Special Inventory ModelsSpecial Inventory ModelsSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Application D.1Application D.1 continuedSlide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Application D.2Application D.2 SolutionSlide 24Slide 25Slide 26Slide 27Solved Problem 1Slide 29Solved Problem 3Slide 31© 2007 Pearson EducationSpecial Inventory ModelsSupplement DSupplement D© 2007 Pearson EducationSpecial Inventory ModelsThree common situations require relaxation of one or more of the assumptions on which the EOQ model is based. Noninstantaneous Replenishment occurs when production is not instantaneous and inventory is replenished gradually, rather than in lots.Quantity Discounts occur when the unit cost of purchased materials is reduced for larger order quantities.One-Period Decisions: Retailers and manufacturers of fashion goods often face situations in which demand is uncertain and occurs during just one period or season.© 2007 Pearson EducationIf an item is being produced internally rather than purchased, finished units may be used or sold as soon as they are completed, without waiting until a full lot is completed.Production rate, p, exceeds the demand rate, d. Cycle inventory accumulates faster than demand occursa buildup of p – d units occurs per time period, continuing until the lot size, Q, has been produced.Noninstantaneous Replenishment© 2007 Pearson EducationProduction quantityProduction quantityDemand during Demand during production intervalproduction intervalMaximum inventoryMaximum inventoryProduction Production and demandand demandDemand Demand onlyonlyTBOTBOOn-hand inventoryOn-hand inventoryQQTimeTimeIImaxmaxp – dNoninstantaneous Replenishment© 2007 Pearson EducationCycle inventory is no longer Q/2, as it was with the basic EOQ method; instead, it is the maximum cycle inventory (Imax / 2)Noninstantaneous ReplenishmentC = ( ) + (S)DQQ p – d2 pD = annual demandd = daily demandp = production rateS = setup costsQ = ELS Imax = (p – d) = Q( )Qpp – dpTotal annual cost (C) = Annual holding cost + annual ordering or setup cost© 2007 Pearson EducationEconomic production lot size (ELS) is the optimal lot size in a situation in which replenishment is not instantaneous.Economic Lot Size (ELS)ELS =pp – d2DSHD = annual demandd = daily demandp = production rateS = setup costsH = annual unit holding cost© 2007 Pearson EducationFinding the ELSFinding the ELSExample D.1Example D.1The manager of a chemical plant must determine the following for a particular chemical:1. Determine the economic production lot size (ELS).2. Determine the total annual setup and inventory holding costs. 3. Determine the TBO, or cycle length, for the ELS.4. Determine the production time per lot.•What are the advantages of reducing the setup time by 10 percent?Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/year© 2007 Pearson EducationELSELS = = pppp – – dd22DSDSHHFinding the ELS for the Finding the ELS for the Example D.1Example D.1 chemical chemical Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/yearELSELS = = 190190190190 – – 30302(2(10,50010,500)()($200$200))$0.21$0.21ELSELS = 4873.4 barrels = 4873.4 barrelsD = annual demandd = daily demandp = production rateS = setup costsH = unit holding costQ = ELS© 2007 Pearson EducationFinding the Finding the Total Annual Cost Total Annual Cost Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/yearD = annual demandd = daily demandp = production rateS = setup costsH = unit holding costQ = ELS CC = = ( ( ))((HH) + () + (SS))DDQQQ Q pp – – d2 2 pp CC = = ( ( )) ($0.21) + ( ($0.21) + ($200$200))10,50010,5004873.44873.44873.4 4873.4 190190 – – 30 2 2 190190CC = $430.91 + $430.91 = $430.91 + $430.91CC = $861.82 = $861.82Example D.1Example D.1© 2007 Pearson EducationFinding the TBO Finding the TBO Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/yearD = annual demandd = daily demandp = production rateS = setup costsH = unit holding costQ = ELS TBOTBOELSELS = (350 days/year) = (350 days/year)ELSELSDDTBOTBOELSELS = (350 days/year) = (350 days/year)4873.44873.410,50010,500TBOTBOELSELS = 162.4, or 162 days = 162.4, or 162 daysExample D.1Example D.1© 2007 Pearson EducationFinding the Finding the Production Time per Lot Production Time per Lot Demand = 30 barrels/day Setup cost = $200Production rate = 190 barrels/day Annual holding cost = $0.21/barrelAnnual demand = 10,500 barrels Plant operates 350 days/yearD = annual demandd = daily demandp = production rateS = setup costsH = unit holding costQ = ELS Production time = Production time = ELSELSppProduction time = Production time = 4873.44873.4190190Production time = 25.6, or 26 daysProduction time = 25.6, or 26 daysExample D.1Example D.1© 2007 Pearson EducationAdvantage of Reducing Advantage of Reducing Setup TimeSetup TimeOM Explorer Solver for the Economic Production Lot Size Showing the effect of a 10 Percent Reduction in setup cost. $180 vs original $200© 2007 Pearson EducationApplication D.1  38.1555356060000,2000,100080,1022dppHDSELSor 1555 engines© 2007 Pearson EducationApplication D.1continued© 2007 Pearson EducationQuantity DiscountsQuantity discounts, which are price incentives to purchase large quantities, create pressure to maintain a large inventory.For any per-unit price level, P, the total cost is:Total annual cost = Annual holding cost + Annual ordering or setup cost + Annual cost of materialsCC = ( = (HH) + () + (SS) + ) + PDPDQQ22DDQQD = annual demandS = setup costsP = per-unit price levelH = unit holding costQ = ELS© 2007 Pearson EducationTotal cost curves with Total cost curves with purchased materials addedpurchased materials addedQuantity Discounts EOQs and price break