Volume 11 Issue 2 Article 1 12-31-2009 Minimising inventory costs by properly choosing the level of safety stock Liljana Ferbar Tratar Follow this and additional works at: https://www.ebrjournal.net/home Recommended Citation Ferbar Tratar, L. (2009). Minimising inventory costs by properly choosing the level of safety stock. Economic and Business Review, 11(2). https://doi.org/10.15458/2335-4216.1262 This Original Article is brought to you for free and open access by Economic and Business Review. It has been accepted for inclusion in Economic and Business Review by an authorized editor of Economic and Business Review. 109 ECONOMIC AND BUSINESS REVIEW | VOL. 11 | No. 2 | 2009 | 109–117 MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING THE LEVEL OF SAFETY STOCK LILJANA FERBAR TRATAR* ABSTRACT: Markets are everyday becoming ever more demanding and companies are adjusting in different ways. The objective of forecasting in a demand-driven supply network is to identify the probable range of expected demand so that supply can cov- er demand anywhere within the statistical range. Supply can cover the range either through having the capacity to replenish within lead times or by carrying excess inven- tory (safety stock). Nowadays, many companies put a lot of their energy and finance into setting the right level of safety stock and reducing related expenses. In this paper, we improve an existing method for calculating the safety stock for a particular Slov- enian company. We present the existing and proposed methods for calculating safety stock and derive a cost model. Finally, we prove that the proposed method not only reduces average costs but also helps to meet the target customer service level – making it also applicable to other Slovenian companies encountering situations where demand is seasonal. Keywords: Safety stock; Inventory; Cost model; Optimisation UDC: 330.522.4 JEL classification: G31; C61 1. INTRODUCTION Th e objective of forecasting in a demand-driven supply network is to identify the prob- able range of expected demand so that supply can cover demand anywhere within the statistical range. Supply can cover the range either through having the capacity to re- plenish within lead times or by carrying excess inventory (safety stock). Safety stock is the amount of material needed to compensate for supply and demand ineffi ciencies. In an organisation where marketing is tasked with growing the market, and supply is tasked with reducing working capital, the decision on the amount of safety stock to carry can become very contentious. * University of Ljubljana, Faculty of Economics, ,Kardeljeva ploščad 17, 1000 Ljubljana, Slovenia, Email: liljana.ferbar@ef.uni-lj.si ECONOMIC AND BUSINESS REVIEW | VOL. 11 | No. 2 | 2009110 Companies are aware of the importance of safety stock so they set it in many diff erent ways. Unfortunately, there is no universal method that would yield the optimal level of safety stock. As a result, many companies set their level of safety stock in relation to actu- al sales in the past year. Most safety stock calculations within ERP systems use standard APICS calculation methods (Akkermans, et al. (2003), Kelle and Akbulut (2005), Gupta and Kohli (2006) et al.). Th ese methods appear to work well for situations where demand is stable, but not for situations where demand is seasonal. Th e objective of this paper is to propose an alternate method for calculating safety stock for seasonal products in order to reduce total costs and retain the service level according to the company’s policy (as is established in the existing method). Th e paper is organised as follows. First, we present the existing method for calculating safety stock, which is used by Danfoss District Heating, a Slovenian company. Th en we describe the proposed method for calculating safety stock for seasonal products, which is an extension of Herrin’s method (Herrin, 2005). In the third chapter, we derive a cost model in order to compare the existing and proposed method. Finally, based on our study in which we have included 4,247 products we prove that the proposed method for calculating safety stock can reduce average costs by almost 12%. 2. CALCULATION OF SAFETY STOCK Th e optimal level of safety stock is related to many components and some of them can hardly be controlled (Winston, 1993). Th is paper will only address the demand compo- nent or amount needed to cover the inherent variability in the sales forecast. 2.1 Th e existing method To calculate safety stock according to the existing method used in the company Danfoss District Heating we have to rely on sales in the previous year. At the beginning we must divide a year into 14-day periods and count out the number of products to be sold per period (see Table 1). TABLE 1: Yearly sales for 2006 for product X divided into 14-day periods Period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Sale 21 2 3 13 14 14 22 14 18 6 33 20 24 28 41 31 31 48 43 16 4 2 7 8 13 15 Aft er doing this, we calculate the average sales for each product i: (1) In our case, the average sales for product X is 19 (rounded value). 