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- 1. © 2006 Prentice Hall, Inc. 12 – 1OperationsManagementChapter 12 –Inventory Management© 2006 Prentice Hall, Inc.PowerPoint presentation to accompanyPowerPoint presentation to accompanyHeizer/RenderHeizer/RenderPrinciples of Operations Management, 6ePrinciples of Operations Management, 6eOperations Management, 8eOperations Management, 8e
- 2. © 2006 Prentice Hall, Inc. 12 – 2InventoryInventory One of the most expensive assetsOne of the most expensive assetsof many companies representing asof many companies representing asmuch as 50% of total investedmuch as 50% of total investedcapitalcapital Operations managers must balanceOperations managers must balanceinventory investment and customerinventory investment and customerserviceservice
- 3. © 2006 Prentice Hall, Inc. 12 – 3Types of InventoryTypes of Inventory Raw materialRaw material Purchased but not processedPurchased but not processed Work-in-processWork-in-process Undergone some change but not completedUndergone some change but not completed A function of cycle time for a productA function of cycle time for a product Maintenance/repair/operating (MRO)Maintenance/repair/operating (MRO) Necessary to keep machinery and processesNecessary to keep machinery and processesproductiveproductive Finished goodsFinished goods Completed product awaiting shipmentCompleted product awaiting shipment
- 4. © 2006 Prentice Hall, Inc. 12 – 4Holding, Ordering, andHolding, Ordering, andSetup CostsSetup Costs Holding costs - the costs of holdingHolding costs - the costs of holdingor “carrying” inventory over timeor “carrying” inventory over time Ordering costs - the costs ofOrdering costs - the costs ofplacing an order and receivingplacing an order and receivinggoodsgoods Setup costs - cost to prepare aSetup costs - cost to prepare amachine or process formachine or process formanufacturing an ordermanufacturing an order
- 5. © 2006 Prentice Hall, Inc. 12 – 5Holding CostsHolding CostsTable 12.1Table 12.1•Housing costs (including rent or depreciation,Housing costs (including rent or depreciation,operating costs, taxes, insurance)operating costs, taxes, insurance)•Material handling costs (equipment lease orMaterial handling costs (equipment lease ordepreciation, power, operating cost)depreciation, power, operating cost)•Labor costLabor cost•Investment costs (borrowing costs, taxes, andInvestment costs (borrowing costs, taxes, andinsurance on inventory)insurance on inventory)•Pilferage, space, and obsolescencePilferage, space, and obsolescence
- 6. © 2006 Prentice Hall, Inc. 12 – 6Inventory Models forInventory Models forIndependent DemandIndependent Demand Basic economic order quantityBasic economic order quantity Production order quantityProduction order quantity Quantity discount modelQuantity discount modelNeed to determine when and howNeed to determine when and howmuch to ordermuch to order
- 7. © 2006 Prentice Hall, Inc. 12 – 7Basic EOQ ModelBasic EOQ Model1.1. Demand is known, constant, andDemand is known, constant, andindependentindependent2.2. Lead time is known and constantLead time is known and constant3.3. Receipt of inventory is instantaneous andReceipt of inventory is instantaneous andcompletecomplete4.4. Quantity discounts are not possibleQuantity discounts are not possible5.5. Only variable costs are setup and holdingOnly variable costs are setup and holding6.6. Stockouts can be completely avoidedStockouts can be completely avoidedImportant assumptionsImportant assumptions
- 8. © 2006 Prentice Hall, Inc. 12 – 8Inventory Usage Over TimeInventory Usage Over TimeFigure 12.3Figure 12.3OrderOrderquantity = Qquantity = Q(maximum(maximuminventoryinventorylevel)level)InventorylevelInventorylevelTimeTimeUsage rateUsage rate AverageAverageinventoryinventoryon handon handQQ22MinimumMinimuminventoryinventory
