MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING THE LEVEL OF SAFETY STOCK

ECONOMIC AND BUSINESS REVIEW VOL. No. 2 2009 09 7 09 MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING THE LEVEL OF SAFETY STOCK LILJANA FERBAR TRATAR* ABSTRACT: Markets are everyday becomng ever more demandng and companes are adjustng n dfferent ways. The objectve of forecastng n a demand-drven supply network s to dentfy the probable range of expected demand so that supply can cover demand anywhere wthn the statstcal range. Supply can cover the range ether through havng the capacty to replensh wthn lead tmes or by carryng excess nventory (safety stock). Nowadays, many companes put a lot of ther energy and fnance nto settng the rght level of safety stock and reducng related expenses. In ths paper, we mprove an exstng method for calculatng the safety stock for a partcular Slovenan company. We present the exstng and proposed methods for calculatng safety stock and derve a cost model. Fnally, we prove that the proposed method not only reduces average costs but also helps to meet the target customer servce level makng t also applcable to other Slovenan companes encounterng stuatons where demand s seasonal. Keywords: Safety stock; Inventory; Cost model; Optmsaton UDC: 330.522.4 JEL classfcaton: G3; C6. INTRODUCTION The objectve of forecastng n a demand-drven supply network s to dentfy the probable range of expected demand so that supply can cover demand anywhere wthn the statstcal range. Supply can cover the range ether through havng the capacty to replensh wthn lead tmes or by carryng excess nventory (safety stock). Safety stock s the amount of materal needed to compensate for supply and demand neffcences. In an organsaton where marketng s tasked wth growng the market, and supply s tasked wth reducng workng captal, the decson on the amount of safety stock to carry can become very contentous. * Unversty of Ljubljana, Faculty of Economcs,,Kardeljeva ploščad 7, 000 Ljubljana, Slovena, Emal: lljana.ferbar@ef.un-lj.s

0 ECONOMIC AND BUSINESS REVIEW VOL. No. 2 2009 Companes are aware of the mportance of safety stock so they set t n many dfferent ways. Unfortunately, there s no unversal method that would yeld the optmal level of safety stock. As a result, many companes set ther level of safety stock n relaton to actual sales n the past year. Most safety stock calculatons wthn ERP systems use standard APICS calculaton methods (Akkermans, et al. (2003), Kelle and Akbulut (2005), Gupta and Kohl (2006) et al.). These methods appear to work well for stuatons where demand s stable, but not for stuatons where demand s seasonal. The objectve of ths paper s to propose an alternate method for calculatng safety stock for seasonal products n order to reduce total costs and retan the servce level accordng to the company s polcy (as s establshed n the exstng method). The paper s organsed as follows. Frst, we present the exstng method for calculatng safety stock, whch s used by Danfoss Dstrct Heatng, a Slovenan company. Then we descrbe the proposed method for calculatng safety stock for seasonal products, whch s an extenson of Herrn s method (Herrn, 2005). In the thrd chapter, we derve a cost model n order to compare the exstng and proposed method. Fnally, based on our study n whch we have ncluded 4,247 products we prove that the proposed method for calculatng safety stock can reduce average costs by almost 2%. 2. CALCULATION OF SAFETY STOCK The optmal level of safety stock s related to many components and some of them can hardly be controlled (Wnston, 993). Ths paper wll only address the demand component or amount needed to cover the nherent varablty n the sales forecast. 2. The exstng method To calculate safety stock accordng to the exstng method used n the company Danfoss Dstrct Heatng we have to rely on sales n the prevous year. At the begnnng we must dvde a year nto 4-day perods and count out the number of products to be sold per perod (see Table ). TABLE : Yearly sales for 2006 for product X dvded nto 4-day perods Perod 2 3 4 5 6 7 8 9 0 2 3 4 5 6 7 8 9 20 2 22 23 24 25 26 Sale 2 2 3 3 4 4 22 4 8 6 33 20 24 28 4 3 3 48 43 6 4 2 7 8 3 5 After dong ths, we calculate the average sales for each product : salesyear y = 26 In our case, the average sales for product X s 9 (rounded value). ()