26 year∑= sales yi 2 LILJANA FERBAR TRATAR | MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING ... 111 Th en we have to sort the quantities by ascending the value of sales and calculate the per- centile of the sorted values according to an ABC classifi cation and related service level. Th e company classifi es its products in A, B or C classes. Th is classifi cation depends on the price and predicted number of orders in the next year (products with classifi cation A have more than 48 orders per year and products with classifi cation C have fewer than 5 orders in one year). If the selected product is in class A the related service level (accord- ing to the company policy) is 98% (products in class B have a service level of 90% and the service level for class C products is 0% as they are only made when specially demanded by the customer). Th is means that 98% of the market demand can be covered by products that are in the warehouse. Now we compare average sales and sales in the 98th percentile (because the related serv- ice level is 98%). If the ratio is greater than 1:5, we have to calculate the sales value at the 90th percentile. With this correction we eliminate products with a high deviation. In our case, for product X, with classifi cation A, the sales value at the 98th percentile is 50 (yX;0,98 = 50). Since the ratio yX;0,98/yX = 50/19 = 2,6 is less than 5, product X is a product with a low deviation and its service level is 98%. Aft er that, we calculate the diff erence between the maximal admissible value at the 98th (or 90th) percentile (NPVNi) and average sales: . (2) In our case, the value of NPVNX is 50 and the diff erence is DIFX = 31. Th e supply time of the product (lead time) is also taken into account. Usually the lead time (LTi) is in days so we have to recalculate it on a 14-day basis: (3) Th e supply time of the selected product X is 18 days, so LTX = √18/14 = 1,13389. Th e next step is multiplying the calculated diff erence and lead time to obtain the fi rst value of safety stock: (4) Th en we have to consider some obligations such as: (5) iii yNPVNDIF −= LTi = lead _time(in _days) 14 ⎪ ⎩ ⎪ ⎨ ⎧ ⋅<> ⋅>>⋅ < = iiiii iiiii iii i ySySS ySySy ySy S 3 and 2/ if; 3 and 2/ if;3 2/ if;2/ 111 11 1 2S if Si1 if Si1 if Si1 SSi1 SSi1 SSi1 = DIFi · LTi. ECONOMIC AND BUSINESS REVIEW | VOL. 11 | No. 2 | 2009112 Th e collected results have to be compared with the production status of the product, the ABC classifi cation and the safety stock in the previous year: (6) where XP means that the product can be produced. Finally, safety stock for the product is calculated by the following equation which takes into account the predicted growth of sales (r is the predicted growth of sales in the fol- lowing year (in %)): (7) For our selected product X we calculate (from equation (4)): SSX 1 =· 35 SSX 1 =· 35. Since 35 = SSX 1 > yx/2 = 9,5 and 35 = SSX 1 > 3·yx/2 = 57, we obtain (from equation (5)): SSX 2 = SSX 1 = 35. As product X with classifi cation A has an XP status, we obtain (from equation (6)): SSX 3 = SSX 3 = 35. If we assume that we will sell 550 units of product X in the next year, the predicted growth is 12% and the fi nal value of the safety stock is calculated with regard to equation (7): SSX 4 = SSX 3 √1,12 = 37. TABLE 2: Data for product X and results obtained with the existing method Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Actual sales 23 16 28 36 24 53 52 72 79 59 6 43 Month’s sales (in %) of the annual total 4.68 3.26 5.70 7.33 4.89 10.79 10.59 14.66 16.09 12.02 1.22 8.76 Forecast 27 27 34 30 20 30 44 43 40 55 45 28 Safety stock 37 37 37 37 37 37 37 37 37 37 37 37 »Pumping« from safety stock 0 0 0 6 4 23 8 29 39 4 0 15 As Table 2 shows, the monthly sales were between 1.22% and 16.09% of the annual to- tal, which means that sales are highly seasonal. In this case, the safety stock of 37 units would have seen a shortfall in the month of September of 2 [79 — (40+37)] units and over-estimated the safety stock for all of the out-of-season months. ⎪⎩ ⎪ ⎨ ⎧ =≠ ≠≠ = = − XPstatusCtionclassificaS XPstatusCtionclassificaS Ctionclassifica S i tii and if; and if; if;0 2 3 1, 3Si 2 Si,t-1; Si if if if P P 100 1 r+SSi 4 = SSi 3* LILJANA FERBAR TRATAR | MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING ... 113 2.2 Th e proposed method Th e standard method for calculating safety stock uses the targeted customer service level and cumulative forecast error over the most recent historical periods to determine the minimum amount of safety stock needed to cover sales until the next scheduled re- supply, which is computed as follows: 1. Compute the forecast deviation for each month. 2. Square each deviation. 3. Compute the standard deviation: , (8) where N is the number of observations. 