- 9. © 2006 Prentice Hall, Inc. 12 – 9Minimizing CostsMinimizing CostsObjective is to minimize total costsObjective is to minimize total costsTable 11.5Table 11.5AnnualcostAnnualcostOrder quantityOrder quantityCurve for totalCurve for totalcost of holdingcost of holdingand setupand setupHolding costHolding costcurvecurveSetup (or order)Setup (or order)cost curvecost curveMinimumMinimumtotal costtotal costOptimalOptimalorderorderquantityquantity
- 10. © 2006 Prentice Hall, Inc. 12 – 10The EOQ ModelThe EOQ ModelQQ = Number of pieces per order= Number of pieces per orderQ*Q* = Optimal number of pieces per order (EOQ)= Optimal number of pieces per order (EOQ)DD = Annual demand in units for the Inventory item= Annual demand in units for the Inventory itemSS = Setup or ordering cost for each order= Setup or ordering cost for each orderHH = Holding or carrying cost per unit per year= Holding or carrying cost per unit per yearAnnual setup costAnnual setup cost == ((Number of orders placed per yearNumber of orders placed per year))x (x (Setup or order cost per orderSetup or order cost per order))Annual demandAnnual demandNumber of units in each orderNumber of units in each orderSetup or orderSetup or ordercost per ordercost per order=== (= (SS))DDQQAnnual setup cost = SDQ
- 11. © 2006 Prentice Hall, Inc. 12 – 11The EOQ ModelThe EOQ ModelQQ = Number of pieces per order= Number of pieces per orderQ*Q* = Optimal number of pieces per order (EOQ)= Optimal number of pieces per order (EOQ)DD = Annual demand in units for the Inventory item= Annual demand in units for the Inventory itemSS = Setup or ordering cost for each order= Setup or ordering cost for each orderHH = Holding or carrying cost per unit per year= Holding or carrying cost per unit per yearAnnual holding costAnnual holding cost == ((Average inventory levelAverage inventory level))x (x (Holding cost per unit per yearHolding cost per unit per year))Order quantityOrder quantity22= (= (Holding cost per unit per yearHolding cost per unit per year))= (= (HH))QQ22Annual setup cost = SDQAnnual holding cost = HQ2
- 12. © 2006 Prentice Hall, Inc. 12 – 12The EOQ ModelThe EOQ ModelQQ = Number of pieces per order= Number of pieces per orderQ*Q* = Optimal number of pieces per order (EOQ)= Optimal number of pieces per order (EOQ)DD = Annual demand in units for the Inventory item= Annual demand in units for the Inventory itemSS = Setup or ordering cost for each order= Setup or ordering cost for each orderHH = Holding or carrying cost per unit per year= Holding or carrying cost per unit per yearOptimal order quantity is found when annual setup costOptimal order quantity is found when annual setup costequals annual holding costequals annual holding costAnnual setup cost = SDQAnnual holding cost = HQ2DDQQSS == HHQQ22Solving for Q*Solving for Q*22DS = QDS = Q22HHQQ22== 22DS/HDS/HQ* =Q* = 22DS/HDS/H
- 13. © 2006 Prentice Hall, Inc. 12 – 13An EOQ ExampleAn EOQ ExampleDetermine optimal number of needles to orderDetermine optimal number of needles to orderDD = 1,000= 1,000 unitsunitsSS = $10= $10 per orderper orderHH = $.50= $.50 per unit per yearper unit per yearQ* =Q* =22DSDSHHQ* =Q* =2(1,000)(10)2(1,000)(10)0.500.50= 40,000 = 200= 40,000 = 200 unitsunits
- 14. © 2006 Prentice Hall, Inc. 12 – 14An EOQ ExampleAn EOQ ExampleDetermine optimal number of needles to orderDetermine optimal number of needles to orderDD = 1,000= 1,000 unitsunits Q*Q* = 200= 200 unitsunitsSS = $10= $10 per orderper orderHH = $.50= $.50 per unit per yearper unit per year= N = == N = =ExpectedExpectednumber ofnumber ofordersordersDemandDemandOrder quantityOrder quantityDDQ*Q*NN = = 5= = 5 orders per yearorders per year1,0001,000200200
