplexi‐ ty o f th e RW_PS optimization problem is a dded by two d ifferent product types, which a dd one dimension a l complexit y t o the optimi zation probl em. In a r eal‐world m anufacturing s y s t e m , m a c h i n e s m a r k e d M 1 t o M 10 p e r f o r m t h e f o l l o w i n g o p ‐ erations: • M 1 and M 2 f o r raw m ateri a l cuttin g , • M 3 to M 5 CN C m achinin g , • M 6 and M 7 w elding, • M 8 and M 9 a s se m b ling a nd • M 10 final co n trol operati o n . The main t ask of t he o p t imizati on al gorithm is t o optimally d ete r m i n e t h e j o b s e q u e n c e o f operatio ns o n the av ailable m a chine. T he a lgorit hm m ust de termin e w h i c h o f t h e m a c h i n e s i s capable o f p erformi n g th e indivi dual o perations according to the four o ptimization criteria. T he simulation model was built in t he S i m io s oftw ar e envir onment, i n which a transf er m ethod for integr atin g optimiz a tion r esults f rom the MOH K A met h od t o conve ntio nal simulati on decisio n logic was used [ 18]. Using the MOH K A a l g o r i t h m , w e s o l v e d t h e F JSSP o pti m izati on problem, s o w e d e c i d e d t o e x t e n d o u r e x i s t i n g o p t i m i z a t i o n r e s u l t s w i t h a s uitable simulation mod e l. F ig. 4 shows a simulation model of a r eal‐wold m anufacturing s ys tem ru nni ng on an o rder j ob s e‐ quence deter mined by t he MOHKA o pti m izati on algorithm. Due date optimization in multi‐objective scheduling of flexible job shop production Advances in Production Engineering & Management 15(4) 2020  489 Table 3 Real‐world manufacturing sy stem characteri s ti cs M a c h i n e M 1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 M 9 M 10 x loc (m) 8 8 12.5 18.5 24.5 30.5 36 36 24.5 19.5 y loc (m) 9.5 4.5 0 0 0 0 5.5 10.5 16.5 12 Product 1 Pro cessi ng time (min) 20 24 40 45 38 47 20 25 11 22 Oc (EUR/h) 45 45 35 35 35 35 52 52 59 43 Ic [EUR/h] 22.5 22.5 14 14 14 14 31.2 31.2 35.4 21.5 Product 2 Pro cessi ng time (min) 22 22 43 43 43 43 23 23 12 25 Oc (EUR/h) 43 43 36 36 36 36 53 53 59 45 Ic [EUR/h] 21.5 21.5 14.4 14.4 14.4 14.4 31.8 3 1.8 35.4 22.5 Fig. 4 Simulation model in Simio Due date scheduling results T a b l e 4 a n d F i g . 5 s h o w t h e r e s u l t s o f o p t i m i z i n g t h e R W _ P S d a t a s e t a c c o r d i n g t o t h e o r d e r d u e d a t e p a r a m e t e r . A s s h o w n i n s e c t i o n 3 , t h e T W K m e t h o d w i t h a t i ghtn ess coefficient K x = 3 w a s used w hen evaluati ng R W_PS d ataset. The opti mization r e sults sho w t h a t w i t h t h e M O H K A o p ‐ timizati on al gorithm only one j ob m i ssed a tight due date w ith a n a v e r a g e j o b t a r d i n e s s o f 4 6 min. W ith the BBMOPSO o ptimizatio n algorithm also, one j ob m isse d t h e d u e d a t e , b u t j o b i s t a r d y b y a n a v e r a g e j o b t a r d i n e s s o f 1 5 4 m i n , w h i c h c o r r e s p o n d s t o a 2 3 4 % l o n g e r t a r d y t i m e o f the missed job th an the t ardy j ob w it h the MOHKA al gorithm. I n th e MOPSO algorith m, two j obs are tardy with a n average job tardines s of 58 minutes, w hich is 26.1% l onger tardy time than the d e l a y w i t h t h e M O H K A a l g o r i t h m . S i n c e t h e v a l u e o f t a r d y j o b s c osts i s low, the p ercentage dif‐ ferenc e bet w een them i s s ignific a nt. In this cas e , the MOHKA al gorithm p r oves t o b e the m ost e f f i c i e n t , s i n c e i t i s t h e o n l y a l g o r i t h m a b l e t o t a k e d u e d a t e s into a ccount as a d ecision criterion when det er minin g th e j ob seq uenc e. T h e ta r d y j ob s c o s t s i n t he M O P S O al gorithm ar e 1 30.2% high e r i n the MOP S O algorith m than i n t h e M O H K A a l g o r i t h m . E v e n i f o n l y o n e j o b w i t h t h e B B M O P S O a lgorithm m issed the sched‐ u l e d d u e d a t e , t h i s w a s d e l a y e d b y a m u c h l o n g e r t i m e t h a n t h e tardy j o b with the M O H KA a l g o‐ rithm. T his is r eflected in 230.7% h igher tardy j o b costs. T he makespan o f orders is shortest w i t h t h e M O H K A a l g o r i t h m a t 3 9 2 . 4 5 m i n , w h i l e t h e m a k e s p a n o f o r d e r s i s l o n g e r b y 2 . 