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The Application Of Monte Carlo Simulation For Inventory .

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The Application of Monte Carlo Simulationfor Inventory Management:a Case Study of a Retail StoreSudawan Leepaitoon1and Chayut Bunterngchit2Division of Industrial and Logistics Engineering Technology,Faculty of Engineering and Technology,King Mongkut’s University of Technology North Bangkok, Rayong Campus, mutnb.ac.thAbstract - This research aimed to findeconomic order quantity and reorder pointof the inventory in a retail store under theuncertainty of lead time and demand. Fromthe past, the store manager purchased alarge amount of inventory to fulfill thecustomer demand without the appropriatetechniques, which led to over-inventory.The store had lost more than THB 1 Millionper year from the excess inventory. TheMonte Carlo Simulation was applied in thisresearch in order to determine the purchaseorder policy with the selected best salesgoods. The inventory goods was classifiedby using ABC analysis. This research wasonly focus on the class A goods because theyaffected almost all of the inventory cost. Asa result, 10 best sales goods in class A wereselected. Then collecting the data of thesales for those goods for 12 months. Aftersimulated the data for all selected goods andgained the optimal order quantity by usingMonte Carlo Simulation, it was found thatthe new economic order quantity and reorderpoint would save the inventory cost, whichwas currently incurred from THB 1,462,281.77to THB 371,142.73 per year or 74.62% ofreduction. In addition, the inventory wouldreduce from 46,166,784 units to 2,638,808units per year or 94.28% of reduction.I. INTRODUCTIONDue to the business survivability in thepresent day, it is necessary to maintain servicelevel and minimize cost. In the case of retailstores, the most important cost comes frominventory. To maintain the service level, goodsmust be available for customers at any time. Inorder to minimize inventory cost, the orderquantity of goods must be equal to customersdemand. If the order quantity is less thancustomers demand, the service level will bereduced. If the order quantity exceedscustomers demand, there will be sunk cost ofinventory, obsolescence of goods and excessstorage cost. Therefore, inventory managementis an important factor for business achievement ofretail stores.To do this research, a retail store has beenchosen to be a case study. In the past, the storehad lost more than THB 1 Million per yearfrom the excess inventory. Therefore, it wasneeded to solve the problem. By collecting thedata, there were 10,218 stock keeping unit(SKU) in the retail store that can be classifiedinto three classes (A, B, and C) by using ABCanalysis. Class A accounted for a largeproportion of the overall sales but a smallpercentage of the number of items. Class Band class C had less overall sales but had aKeywords - Monte Carlo Simulation, higher percentage of the number of items thanclass A respectively. As a result, there wereInventory Management, Retail Store230 SKU (70% of sales) in class A, 1,496SKU (20% of sales) in class B and 8,492 SKUInternational Journal of the Computer, the Internet and Management Vol.27 No.2 (May-August, 2019) pp. 76-8376

Sudawan Leepaitoon and Chayut Bunterngchit(10% of sales) in class C as shown in Fig. 1.Fig. 1 Goods Classification by ABC AnalysisThis research focused only 10 most salesgoods (10 SKU) in class A which were A1008,B6011, C0414, D0613, E0803, F0797, G3002,H0483, I0377, and J0155 as shown in Table I.Customers demand and order quantity fromAugust 2016 to July 2017 of each item areshown in Fig. 2.TABLE IFOCUSED GOODS (10 SKU)Barcode of 17000048388547960003778850170000155Representative 0155Fig. 2 Customers Demand and Order Quantityfrom August 2016 to July 2017TABLE IISUNK COST OF FOCUSED GOODSQuantity (Units)No.From Fig. 2, it can be concluded that theretail store ordered goods more than customerdemand, which led to over-inventory. The totalinventory for 10 goods was 151,057 units peryear and the sunk cost of inventory was THB7,871,650 per year as shown in Table II.GoodsDemandOrderQuantityInventory(Unitsper year)SunkCost(THBper alInternational Journal of the Computer, the Internet and Management Vol.27 No.2 (May-August, 2019) pp. 76-8377