LILJANA FERBAR TRATAR MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING... Then we have to sort the quanttes by ascendng the value of sales and calculate the percentle of the sorted values accordng to an ABC classfcaton and related servce level. The company classfes ts products n A, B or C classes. Ths classfcaton depends on the prce and predcted number of orders n the next year (products wth classfcaton A have more than 48 orders per year and products wth classfcaton C have fewer than 5 orders n one year). If the selected product s n class A the related servce level (accordng to the company polcy) s 98% (products n class B have a servce level of 90% and the servce level for class C products s 0% as they are only made when specally demanded by the customer). Ths means that 98% of the market demand can be covered by products that are n the warehouse. Now we compare average sales and sales n the 98th percentle (because the related servce level s 98%). If the rato s greater than :5, we have to calculate the sales value at the 90th percentle. Wth ths correcton we elmnate products wth a hgh devaton. In our case, for product X, wth classfcaton A, the sales value at the 98th percentle s 50 (y X;0,98 = 50). Snce the rato y X;0,98 /y X = 50/9 = 2,6 s less than 5, product X s a product wth a low devaton and ts servce level s 98%. After that, we calculate the dfference between the maxmal admssble value at the 98th (or 90th) percentle (NPVN ) and average sales: DIF = NPVN y. (2) In our case, the value of NPVN X s 50 and the dfference s DIF X = 3. The supply tme of the product (lead tme) s also taken nto account. Usually the lead tme (LT ) s n days so we have to recalculate t on a 4-day bass: LT = lead _tme(n _days) 4 (3) The supply tme of the selected product X s 8 days, so LT X = 8/4 =,3389. The next step s multplyng the calculated dfference and lead tme to obtan the frst value of safety stock: SS = DIF LT. (4) Then we have to consder some oblgatons such as: SSS 2 y / 2; = 3 y; S ; S f SS f S f SS f f SS S < y > y > y / 2 / 2 / 2 and and SSS SSS > 3 y < 3 y (5)

2 ECONOMIC AND BUSINESS REVIEW VOL. No. 2 2009 The collected results have to be compared wth the producton status of the product, the ABC classfcaton and the safety stock n the prevous year: 0; f f 23 SS S = SS 3 t ; ; f f,t- 2 SSS ; f f classfcaton = C classfcaton C and status XP classfcaton C and status = XP (6) where XP means that the product can be produced. Fnally, safety stock for the product s calculated by the followng equaton whch takes nto account the predcted growth of sales (r s the predcted growth of sales n the followng year (n %)): SS 4 = SS 3 * r + 00 For our selected product X we calculate (from equaton (4)): SS X = 35 SS X = 35. Snce 35 = SS X > yx/2 = 9,5 and 35 = SS X > 3 yx/2 = 57, we obtan (from equaton (5)): SS X 2 = SS X = 35. As product X wth classfcaton A has an XP status, we obtan (from equaton (6)): SS X 3 = SS X 3 = 35. If we assume that we wll sell 550 unts of product X n the next year, the predcted growth s 2% and the fnal value of the safety stock s calculated wth regard to equaton (7): SS X 4 = SS X 3,2 = 37. (7) TABLE 2: Data for product X and results obtaned wth the exstng method Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Actual sales 23 6 28 36 24 53 52 72 79 59 6 43 Month s sales (n %) of the annual total 4.68 3.26 5.70 7.33 4.89 0.79 0.59 4.66 6.09 2.02.22 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»Pumpng«from safety stock 0 0 0 6 4 23 8 29 39 4 0 5 As Table 2 shows, the monthly sales were between.22% and 6.09% of the annual total, whch means that sales are hghly seasonal. In ths case, the safety stock of 37 unts would have seen a shortfall n the month of September of 2 [79 (40+37)] unts and over-estmated the safety stock for all of the out-of-season months.