- 15. © 2006 Prentice Hall, Inc. 12 – 15An EOQ ExampleAn EOQ ExampleDetermine optimal number of needles to orderDetermine optimal number of needles to orderDD = 1,000= 1,000 unitsunits Q*Q* = 200= 200 unitsunitsSS = $10= $10 per orderper order NN = 5= 5 orders per yearorders per yearHH = $.50= $.50 per unit per yearper unit per year= T == T =ExpectedExpectedtime betweentime betweenordersordersNumber of workingNumber of workingdays per yeardays per yearNNTT = = 50= = 50 days between ordersdays between orders25025055
- 16. © 2006 Prentice Hall, Inc. 12 – 16An EOQ ExampleAn EOQ ExampleDetermine optimal number of needles to orderDetermine optimal number of needles to orderDD = 1,000= 1,000 unitsunits Q*Q* = 200= 200 unitsunitsSS = $10= $10 per orderper order NN = 5= 5 orders per yearorders per yearHH = $.50= $.50 per unit per yearper unit per year TT = 50= 50 daysdaysTotal annual cost = Setup cost + Holding costTotal annual cost = Setup cost + Holding costTC = S + HTC = S + HDDQQQQ22TCTC = ($10) + ($.50)= ($10) + ($.50)1,0001,00020020020020022TCTC = (5)($10) + (100)($.50) = $50 + $50 = $100= (5)($10) + (100)($.50) = $50 + $50 = $100
- 17. © 2006 Prentice Hall, Inc. 12 – 17Robust ModelRobust Model The EOQ model is robustThe EOQ model is robust It works even if all parametersIt works even if all parametersand assumptions are not metand assumptions are not met The total cost curve is relativelyThe total cost curve is relativelyflat in the area of the EOQflat in the area of the EOQ
- 18. © 2006 Prentice Hall, Inc. 12 – 18Reorder PointsReorder Points EOQ answers the “how much” questionEOQ answers the “how much” question The reorder point (ROP) tells when toThe reorder point (ROP) tells when toorderorderROPROP ==Lead time for aLead time for anew order in daysnew order in daysDemandDemandper dayper day== d x Ld x Ld =d =DDNumber of working days in a yearNumber of working days in a year
- 19. © 2006 Prentice Hall, Inc. 12 – 19Reorder Point CurveReorder Point CurveQ*Q*ROPROP(units)(units)Inventorylevel(units)Inventorylevel(units)Time (days)Time (days)Figure 12.5Figure 12.5 Lead time = LLead time = LSlope = units/day = dSlope = units/day = d
- 20. © 2006 Prentice Hall, Inc. 12 – 20Reorder Point ExampleReorder Point ExampleDemandDemand = 8,000= 8,000 DVDs per yearDVDs per year250250 working day yearworking day yearLead time for orders isLead time for orders is 33 working daysworking daysROP =ROP = d x Ld x Ld =d =DDNumber of working days in a yearNumber of working days in a year= 8,000/250 = 32= 8,000/250 = 32 unitsunits= 32= 32 units per day xunits per day x 33 daysdays = 96= 96 unitsunits
- 21. © 2006 Prentice Hall, Inc. 12 – 21Production Order QuantityProduction Order QuantityModelModel Used when inventory builds up overUsed when inventory builds up overa period of time after an order isa period of time after an order isplacedplaced Used when units are produced andUsed when units are produced andsold simultaneouslysold simultaneously
- 22. © 2006 Prentice Hall, Inc. 12 – 22Production Order QuantityProduction Order QuantityModelModelInventorylevelInventorylevelTimeTimeDemand part of cycleDemand part of cyclewith no productionwith no productionPart of inventory cycle duringPart of inventory cycle duringwhich production (and usage)which production (and usage)is taking placeis taking placettMaximumMaximuminventoryinventoryFigure 12.6Figure 12.6
- 23. © 2006 Prentice Hall, Inc. 12 – 23Production Order QuantityProduction Order QuantityModelModelQ =Q = Number of pieces per orderNumber of pieces per order p =p = Daily production rateDaily production rateH =H = Holding cost per unit per yearHolding cost per unit per year d =d = Daily demand/usage rateDaily demand/usage rateD =D = Annual demandAnnual demandSetup costSetup cost == ((DD//QQ))SSHolding costHolding cost == 1/21/2 HQHQ[1 - ([1 - (dd//pp)])]((DD//QQ))S =S = 1/21/2 HQHQ[1 - ([1 - (dd//pp)])]QQ22==22DSDSHH[1 - ([1 - (dd//pp)])]QQ* =* =22DSDSHH[1 - ([1 - (dd//pp)])]
