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### Heizer om10 ch12

1. 1. 12 - 1© 2011 Pearson Education, Inc. publishing as Prentice Hall12 InventoryManagementPowerPoint presentation to accompanyHeizer and RenderOperations Management, 10ePrinciples of Operations Management, 8ePowerPoint slides by Jeff Heyl
2. 2. 12 - 2© 2011 Pearson Education, Inc. publishing as Prentice HallOutline Global Company Profile:Amazon.com The Importance of Inventory Functions of Inventory Types of Inventory
3. 3. 12 - 3© 2011 Pearson Education, Inc. publishing as Prentice HallOutline – Continued Managing Inventory ABC Analysis Record Accuracy Cycle Counting Control of Service Inventories Inventory Models Independent vs. Dependent Demand Holding, Ordering, and Setup Costs
4. 4. 12 - 4© 2011 Pearson Education, Inc. publishing as Prentice HallOutline – Continued Inventory Models for IndependentDemand The Basic Economic Order Quantity(EOQ) Model Minimizing Costs Reorder Points Production Order Quantity Model Quantity Discount Models
5. 5. 12 - 5© 2011 Pearson Education, Inc. publishing as Prentice HallOutline – Continued Probabilistic Models and SafetyStock Other Probabilistic Models Single-Period Model Fixed-Period (P) Systems
6. 6. 12 - 6© 2011 Pearson Education, Inc. publishing as Prentice HallLearning ObjectivesWhen you complete this chapter youshould be able to:1. Conduct an ABC analysis2. Explain and use cycle counting3. Explain and use the EOQ model forindependent inventory demand4. Compute a reorder point and safetystock
7. 7. 12 - 7© 2011 Pearson Education, Inc. publishing as Prentice HallLearning ObjectivesWhen you complete this chapter youshould be able to:5. Apply the production order quantitymodel6. Explain and use the quantitydiscount model7. Understand service levels andprobabilistic inventory models
8. 8. 12 - 8© 2011 Pearson Education, Inc. publishing as Prentice HallAmazon.com Amazon.com started as a “virtual”retailer – no inventory, nowarehouses, no overhead; justcomputers taking orders to be filledby others Growth has forced Amazon.com tobecome a world leader inwarehousing and inventorymanagement
9. 9. 12 - 9© 2011 Pearson Education, Inc. publishing as Prentice HallAmazon.com1. Each order is assigned by computer tothe closest distribution center that hasthe product(s)2. A “flow meister” at each distributioncenter assigns work crews3. Lights indicate products that are to bepicked and the light is reset4. Items are placed in crates on a conveyor,bar code scanners scan each item 15times to virtually eliminate errors
10. 10. 12 - 10© 2011 Pearson Education, Inc. publishing as Prentice HallAmazon.com5. Crates arrive at central point where itemsare boxed and labeled with new bar code6. Gift wrapping is done by hand at 30packages per hour7. Completed boxes are packed, taped,weighed and labeled before leavingwarehouse in a truck8. Order arrives at customer within 2 - 3days
11. 11. 12 - 11© 2011 Pearson Education, Inc. publishing as Prentice HallInventory ManagementThe objective of inventorymanagement is to strike a balancebetween inventory investment andcustomer service
12. 12. 12 - 12© 2011 Pearson Education, Inc. publishing as Prentice HallImportance of Inventory One of the most expensive assetsof many companies representing asmuch as 50% of total investedcapital Operations managers must balanceinventory investment and customerservice
13. 13. 12 - 13© 2011 Pearson Education, Inc. publishing as Prentice HallFunctions of Inventory1. To decouple or separate variousparts of the production process2. To decouple the firm fromfluctuations in demand andprovide a stock of goods that willprovide a selection for customers3. To take advantage of quantitydiscounts4. To hedge against inflation