1 % l o n g ‐ e r w i t h M O P S O a n d 7 . 6 % l o n g e r w i t h B B M O P S O . F r o m t h e p e r s p e c t i v e o f t h e m u l t i ‐ o b j e c t i v e decision making p roc e ss, w e can c o nclude that the MOHKA al gorit hm p rovides a hi gh d egree of FJSSP s cheduling capabilities e ven in r eal‐world d atasets, c ons idering the ability to a chieve a tight job due date. Ojstersek, Tang, Buchmeister    490  Advances in Production Engineering & Management 15(4) 2020 Table 4 Optimization results of real ‐world manufacturing system Algorithm M OHKA MOPSO BBMOPSO Number of tardy job 1 2 1 Average job tardiness (min) 46 58 154 Tardy jobs costs (EUR ) 14.9 34.3 46.3 Orders makespan (min) 392.45 400.48 422.21   Fig. 5 Optimiza t ion results: (a) avera ge job tardiness, (b) tard y job s co sts, and (c) o rders m a k espan 4. Discussion and conclusions  Scheduling m ulti‐objecti ve F JSSP o p timizati on p r oblem is d efined a s a N P ‐ h a r d o p t i m i z a t i o n p r o b l e m . T h e i n i t i a l r e s e a r c h q u e s t i o n o f s c h e d u l i n g F J S S P p r o d uction with the o pt imizati o n p a r a m e t e r o f t h e d u e d a t e s i m p o r t a n c e a n d t a k i n g i n t o a c c o u n t t he s tand ard optimization pa‐ r a m e t e r s r e l a t e d t o t h e m a k e s p a n o f o r d e r s a n d m a c h i n e u t i l i z a t ion, w as e valu ated i n the pre‐ sented r esearch w ith the MOHKA opti mizati on method and the SLK and TW K met h ods to m odel due dates. W ith increasin g nu mb er o f optimiz a tion p aram eters, t he c o m put a tion al c omp l exity of the optimiz a tion algorith m increases. The present e d research w o rk p resents the integr ation of the mathematical structure of the S L K ( f o r l o w d i m e n s i o n a l o p t i m i z a t i o n p r o b l e m s ) a n d T W K methods ( f o r m edium and high d i m ensio n al o ptimizati on problems) i nto the opti mizati on MOHKA algorithm, w hich i s capable of s cheduling FJSSP p roduction . T h e p r o p o s e d M O H K A a l g o ‐ rithm was used to schedule test datasets w ith emphasis on achiev i n g a t i g h t d u e d a t e o f t h e o r ‐ ders. The optimization results were c ompared w i th the r esults o f the opt i mizati on al gorithms MOPSO and BBMOPSO, which termi n ate orders only at o rdinary opti mization p a rameters: MC, TW and MW . The disadvantage o f th e comp arati v e opti mizat i on methods beco mes apparent w h e n w e t a l k a b o u t m e d i u m a n d h i g h d i m e n s i o n a l o p t i m i z a t i o n p r o b l e m s i n t h e s c h e d u l i n g o f FJSSP. The li mited sched u ling c apabil ities of the M OPSO a nd BBM OPSO a lgorithms are reflected i n t h e l i m i t e d m a t h e m a t i c a l s t r u cture of t he a lgorithms, which do not c onsider the SLK and T W K methods as d ecision parameters i n achievin g optimally s cheduled o r d e r s f r o m t h e p o i n t o f d u e d a t e s . T h e o p t i m i z a t i o n r e s u l t s o f t h e r e f e r e n c e M O H K A a l g o r i t h m prove the high i mp ortance o f t h e d u e d a t e o p t i m i z a t i o n p a r a m e t e r , s i n c e t h e p r o p o s e d m e t h o d optimizes order schedulin g w i t h r e g a r d t o t h e t w o c o m p a r a t i v e a l g o r i t h m s f o r l o w , m e d i u m a nd h igh dimensional optimiza‐ tion problems. Since we a re talking a bout m ulti‐objective d ecis ion makin g a nd f indin g c ompro‐ mises betw een different (even contr a dictory) o ptimizati on p a rame t e r s , t h e r e s u l t s o f t h e M O H ‐ K A a l g o r i t h m p r o v e t h e h i g h a b i l i t y t o r e a c h a l l f o u r o p t i m i z a t ion parameters e qually a nd e ffi‐ ciently (MC, TW, MW a n d d j ). A s evidenced the short order mak e span, tight due dates, l ow aver‐ age order t a rdiness and the associate d l ow a ssoci ated j ob tard iness costs are achieved. The an‐ swer t o th e question a b o ut t h e e ffic i ency o f ev o l utionary m etho ds in multi‐objective decision m a k i n g c o m p a r e d t o t h e c o n v e n t i o n a l o p t i m i z a t i o n a p p r o a c h o f p r i o r i t y r u l e s w a s g i v e n b y t h e presented st udy, i n which