4. Compute the safety stock: (9) where Z is the value based on customer service and LT means the lead time. However, the standard method for calculating safety stock does not give satisfactory results for the highly seasonal products we have in the company Danfoss District Heat- ing. Seasonality occurs across multiple months within a given year. However, looking at a given month across multiple years helps to account for seasonality. Based on this observation we propose a slight change in the method. Instead of calculating the stand- ard deviation across months within a given year, we calculate the standard deviation for a specifi c month across all available years. We then calculate the safety stock for each month independently. As mentioned, the safety stock depends on many factors and probably the most prob- lematic one is the diff erence between the forecast and actual sales. With the intention of achieving better demand forecasting, in our proposed method we use the additive Holt- Winter method which takes into account the trend, seasonality and the average worth value of the variable (e.g., Makridakis et al. 1998 and Winston, 1993). We optimise the forecast with regard to smoothing and initial parameters (the forecast results for product X are in Table 3), what is also our contribution to the article on which this research is based (Herrin, 2005) - the results obtained with the basic Herrin’s meth- od are not better from those calculated with the existing method. 1 Squared Deviations − = N σ SS = Z √LT · σ 2 ECONOMIC AND BUSINESS REVIEW | VOL. 11 | No. 2 | 2009114 TABLE 3: Comparison of actual sales and forecast as calculated by the additive Holt-Win- ter method for product X Months 2003 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Forecast Actual sale 9 20 8 15 44 50 47 25 29 50 11 7 Months 2004 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Forecast 37 23 29 36 36 37 45 59 50 42 16 18 Actual sale 42 31 36 33 39 36 38 62 41 48 43 9 Months 2005 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Forecast 24 11 17 25 27 29 39 55 48 43 18 20 Actual sale 31 10 13 32 43 21 50 53 46 42 27 28 Months 2006 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Forecast 29 17 24 34 37 38 50 67 61 58 36 36 Actual sale 23 16 28 36 24 53 52 72 79 59 6 43 To calculate the safety stock we must take the next four steps: 1. Instead of calculating the standard deviation across months within a given year (equation (8)), we now calculate the standard deviation for a specifi c month across all available years (equation (10)). In Table 4 you can fi nd the calculations for prod- uct X, where the actual and forecast data for the month of May in 2004-2006 are given. TABLE 4: Calculating the deviation between the forecast and actual sales Product X Sale Forecast Deviation Deviation squared May 2004 39 36 -3 9 May 2005 43 27 -16 256 May 2006 24 37 13 169 Sum 434 We calculate the deviation between sales and the forecast and use the following formula to calculate the standard deviation: (10) 1 squaredDeviation − ∑= N σ LILJANA FERBAR TRATAR | MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING ... 115 In our case, we obtain 2. To use the proposed method in a proper way, we also have to adjust the supply time of a product. Th e lead time (LT) of a product is usually in days and it must be recal- culated on a monthly basis. Th e supply time of the selected product is 18 days so the recalculated lead time is LT = 0,592 [18 days 18/(30.4167) 0.592 month (30.4167 = average number of days in one month (365/12)]. 3. Now we have to adjust the desired level of service. Since the product we are dealing with is an A class product, i.e. its related service level is 98%, we have to recalcu- late this using standard statistical tables. Assuming that sales fi t a normal distribu- tion, the Z value (which is based on customer service) can be obtained by using the NORMSINV function in Excel, which gives us Z = 2.054. 4. Finally, we calculate the safety stock by using equation (9): 3. COMPARISON OF THE EXISTING AND THE PROPOSED METHODS In this study, in which we have included 4,247 products, we calculated the safety stock for every product using both methods presented above and formed a cost model to examine which method is more cost-effi cient. Based on the reports gathered from the company and information acquired about the actual sales for the fi rst six months of 2007 (Demand plan and monthly sales, 2007), we formed a table with the amounts of sales, safety stock and sales forecast. If we defi ne [ ] max=+X {0,x}, we can calculate the costs using the following formula: , (11) where: C t = costs in period t Y t = actual sales in period t F t = sales forecast in period t SS t = safety stock in period t hc = holding costs sc = stockout costs We defi ned the expenses that have arisen according to calculated diff erence in the data. When there is a