14. 14. 12 - 14© 2011 Pearson Education, Inc. publishing as Prentice HallTypes of Inventory Raw material Purchased but not processed Work-in-process Undergone some change but not completed A function of cycle time for a product Maintenance/repair/operating (MRO) Necessary to keep machinery andprocesses productive Finished goods Completed product awaiting shipment
15. 15. 12 - 15© 2011 Pearson Education, Inc. publishing as Prentice HallThe Material Flow CycleFigure 12.1Input Wait for Wait to Move Wait in queue Setup Run Outputinspection be moved time for operator time timeCycle time95% 5%
16. 16. 12 - 16© 2011 Pearson Education, Inc. publishing as Prentice HallManaging Inventory1. How inventory items can beclassified2. How accurate inventory recordscan be maintained
17. 17. 12 - 17© 2011 Pearson Education, Inc. publishing as Prentice HallABC Analysis Divides inventory into three classesbased on annual dollar volume Class A - high annual dollar volume Class B - medium annual dollarvolume Class C - low annual dollar volume Used to establish policies that focuson the few critical parts and not themany trivial ones
18. 18. 12 - 18© 2011 Pearson Education, Inc. publishing as Prentice HallABC AnalysisItemStockNumberPercent ofNumber ofItemsStockedAnnualVolume(units) xUnitCost =AnnualDollarVolumePercent ofAnnualDollarVolume Class#10286 20% 1,000 \$ 90.00 \$ 90,000 38.8% A#11526 500 154.00 77,000 33.2% A#12760 1,550 17.00 26,350 11.3% B#10867 30% 350 42.86 15,001 6.4% B#10500 1,000 12.50 12,500 5.4% B72%23%
19. 19. 12 - 19© 2011 Pearson Education, Inc. publishing as Prentice HallABC AnalysisItemStockNumberPercent ofNumber ofItemsStockedAnnualVolume(units) xUnitCost =AnnualDollarVolumePercent ofAnnualDollarVolume Class#12572 600 \$ 14.17 \$ 8,502 3.7% C#14075 2,000 .60 1,200 .5% C#01036 50% 100 8.50 850 .4% C#01307 1,200 .42 504 .2% C#10572 250 .60 150 .1% C8,550 \$232,057 100.0%5%
20. 20. 12 - 20© 2011 Pearson Education, Inc. publishing as Prentice HallC ItemsABC AnalysisA ItemsB ItemsPercentofannualdollarusage80 –70 –60 –50 –40 –30 –20 –10 –0 – | | | | | | | | | |10 20 30 40 50 60 70 80 90 100Percent of inventory itemsFigure 12.2
21. 21. 12 - 21© 2011 Pearson Education, Inc. publishing as Prentice HallABC Analysis Other criteria than annual dollarvolume may be used Anticipated engineering changes Delivery problems Quality problems High unit cost
22. 22. 12 - 22© 2011 Pearson Education, Inc. publishing as Prentice HallABC Analysis Policies employed may include More emphasis on supplierdevelopment for A items Tighter physical inventory control forA items More care in forecasting A items
23. 23. 12 - 23© 2011 Pearson Education, Inc. publishing as Prentice HallRecord Accuracy Accurate records are a criticalingredient in production and inventorysystems Allows organization to focus on whatis needed Necessary to make precise decisionsabout ordering, scheduling, andshipping Incoming and outgoing recordkeeping must be accurate Stockrooms should be secure
24. 24. 12 - 24© 2011 Pearson Education, Inc. publishing as Prentice HallCycle Counting Items are counted and records updatedon a periodic basis Often used with ABC analysisto determine cycle Has several advantages1. Eliminates shutdowns and interruptions2. Eliminates annual inventory adjustment3. Trained personnel audit inventory accuracy4. Allows causes of errors to be identified andcorrected5. Maintains accurate inventory records