LILJANA FERBAR TRATAR MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING... 3 2.2 The proposed method The standard method for calculatng safety stock uses the targeted customer servce level and cumulatve forecast error over the most recent hstorcal perods to determne the mnmum amount of safety stock needed to cover sales untl the next scheduled resupply, whch s computed as follows:. Compute the forecast devaton for each month. 2. Square each devaton. 3. Compute the standard devaton: Devatons Squared σ =, (8) N where N s the number of observatons. 4. Compute the safety stock: SS = Z LT σ 2 (9) where Z s the value based on customer servce and LT means the lead tme. However, the standard method for calculatng safety stock does not gve satsfactory results for the hghly seasonal products we have n the company Danfoss Dstrct Heatng. Seasonalty occurs across multple months wthn a gven year. However, lookng at a gven month across multple years helps to account for seasonalty. Based on ths observaton we propose a slght change n the method. Instead of calculatng the standard devaton across months wthn a gven year, we calculate the standard devaton for a specfc month across all avalable years. We then calculate the safety stock for each month ndependently. As mentoned, the safety stock depends on many factors and probably the most problematc one s the dfference between the forecast and actual sales. Wth the ntenton of achevng better demand forecastng, n our proposed method we use the addtve Holt- Wnter method whch takes nto account the trend, seasonalty and the average worth value of the varable (e.g., Makrdaks et al. 998 and Wnston, 993). We optmse the forecast wth regard to smoothng and ntal parameters (the forecast results for product X are n Table 3), what s also our contrbuton to the artcle on whch ths research s based (Herrn, 2005) - the results obtaned wth the basc Herrn s method are not better from those calculated wth the exstng method.

4 ECONOMIC AND BUSINESS REVIEW VOL. No. 2 2009 TABLE 3: Comparson of actual sales and forecast as calculated by the addtve Holt-Wnter method for product X Months 2003 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Forecast Actual sale 9 20 8 5 44 50 47 25 29 50 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 6 8 Actual sale 42 3 36 33 39 36 38 62 4 48 43 9 Months 2005 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Forecast 24 7 25 27 29 39 55 48 43 8 20 Actual sale 3 0 3 32 43 2 50 53 46 42 27 28 Months 2006 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Forecast 29 7 24 34 37 38 50 67 6 58 36 36 Actual sale 23 6 28 36 24 53 52 72 79 59 6 43 To calculate the safety stock we must take the next four steps:. Instead of calculatng the standard devaton across months wthn a gven year (equaton (8)), we now calculate the standard devaton for a specfc month across all avalable years (equaton (0)). In Table 4 you can fnd the calculatons for product X, where the actual and forecast data for the month of May n 2004-2006 are gven. TABLE 4: Calculatng the devaton between the forecast and actual sales Product X Sale Forecast Devaton Devaton squared May 2004 39 36-3 9 May 2005 43 27-6 256 May 2006 24 37 3 69 Sum 434 We calculate the devaton between sales and the forecast and use the followng formula to calculate the standard devaton: σ = Devaton squared N (0)

LILJANA FERBAR TRATAR MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING... 5 In our case, we obtan σ = 434/2 = 4,73. 2. To use the proposed method n a proper way, we also have to adjust the supply tme of a product. The lead tme (LT) of a product s usually n days and t must be recalculated on a monthly bass. The supply tme of the selected product s 8 days so the recalculated lead tme s LT = 0,592 [8 days 8/(30.467) 0.592 month (30.467 = average number of days n one month (365/2)]. 3. Now we have to adjust the desred level of servce. Snce the product we are dealng wth s an A class product,.e. ts related servce level s 98%, we have to recalculate ths usng standard statstcal tables. Assumng that sales ft a normal dstrbuton, the Z value (whch s based on customer servce) can be obtaned by usng the NORMSINV functon n Excel, whch gves us Z = 2.054. 4. Fnally, we calculate the safety stock by usng equaton (9): 2 2 SS X;May = Z* LT*σ = 2,054 0,592 4,73 0 = 230 3. COMPARISON OF THE EXISTING AND THE PROPOSED METHODS In ths study, n whch we have ncluded 4,247 products, we calculated the safety stock for every product usng both methods presented above and formed a cost model to examne whch method s more cost-effcent. Based on the reports gathered from the company and nformaton acqured about the actual sales for the frst sx months of 2007 (Demand plan and monthly sales, 2007), we formed a table wth the amounts of sales, safety stock and sales forecast. + If we defne [ X ] = max where: C t = costs n perod t Y t = actual sales n perod t F t = sales forecast n perod t SS t = safety stock n perod t c h = holdng costs c s = stockout costs {0,x}, we can calculate the costs usng the followng formula: [( F + S ) Y ] + + c [ Y ( F + S )] + C t = ch * t t t s * t t t, () We defned the expenses that have arsen accordng to calculated dfference n the data. When there s a postve dfference between the actual sales and the amount of the forecasted sales and safety stock, we have holdng costs (presumpton: c h (holdng cost) = EUR). When there s a negatve result, we have stockout costs (presumpton: c s (stockout