positive diff erence between the actual sales and the amount of the fore- casted sales and safety stock, we have holding costs (presumption: ch (holding cost) = 1 EUR). When there is a negative result, we have stockout costs (presumption: cs (stockout σ = √434/2 =· 14,73. SSX;May = Z* √LT*σ = 2,054 · √0,592·14,73 0 =· 230 2 2 ( )[ ] ( )[ ]++ +−+−+= tttstttht SFYcYSFcC ** ECONOMIC AND BUSINESS REVIEW | VOL. 11 | No. 2 | 2009116 cost) = EUR 2). Th e stockout costs are greater than the holding costs because a company that cannot carry out an order at any given moment loses some of its future orders and possible contracts with customers. Considering all the mentioned presumptions we obtain the results presented in Table 5. As is evident, the costs are lower if we use the proposed method for calculating the safety stock. TABLE 5: Total expenses (in EUR) due to the inconsistency between actual sales and the amounts of the forecast sales and safety stock Method/ Period Jan Feb Mar Apr May Jun Jul Σ Proposed method 81,275 88,936 92,449 86,720 103,822 117,606 100,591 671,399 Existing method 81,887 104,097 106,163 111,196 112,030 128,553 117,879 761,805 From the table above we can see that if we calculate the safety stock with the proposed method instead of the existing method the costs can be reduced by almost 12%. However, there are several disadvantages with regard to the proposed method. One of them is universality. It is a general method that works very effi ciently for those markets that can be labelled as more stable than others because they have recurring examples of demand for products. Th e market in which the company Danfoss District Heating operates experiences very sudden and unexpected changes so it can be described as very dynamic. But we have proven that its inventory costs could in any case be reduced. In addition, there are large companies that off er very similar products so the level of com- petition is very high. As a result of such an environment, a company is forced to seek every new opportunity for successful management. Entering a new market is one of these opportunities. In the last year Danfoss District Heating successfully entered the Asian market. It opened a new plant near Beijing to address needs arising in that area. Its success here is also shown in increased sales of products in the past year (the growth of sales was also noted for other markets). As the company expects further growth in its sales, the stocks should be adjusted to those bigger sales, too. If the company were to use the proposed method for calculating its safety stock it would have a more effi cient inventory policy. 4. CONCLUSION Th ere are many ways of reducing costs and they include setting the optimal level of safety stock. In this paper we present the infl uence of diff erent methods for calculating safety stock on inventory costs. At the moment, the proposed method can reduce the costs and keep the service level as was set in the existing method. If the safety stock were calculated by the proposed method, costs related to the safety stock would be approximately 11.87% lower than with the existing method. Due to diff erences between the existing and pro- LILJANA FERBAR TRATAR | MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING ... 117 posed methods, the proposed method has the potential to improve and reduce costs even more (growth is not yet included in the calculations, enhancing the universality of the method etc.). By including these parameters in the proposed method we are confi dent that we can reduce expenses related to safety stock even more and give the company Danfoss District Heating a chance of becoming more competitive than its competitors. RECEIVED: MAY 2008 REFERENCES Akkermans, H. A., Bogerd, P., Yücesan, E., van Wassenhove, L. N. (2003), “Th e impact of ERP on supply chain management: Exploratory fi ndings from a European Delphi study”, European Journal of Operational Research 146(2), 284–301. Gupta, M., Kohli, A. (2006), “Enterprise resource planning systems and its implications for operations func- tion”, Technovation 26, 687–696. Herrin, R. (2005), “How to calculate safety stocks for highly seasonal products”, Th e Journal of Business Fore- casting 24 (2), 6–10. Kelle, P., Akbulut, A. (2005), “Th e role of ERP tools in supply chain information sharing, cooperation, and cost optimization”, International Journal of Production Economics Volumes 93-94, 41–52. Makridakis, S., Wheelwright, S.C. and Hyndman, R.J. (1998), Forecasting: methods and applications, United States of America: John Wiley & Sons, Inc. Wild, T. (1997), Best practice in inventory management, United States of America, Woodhead Publishing Ltd. Winston, W.L. (1993), Operations Research: applications and algorithms, Belmont: Duxbury Press. Demand plan (2003-2007), Company’s internal report, Ljubljana. Monthly sale (2003-2007), Company’s internal monthly sales reports, Ljubljana.