the optimi zation r e sults of t he M O H KA a l g o r i t h m a r e c o m p a r e d w i t h the opti miz a tion results of s i x p riority rules and an integrate d heuristic method in t h e Lekin software e n v ironment. T he o btai ned results prove th e high d omin ance o f the optimization r e ‐ s u l t s o f t h e e v o l u t i o n a r y m e t h o d M O H K A , w h i c h t e r m i n a t e s t h e F J SSP production according to the used l ow‐dimensio n al d ataset f or a ll optimization par a meter s most e fficientl y. R andomly Due date optimization in multi-objective scheduling of flexible job shop production generated datasets were the basis for carrying out the validation of the applicability of the pro- posed method in real-world manufacturing systems, whereby the satisfactory optimization re- sults were demonstrated in the experiment. The scheduling of the FJSSP production to achieve tight due dates was carried out using the example of a dataset of a real-world manufacturing system. In this case, the TWK method, which is integrated into the decision logic of the MOHKA algorithm, proved the high ability to terminate the significance of real-world datasets im- portance in relation to the parameter of due date optimization. Since the presented research work deals only with FJSSP, which is the main part of the re- search problem of multi-objective optimization job shop production, it is necessary to further investigate the importance of scheduling due dates in dynamic job shop production (DJSSP). Where the main features are dynamic order changes during the execution of the algorithm (at initialization stage the whole order dataset is unknown), machine failures during the execution of operations and the determination of the importance of orders need to be studied. Further research on the research problem of DJSSP would remove the limitations of current research, where the FJSSP optimization problem is based on the assumption of an initially known order dataset, an initially empty production system, a uniform meaning of orders, and known produc- tion capacities that do not change during operation. Acknowledgement The authors gratefully acknowledge the support of the Slovenian Research Agency (ARRS), Research Core Funding No. P2-0190. References [1] Prester, J., Buchmeister, B., Pal čič, I. (2018). Effects of advanced manufacturing technologies on manufacturing company performance, Strojniški Vestnik – Journal of Mechanical Engineering, Vol. 64, No. 12, 763-771, doi: 10.5545/sv-jme.2018.5476. [2] Baker, K.R. (1984). Sequencing rules and due-date assignments in a job shop, Management Science, Vol. 30, No. 9, 1093-1104, doi: 10.1287/mnsc.30.9.1093. [3] Udo, G.J. (1994). A simulation study of due-date assignment rules in a dynamic job shop, Journal of the Operational Research Society, Vol. 45, No. 12, 1425-1435, doi: 10.1057/jors.1994.219. [4] Gordon, V.S., Proth, J.-M., Chu, C. (2002). Due date assignment and scheduling: SLK, TWK and other due date assignment models, Production Planning & Control, Vol. 13, No. 2, 117-132, doi: 10.1080/09537280110069621. [5] Modrák, V., Pandian, R.S. (2010). Flow shop scheduling algorithm to minimize completion time for n-jobs m- machines problem, Tehnički Vjesnik – Technical Gazette, Vol. 17, No. 3, 273-278. [6] Demir, H.I., Uygun, O., Cil, I., Ipek, M., Sari, M. (2015). Process planning and scheduling with SLK due-date assignment where earliness, tardiness and due-dates are punished, Journal of Industrial and Intelligent Information, Vol. 3, No. 3, 173-180, doi: 10.12720/jiii.3.3.173-180. [7] Ojstersek, R., Brezocnik, M., Buchmeister, B. (2020). Multi-objective optimization of production scheduling with evolutionary computation: A review, International Journal of Industrial Engineering Computations, Vol. 11, No. 3, 359-376, doi: 10.5267/j.ijiec.2020.1.003. [8] Janes, G., Perinic, M., Jurkovic, Z. (2017). An efficient genetic algorithm for job shop scheduling problems, Tehnički Vjesnik – Technical Gazette, Vol. 24, No. 4, 1243-1247, doi: 10.17559/TV-20150527133957. [9] Scrich, C.R., Armentano, V.A., Laguna, M. (2004). Tardiness minimization in a flexible job shop: A tabu search approach, Journal of Intelligent Manufacturing, Vol. 15, No. 1, 103-115, doi: 10.1023/B:JIMS.0000010078. 