The Application of Monte Carlo Simulation for Inventory Management: a Case Study of a Retail StoreThe data in Table II only showed sunk costof 10 goods, the total sunk cost of all goodsshould be higher than that. Therefore, theimprovement of inventory management isneeded for this retail store.II. LITERATURE REVIEWSlarge amount of random number to obtainnumerical results. The key of simulation is torepeat random sampling many times to gainthe least deviation [5]. Peterson, Sui and Heiser[6], Marcoulaki, Broulias and Chondrocoukis [7]and Tsige [8] simulated Monte Carlo Simulation toimprove order-picking efficiency. Muansrichai[9] applied Monte Carlo Simulation toautomotive industry to find the EOQ and ROPunder uncertainties. As a result, the inventorycost was reduced approximately 26% perquarter comparing to the traditional purchasingpolicy. Phupha [10], Rujirawisarut [11],Manchu [12] and Chaimunin [13] also appliedMonte Carlo Simulation to calculate EOQ ofprocessed food industry, retail company,pallet-manufacturing factory, and petrochemicalindustry respectively. The total inventory costwas reduced by 38.35%, 54%, 9.28%, and 22%respectively.Inventory management is one of logisticsactivities, which can utilize the space forgoods storage. The goal is to find the methodto minimize the space but still meet thecustomers demand and service level. However,many firms decided to order a large amount ofgoods in order to get lower price even thoughonly some of them could be sold. To decreasethe unnecessary order, ABC Classification isan approach which has been applied to analyzethe importance of each item of goods andprioritize them. Tanwari, Lakhiar, and Shaikh[1] applied ABC Classification to manage thespare parts in a warehouse, which could reduceFrom the reviews above, it can be concluded thatthe storage space of those spare parts. After Monte Carlo Simulation is an appropriatethat, Economic Order Quantity (EOQ) and approach to calculate EOQ under uncertaintyreorder point (ROP) should be calculated to lead time and demand.reach the goal of inventory management.III. RESEARCH METHODOLOGYIn real life, the customers demand and leadtime of goods are uncertainties. The companyThe case study of this research hadshould have safety stock to feed customers. uncertainty demand and lead time as shown inStatistical data is used to calculate safety stock Table III and Table IV. Therefore, Montebased on seasonal demand or trend. Tamwai Carlo Simulation was applied to calculate[2] calculated safety stock based on statistical EOQ and ROP.seasonal demand, based on median absoluteMonte Carlo Simulation started by calculatingdeviation varies over time, and based ontheranges of random number and thenhighest demand. Then Monte Carlo techniquewas applied to simulate the sales behaviors. generating random number according to thatThe simulation result showed that 56% of range. The ranges of random number for dailyaverage inventory and holding cost could be demand and lead time of A1008 are shown incut. Total inventory cost could be calculated Table III and Table IV respectively.from ordering cost, unit cost, holding cost, andFrom Table III, Probability of 153 units ofshortage cost. Sedtakomkul [3] and Vararittichai [4]applied ABC analysis and then calculated demand of A1008 was 1 / 323 0.003096.EOQ and ROP by implementing Monte Carlo Then did the same procedure for all dailySimulation. The result showed that 7.4% and demand to find the ranges of random number.71% of total inventory cost per year wasFrom Table IV, probability of 1-day leadreduced comparing to the traditional purchasingtime of A1008 was 41 / 121 0.33884. Thenpolicy respectively.did the same procedure for all lead time to findMonte Carlo Simulation has been widely the ranges of random number.used for inventory management by generate aInternational Journal of the Computer, the Internet and Management Vol.27 No.2 (May-August, 2019) pp. 76-8378

Sudawan Leepaitoon and Chayut BunterngchitTABLE IIIRANGES OF RANDOM NUMBER OF ANNUAL DEMANDDaily Demand(Units per 2.11323ProbabilityCumulative ProbabilityRanges of Random Number 09610.0030960.0061920.009288.0.074303.0.99690410 r 0.0030960.003096 r 0.0061920.006192 r 0.009288.0.068111 r 0.074303.0.993808 r 0.9969040.996904 r 1TABLE IVRANGES OF RANDOM NUMBER OF LEAD TIMELead 21ProbabilityCumulative Probability Ranges of Random Number 462810.61157.0.82645.1To calculate ROP, Lordahl and Bookbinder’sapproach [14] was applied by resequencing thedemand of customer from smallest to largest.The sequenced demand is shown in Table V. n 1 P Xy(1)n; ROP (1 ) X y X y 1 (2)is the number of data.Pdenote customer service level (95%).Xy is the demand of yth.ω n 1 P (323 1) x 0.95 307.8307.8 323 So, y nROP (1 0.8)(1375) 0.8(1426) 1415.8 1416 unitsMaximum, minimum and average of thedata from Table V were calculated to be theinput for Monte Carlo Simulation to find EOQ.From Table V, maximum, minimum andaverage of the data were 1,914, 153, and 762units respectively.wherenFrom the data in Table V using (1) and (2):Thus, y 307 and 0.8 .The approach showed that if: n 1 P n; ROP0 r 0.338840.33884 r 0.462810.46281 r 0.61157.0.72727 r 0.82645.0.99174 r 1After that, random number (20,000 times)was generated by using RAND() in MicrosoftExcel. Then, the ranges of random number inTable III and IV were used for identifyingdemand and lead time of that random numberby using VLOOKUP() in Microsoft Excel asshown in Table VI.is the decimal of (n 1)P.International Journal of the Computer, the Internet and Management Vol.27 No.2 (May-August, 2019) pp. 76-8379