25. 25. 12 - 25© 2011 Pearson Education, Inc. publishing as Prentice HallCycle Counting Example5,000 items in inventory, 500 A items, 1,750 B items, 2,750 CitemsPolicy is to count A items every month (20 working days), Bitems every quarter (60 days), and C items every six months(120 days)ItemClass Quantity Cycle Counting PolicyNumber of ItemsCounted per DayA 500 Each month 500/20 = 25/dayB 1,750 Each quarter 1,750/60 = 29/dayC 2,750 Every 6 months 2,750/120 = 23/day77/day
26. 26. 12 - 26© 2011 Pearson Education, Inc. publishing as Prentice HallControl of ServiceInventories Can be a critical componentof profitability Losses may come fromshrinkage or pilferage Applicable techniques include1. Good personnel selection, training, anddiscipline2. Tight control on incoming shipments3. Effective control on all goods leavingfacility
27. 27. 12 - 27© 2011 Pearson Education, Inc. publishing as Prentice HallIndependent VersusDependent Demand Independent demand - thedemand for item is independentof the demand for any otheritem in inventory Dependent demand - thedemand for item is dependentupon the demand for someother item in the inventory
28. 28. 12 - 28© 2011 Pearson Education, Inc. publishing as Prentice HallHolding, Ordering, andSetup Costs Holding costs - the costs of holdingor “carrying” inventory over time Ordering costs - the costs ofplacing an order and receivinggoods Setup costs - cost to prepare amachine or process formanufacturing an order
29. 29. 12 - 29© 2011 Pearson Education, Inc. publishing as Prentice HallHolding CostsCategoryCost (and range)as a Percent ofInventory ValueHousing costs (building rent ordepreciation, operating costs, taxes,insurance)6% (3 - 10%)Material handling costs (equipment lease ordepreciation, power, operating cost)3% (1 - 3.5%)Labor cost 3% (3 - 5%)Investment costs (borrowing costs, taxes,and insurance on inventory)11% (6 - 24%)Pilferage, space, and obsolescence 3% (2 - 5%)Overall carrying cost 26%Table 12.1
30. 30. 12 - 30© 2011 Pearson Education, Inc. publishing as Prentice HallHolding CostsCategoryCost (and range)as a Percent ofInventory ValueHousing costs (building rent ordepreciation, operating costs, taxes,insurance)6% (3 - 10%)Material handling costs (equipment lease ordepreciation, power, operating cost)3% (1 - 3.5%)Labor cost 3% (3 - 5%)Investment costs (borrowing costs, taxes,and insurance on inventory)11% (6 - 24%)Pilferage, space, and obsolescence 3% (2 - 5%)Overall carrying cost 26%Table 12.1
31. 31. 12 - 31© 2011 Pearson Education, Inc. publishing as Prentice HallInventory Models forIndependent Demand1. Basic economic order quantity2. Production order quantity3. Quantity discount modelNeed to determine when and howmuch to order
32. 32. 12 - 32© 2011 Pearson Education, Inc. publishing as Prentice HallBasic EOQ Model1. Demand is known, constant, andindependent2. Lead time is known and constant3. Receipt of inventory is instantaneous andcomplete4. Quantity discounts are not possible5. Only variable costs are setup and holding6. Stockouts can be completely avoidedImportant assumptions
33. 33. 12 - 33© 2011 Pearson Education, Inc. publishing as Prentice HallInventory Usage Over TimeFigure 12.3Orderquantity = Q(maximuminventorylevel)Usage rate Averageinventoryon handQ2MinimuminventoryInventorylevelTime0
34. 34. 12 - 34© 2011 Pearson Education, Inc. publishing as Prentice HallMinimizing CostsObjective is to minimize total costsTable 12.4(c)AnnualcostOrder quantityTotal cost ofholding andsetup (order)Holding costSetup (or order)costMinimumtotal costOptimal orderquantity (Q*)
35. 35. 12 - 35© 2011 Pearson Education, Inc. publishing as Prentice HallThe EOQ ModelQ = Number of pieces per orderQ* = Optimal number of pieces per order (EOQ)D = Annual demand in units for the inventory itemS = Setup or ordering cost for each orderH = Holding or carrying cost per unit per yearAnnual setup cost = (Number of orders placed per year)x (Setup or order cost per order)Annual demandNumber of units in each orderSetup or ordercost per order=Annual setup cost = SDQ= (S)DQ