30713.e9. [10] Simchi-Levi, D., Wu, S.D., Shen, Z.-J.M. (2004). Handbook of quantitative supply chain analysis: Modeling in the e- business era, Springer Science & Business Media, New York, USA. [11] Wu, Z., Weng, M.X. (2005). Multiagent scheduling method with earliness and tardiness objectives in flexible job shops, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), Vol. 35, No. 2, 293-301, doi: 10.1109/TSMCB.2004.842412. [12] Chen, B., Matis, T.I. (2013). A flexible dispatching rule for minimizing tardiness in job shop scheduling, International Journal of Production Economics, Vol. 141, No. 1, 360-365, doi: 10.1016/j.ijpe.2012.08.019. [13] Ojstersek, R., Buchmeister, B. (2020). The impact of manufacturing flexibility and multi-criteria optimization on the sustainability of manufacturing systems, Symmetry, Vol. 12, No. 1, Paper No. 157, doi: 10.3390/sym1201 0157. [14] Nie, L., Gao, L., Li, P., Li, X. (2013). A GEP-based reactive scheduling policies constructing approach for dynamic flexible job shop scheduling problem with job release dates, Journal of Intelligent Manufacturing, Vol. 24, No. 4, 763-774, doi: 10.1007/s10845-012-0626-9. Advances in Production Engineering & Management 15(4) 2020 491 Ojstersek, Tang, Buchmeister [15] Rajabinasab, A., Mansour, S. (2011). Dynamic flexible job shop scheduling with alternative process plans: An agent-based approach, The International Journal of Advanced Manufacturing Technology, Vol. 54, No. 9-12, 1091- 1107, doi: 10.1007/s00170-010-2986-7. [16] Gao, K.Z., Suganthan, P.N., Pan, Q.K., Chua, T.J., Cai, T.X., Chong, C.S. (2014). Pareto-based grouping discrete harmony search algorithm for multi-objective flexible job shop scheduling, Information Sciences, Vol. 289, 76-90, doi: 10.1016/j.ins.2014.07.039. [17] Ma, D.Y., He, C.H., Wang, S.Q., Han, X.M., Shi, X.H. (2018). Solving fuzzy flexible job shop scheduling problem based on fuzzy satisfaction rate and differential evolution, Advances in Production Engineering & Management, Vol. 13, No. 1, 44-56, doi: 10.14743/apem2018.1.272. [18] Na, H., Park, J. (2014). Multi-level job scheduling in a flexible job shop environment, International Journal of Production Research, Vol. 52, No. 13, 3877-3887, doi: 10.1080/00207543.2013.848487. [19] Xu, H., Bao, Z.R., Zhang, T. (2017). Solving dual flexible job-shop scheduling problem using a bat algorithm, Advances in Production Engineering & Management, Vol. 12, No. 1, 5-16, doi: 10.14743/apem2017.1.235. [20] Fu, H.C., Liu, P. (2019). A multi-objective optimization model based on non-dominated sorting genetic algorithm, International Journal of Simulation Modelling, Vol. 18, No. 3, 510-520, doi: 10.2507/ijsimm18(3)co12. [21] Getachew, F., Berhan, E. (2015). Simulation and comparison analysis of due date assignment methods using scheduling rules in a job shop production system, International Journal of Computer Science & Engineering Survey, Vol. 6, No. 5, 29-40, doi: 10.5121/ijcses.2015.6503. [22] Ojstersek, R., Lalic, D., Buchmeister, B. (2019). A new method for mathematical and simulation modelling interactivity: A case study in flexible job shop scheduling, Advances in Production Engineering & Management, Vol. 14, No. 4, 435-448, doi: 10.14743/apem2019.4.339. [23] Yin, Y., Wang, D., Cheng, T.C.E. (2020). Due date-related scheduling with two agents: Models and algorithms, Springer Nature Singapore, Singapore, doi: 10.1007/978-981-15-2105-8. [24] Hajduk, M., Sukop, M., Semjon, J., Jánoš, R., Varga, J., Vagaš, M. (2018). Principles of formation of flexible manufacturing systems, Tehnički Vjesnik – Technical Gazette, Vol. 25, No. 3, 649-654, doi: 10.17559/TV- 20161012132937. [25] Moslehi, G., Mahnam, M. (2011). A Pareto approach to multi-objective flexible job-shop scheduling problem using particle swarm optimization and local search, International Journal of Production Economics, Vol. 129, No. 1, 14-22, doi: 10.1016/j.ijpe.2010.08.004. [26] Zhang, Y., Gong, D.-W., Ding, Z. (2012). A bare-bones multi-objective particle swarm optimization algorithm for environmental/economic dispatch, Information Sciences, Vol. 192, 213-227, doi: 10.1016/j.ins.2011.06.004. 492 Advances in Production Engineering & Management 15(4) 2020