The Application of Monte Carlo Simulation for Inventory Management: a Case Study of a Retail StoreFrom Table VI, the first column is workingday of a retail store. The second column showsthe number of starting inventory of the day.The third column shows the EOQ frommaximum, minimum and average value ofTable V, but this table shows only themaximum value. The fourth column is randomnumber of demand. The fifth column is theamount of demand according to Table III. Thesixth column shows whether the amount ofstarting inventory is higher than demand ornot. If the demand is higher than startinginventory, it will lead to shortage in theseventh column. The eighth column is theremaining inventory, which is the differencebetween starting inventory and demand. Theninth column shows the order decision. If theremaining inventory is less than ROP, the retailstore has to order on amount of EOQ. Thetenth column shows random number of leadtime. The eleventh column is lead timeaccording to Table IV. The twelfth column isthe arrival day calculated by starting day pluslead time.TABLE VSMALLEST TO LARGEST SEQUENCED 3156215831638164516901718173718001914The thirteenth column is total inventorycost, which can be calculated by: DP QH TC nCS Q 2 International Journal of the Computer, the Internet and Management Vol.27 No.2 (May-August, 2019) pp. 76-8380(3)

Sudawan Leepaitoon and Chayut BunterngchitwhereFor item A1008, by substituting (3),ordering cost is 20.83 THB/order calculatedTC denotes total inventory cost [THB].from salary of employee and ordering time.Carrying cost equals 0.03 THB/unit calculatedD denotes annual demand [unit/year].from salary of warehouse keepers. Shortagecost (CS) equals 3 THB/unit calculated fromP denotes setup or ordering cost for each the loss of profit. Total inventory cost afterorder [THB].20,000 replications of Monte Carlo Simulationis 140,133.09 THB/year.Q denotes number of pieces per order [unit].HnCSTo prove that 20,000 replications ofdenotes holding or carrying cost per unitsimulation is not vary, the fourteenth andper year [THB/unit*year].fifteenth column are used to find thecumulative error of each replication. Then, plotdenotes shortages [unit].all 20,000 replications into a graph as shown inFig. 3.denotes shortage cost [THB/unit].TABLE VIMONTE CARLO SIMULATION OF A1008CumulativeAverageErrorDayInventory OrderRandomDemandNumberCheck ShortageRemaining OrderRandom LeadInventory Decision Number TimeArrivalDayTotal CostAverageCost1191400.08922 4224220149200.26921 1044.7644.762149200.54476 723723076910.8936843.944.33376900.74085 908090876910.04736 142767.9952.18667 -907.85667476919140.49842 6906900199300.99545 14059.79729.0875223.0991675199300.21494 5145140147900.91635 6044.37592.144136.94356147900.96199 1462146201710.19229 1721.34497.0195.13471719140.09394 4340434193100.07258 101359.93620.28429 -123.274298193119140.25015 5395390330600.55597 3099.18555.14625 65.13803579330600.19442 4914910281500.78756 5084.45502.84667 52.299583310281500.40755 6346340218100.43237 2065.43459.10543.7416667.1999554100.63334 792079254110.57214 3199982413.06590.39824 -0.09116041999654119140.61962 7850785245500.30295 102428.65590.49017 -0.09193119997245519140.73197 9059050346400.72827 50103.92590.46583 0.0243321619998346419140.60526 7727720460600.46163 20138.18590.44322 0.0226165519999460600.11301 4454450416100.54578 30124.83590.41994 0.0232818220000416100.63395 7927920336900.63852 40101.07590.39547 0.0244675.0.43cumulative average error will occur. Therefore,the simulation of 20,000 replications is goodenough to use in this model.IV. RESULTSAfter substituting the maximum value ofTable V with difference EOQ policies (minimumand average value), total inventory cost couldbe changed as shown in Table VII. Also, doFig. 3 Cumulative Average Error of A1008the same method to all focused goodsFig. 3, shows that the cumulative average (10SKU). The result is shown in Table VII.error is convergence. The more number ofAfter that, apply the appropriate EOQsimulation is performed, the less deviation ofpolicy to each focused goods by using theInternational Journal of the Computer, the Internet and Management Vol.27 No.2 (May-August, 2019) pp. 76-8381