6 ECONOMIC AND BUSINESS REVIEW VOL. No. 2 2009 cost) = EUR 2). The stockout costs are greater than the holdng costs because a company that cannot carry out an order at any gven moment loses some of ts future orders and possble contracts wth customers. Consderng all the mentoned presumptons we obtan the results presented n Table 5. As s evdent, the costs are lower f we use the proposed method for calculatng the safety stock. TABLE 5: Total expenses (n EUR) due to the nconsstency between actual sales and the amounts of the forecast sales and safety stock Method/ Perod Jan Feb Mar Apr May Jun Jul Σ Proposed method 8,275 88,936 92,449 86,720 03,822 7,606 00,59 67,399 Exstng method 8,887 04,097 06,63,96 2,030 28,553 7,879 76,805 From the table above we can see that f we calculate the safety stock wth the proposed method nstead of the exstng method the costs can be reduced by almost 2%. However, there are several dsadvantages wth regard to the proposed method. One of them s unversalty. It s a general method that works very effcently for those markets that can be labelled as more stable than others because they have recurrng examples of demand for products. The market n whch the company Danfoss Dstrct Heatng operates experences very sudden and unexpected changes so t can be descrbed as very dynamc. But we have proven that ts nventory costs could n any case be reduced. In addton, there are large companes that offer very smlar products so the level of competton s very hgh. As a result of such an envronment, a company s forced to seek every new opportunty for successful management. Enterng a new market s one of these opportuntes. In the last year Danfoss Dstrct Heatng successfully entered the Asan market. It opened a new plant near Bejng to address needs arsng n that area. Its success here s also shown n ncreased sales of products n the past year (the growth of sales was also noted for other markets). As the company expects further growth n ts sales, the stocks should be adjusted to those bgger sales, too. If the company were to use the proposed method for calculatng ts safety stock t would have a more effcent nventory polcy. 4. CONCLUSION There are many ways of reducng costs and they nclude settng the optmal level of safety stock. In ths paper we present the nfluence of dfferent methods for calculatng safety stock on nventory costs. At the moment, the proposed method can reduce the costs and keep the servce level as was set n the exstng method. If the safety stock were calculated by the proposed method, costs related to the safety stock would be approxmately.87% lower than wth the exstng method. Due to dfferences between the exstng and pro-

LILJANA FERBAR TRATAR MINIMISING INVENTORY COSTS BY PROPERLY CHOOSING... 7 posed methods, the proposed method has the potental to mprove and reduce costs even more (growth s not yet ncluded n the calculatons, enhancng the unversalty of the method etc.). By ncludng these parameters n the proposed method we are confdent that we can reduce expenses related to safety stock even more and gve the company Danfoss Dstrct Heatng a chance of becomng more compettve than ts compettors. RECEIVED: MAY 2008 REFERENCES Akkermans, H. A., Bogerd, P., Yücesan, E., van Wassenhove, L. N. (2003), The mpact of ERP on supply chan management: Exploratory fndngs from a European Delph study, European Journal of Operatonal Research 46(2), 284 30. Gupta, M., Kohl, A. (2006), Enterprse resource plannng systems and ts mplcatons for operatons functon, Technovaton 26, 687 696. Herrn, R. (2005), How to calculate safety stocks for hghly seasonal products, The Journal of Busness Forecastng 24 (2), 6 0. Kelle, P., Akbulut, A. (2005), The role of ERP tools n supply chan nformaton sharng, cooperaton, and cost optmzaton, Internatonal Journal of Producton Economcs Volumes 93-94, 4 52. Makrdaks, S., Wheelwrght, S.C. and Hyndman, R.J. (998), Forecastng: methods and applcatons, Unted States of Amerca: John Wley & Sons, Inc. Wld, T. (997), Best practce n nventory management, Unted States of Amerca, Woodhead Publshng Ltd. Wnston, W.L. (993), Operatons Research: applcatons and algorthms, Belmont: Duxbury Press. Demand plan (2003-2007), Company s nternal report, Ljubljana. Monthly sale (2003-2007), Company s nternal monthly sales reports, Ljubljana.