- 24. © 2006 Prentice Hall, Inc. 12 – 24Production Order QuantityProduction Order QuantityExampleExampleDD == 1,0001,000 unitsunits pp == 88 units per dayunits per daySS == $10$10 dd == 44 units per dayunits per dayHH == $0.50$0.50 per unit per yearper unit per yearQQ* =* =22DSDSHH[1 - ([1 - (dd//pp)])]= 282.8= 282.8 oror 283283 hubcapshubcapsQQ* = = 80,000* = = 80,0002(1,000)(10)2(1,000)(10)0.50[1 - (4/8)]0.50[1 - (4/8)]
- 25. © 2006 Prentice Hall, Inc. 12 – 25Quantity Discount ModelsQuantity Discount Models Reduced prices are often available whenReduced prices are often available whenlarger quantities are purchasedlarger quantities are purchased Trade-off is between reduced product costTrade-off is between reduced product costand increased holding costand increased holding costTotal cost = Setup cost + Holding cost + Product costTotal cost = Setup cost + Holding cost + Product costTC = S + + PDTC = S + + PDDDQQQHQH22
- 26. © 2006 Prentice Hall, Inc. 12 – 26Quantity Discount ModelsQuantity Discount ModelsDiscountDiscountNumberNumber Discount QuantityDiscount Quantity Discount (%)Discount (%)DiscountDiscountPrice (P)Price (P)11 00 toto 999999 no discountno discount $5.00$5.0022 1,0001,000 toto 1,9991,999 44 $4.80$4.8033 2,0002,000 and overand over 55 $4.75$4.75Table 12.2Table 12.2A typical quantity discount scheduleA typical quantity discount schedule
- 27. © 2006 Prentice Hall, Inc. 12 – 27Quantity Discount ModelsQuantity Discount Models1.1. For each discount, calculate Q*For each discount, calculate Q*2.2. If Q* for a discount doesn’t qualify,If Q* for a discount doesn’t qualify,choose the smallest possible order sizechoose the smallest possible order sizeto get the discountto get the discount3.3. Compute the total cost for each Q* orCompute the total cost for each Q* oradjusted value from Step 2adjusted value from Step 24.4. Select the Q* that gives the lowest totalSelect the Q* that gives the lowest totalcostcostSteps in analyzing a quantity discountSteps in analyzing a quantity discount
- 28. © 2006 Prentice Hall, Inc. 12 – 28Quantity Discount ExampleQuantity Discount ExampleCalculate Q* for every discountCalculate Q* for every discountQ* =2DSIPQQ11** = = 700= = 700 cars ordercars order2(5,000)(49)2(5,000)(49)(.2)(5.00)(.2)(5.00)QQ22** = = 714= = 714 cars ordercars order2(5,000)(49)2(5,000)(49)(.2)(4.80)(.2)(4.80)QQ33** = = 718= = 718 cars ordercars order2(5,000)(49)2(5,000)(49)(.2)(4.75)(.2)(4.75)
- 29. © 2006 Prentice Hall, Inc. 12 – 29Quantity Discount ExampleQuantity Discount ExampleCalculate Q* for every discountCalculate Q* for every discountQ* =2DSIPQQ11** = = 700= = 700 cars ordercars order2(5,000)(49)2(5,000)(49)(.2)(5.00)(.2)(5.00)QQ22** = = 714= = 714 cars ordercars order2(5,000)(49)2(5,000)(49)(.2)(4.80)(.2)(4.80)QQ33** = = 718= = 718 cars ordercars order2(5,000)(49)2(5,000)(49)(.2)(4.75)(.2)(4.75)1,0001,000 — adjusted— adjusted2,0002,000 — adjusted— adjusted
- 30. © 2006 Prentice Hall, Inc. 12 – 30Quantity Discount ExampleQuantity Discount ExampleDiscountDiscountNumberNumberUnitUnitPricePriceOrderOrderQuantityQuantityAnnualAnnualProductProductCostCostAnnualAnnualOrderingOrderingCostCostAnnualAnnualHoldingHoldingCostCost TotalTotal11 $5.00$5.00 700700 $25,000$25,000 $350$350 $350$350 $25,700$25,70022 $4.80$4.80 1,0001,000 $24,000$24,000 $245$245 $480$480 $24,725$24,72533 $4.75$4.75 2,0002,000 $23.750$23.750 $122.50$122.50 $950$950 $24,822.50$24,822.50Table 12.3Table 12.3Choose the price and quantity that givesChoose the price and quantity that givesthe lowest total costthe lowest total costBuyBuy 1,0001,000 units atunits at $4.80$4.80 per unitper unit

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