The Application of Monte Carlo Simulation for Inventory Management: a Case Study of a Retail Storepolicy that incur the lowest cost. The result isThis research is only focus on the goods inshown in Table VIII.class A. If apply the same method to all 10,218SKU of goods, the case study retail storeTABLE VIIwould reduce more money and inventoryCOMPARISON OF TOTAL INVENTORY COSTspace. Moreover, space utilization of this storeFOR 3 EOQ POLICYwill be increased.EOQ [unit/order] and T otal Inventory Cost (T C)(T 3,031 6115,463J0155240,2245216,5251596,686T otal Cost[T HB d in the order of citation in thesame fashion as the case of Footnotes.)[1][2]387,935.20[3]TABLE VIIIAPPROPRIATE EOQ AND TOTAL INVENTORYCOST FOR EACH FOCUSED GOODSGoodsEOQ [unit/order]TC I0377J0155Total .73V. CONCLUSION AND DISCUSSIONIf the case study retail store apply this newEOQ policy found by using Monte Carlo [7]Simulation, it could reduce total inventory costfrom THB 1,462,281.77 per year to THB371,142.73 per year (74.62% reduction).Moreover, inventory could reduce from46,166,784 units per year to 2,638,808 unitsper year (94.28% reduction). The retail store [8]would have more space for doing otheractivities.Tanwari, A., Lakhiar, A.Q., and Shaikh,G.Y. (2000). “ABC Analysis as aInventory Control Technique”. QUESTJournal of Engineering, Science &Technology, Vol. 1(1).Tamwai, A. (2014). “Identifying theOptimal Safety Stock Level by UsingMonte Carlo Simulation: A Case Studyof Consumer Products”. (Master’s thesis),RMUTT, Pathum Thani, Thailand.Sedtakomkul, N. (2011). “The AppliedMonte Carlo Simulation to ReorderPoint and Order Quantity for Purchasingunder Uncertainties of Demand”.(Master’s thesis), KMUTNB, Bangkok,Thailand.Vararittichai, P. (2010). “The MonteCarlo Application for the Order Quantityand Reorder Point Optimistic”. (Master’sthesis), KMUTNB, Bangkok, Thailand.Hillier, F.S. and Hillier, M. (2014).“Introduction to Management Science”.Boston: McGraw-Hill.Peterson, C.G., Siu, C., and Heiser, D.R.(2005). “Improving order picking performanceutilizing slotting and golden zonestorage”. International Journal of Operations& Production Management, Vol. 25(10),pp. 997-1012.Marcoulaki, E.C., Broulias, G.P., andChondrocoukis, G.P. (2005). “Optimizingwarehouse arrangement using orderpicking data and Monte CarloSimulation”. Journal of InterdisciplinaryMathematics, Vol. 8(2) pp. 253-263.Tsige, M.T. (2013). “Improving OrderPicking Efficiency via Storage AssignmentStrategies”. (Master’s thesis), Universityof Twente, Twente, Netherlands.International Journal of the Computer, the Internet and Management Vol.27 No.2 (May-August, 2019) pp. 76-8382

Sudawan Leepaitoon and Chayut Bunterngchit[9][10][11][12][13][14]Muansrichai, J. (2009). “The EconomicOrder Quantity under Uncertainties byMonte Carlo Simulation Method”.(Master’s thesis), KMUTNB, Bangkok,Thailand.Phupha, V. (2014). “An Application ofMonte Carlo Simulation for OptimalOrder Quantity: A Case Study of RawMaterials Procurement in ProcessedFood Industry”. Kasetsart EngineeringJournal, Vol. 27(88), pp. 41-56.Rujirawisarut, P. (2013). “Improvementfor Appropriate Purchasing Method byUsing Monte Carlo Simulation: CaseStudy of XYZ Retailer Company”.(Master’s thesis), Burapha University,Chonburi, Thailand.Manchu, W. (2011). “An Application ofMonte Carlo Simulation for OptimalOrder Quantity A Case Study of RubberWood Procurement in Pallet Industry”.(Master’s thesis), KMUTNB, Bangkok,Thailand.Chaimunin, T. (2009). “The Applicationof Monte Carlo Technique for VendorManagement Inven

economic order quantity and reorder point of the inventory in a retail store under the uncertainty of lead time and demand. From the past, the store manager purchased a large amount of inventory to fulfill the customer demand without the appropriate techniques, which led to over-inventory.