36. 36. 12 - 36© 2011 Pearson Education, Inc. publishing as Prentice HallThe EOQ ModelQ = Number of pieces per orderQ* = Optimal number of pieces per order (EOQ)D = Annual demand in units for the inventory itemS = Setup or ordering cost for each orderH = Holding or carrying cost per unit per yearAnnual holding cost = (Average inventory level)x (Holding cost per unit per year)Order quantity2= (Holding cost per unit per year)= (H)Q2Annual setup cost = SDQAnnual holding cost = HQ2
37. 37. 12 - 37© 2011 Pearson Education, Inc. publishing as Prentice HallThe EOQ ModelQ = Number of pieces per orderQ* = Optimal number of pieces per order (EOQ)D = Annual demand in units for the inventory itemS = Setup or ordering cost for each orderH = Holding or carrying cost per unit per yearOptimal order quantity is found when annual setup costequals annual holding costAnnual setup cost = SDQAnnual holding cost = HQ2DQS = HQ2Solving for Q*2DS = Q2HQ2 = 2DS/HQ* = 2DS/H
38. 38. 12 - 38© 2011 Pearson Education, Inc. publishing as Prentice HallAn EOQ ExampleDetermine optimal number of needles to orderD = 1,000 unitsS = \$10 per orderH = \$.50 per unit per yearQ* =2DSHQ* =2(1,000)(10)0.50= 40,000 = 200 units
39. 39. 12 - 39© 2011 Pearson Education, Inc. publishing as Prentice HallAn EOQ ExampleDetermine optimal number of needles to orderD = 1,000 units Q* = 200 unitsS = \$10 per orderH = \$.50 per unit per year= N = =Expectednumber ofordersDemandOrder quantityDQ*N = = 5 orders per year1,000200
40. 40. 12 - 40© 2011 Pearson Education, Inc. publishing as Prentice HallAn EOQ ExampleDetermine optimal number of needles to orderD = 1,000 units Q* = 200 unitsS = \$10 per order N = 5 orders per yearH = \$.50 per unit per year= T =Expectedtime betweenordersNumber of workingdays per yearNT = = 50 days between orders2505
41. 41. 12 - 41© 2011 Pearson Education, Inc. publishing as Prentice HallAn EOQ ExampleDetermine optimal number of needles to orderD = 1,000 units Q* = 200 unitsS = \$10 per order N = 5 orders per yearH = \$.50 per unit per year T = 50 daysTotal annual cost = Setup cost + Holding costTC = S + HDQQ2TC = (\$10) + (\$.50)1,0002002002TC = (5)(\$10) + (100)(\$.50) = \$50 + \$50 = \$100
42. 42. 12 - 42© 2011 Pearson Education, Inc. publishing as Prentice HallRobust Model The EOQ model is robust It works even if all parametersand assumptions are not met The total cost curve is relativelyflat in the area of the EOQ
43. 43. 12 - 43© 2011 Pearson Education, Inc. publishing as Prentice HallAn EOQ ExampleManagement underestimated demand by 50%D = 1,000 units Q* = 200 unitsS = \$10 per order N = 5 orders per yearH = \$.50 per unit per year T = 50 daysTC = S + HDQQ2TC = (\$10) + (\$.50) = \$75 + \$50 = \$1251,50020020021,500 unitsTotal annual cost increases by only 25%
44. 44. 12 - 44© 2011 Pearson Education, Inc. publishing as Prentice HallAn EOQ ExampleActual EOQ for new demand is 244.9 unitsD = 1,000 units Q* = 244.9 unitsS = \$10 per order N = 5 orders per yearH = \$.50 per unit per year T = 50 daysTC = S + HDQQ2TC = (\$10) + (\$.50)1,500244.9244.921,500 unitsTC = \$61.24 + \$61.24 = \$122.48Only 2% lessthan the totalcost of \$125when theorder quantitywas 200
45. 45. 12 - 45© 2011 Pearson Education, Inc. publishing as Prentice HallReorder Points EOQ answers the “how much” question The reorder point (ROP) tells “when” toorderROP =Lead time for anew order in daysDemandper day= d x Ld =DNumber of working days in a year
46. 46. 12 - 46© 2011 Pearson Education, Inc. publishing as Prentice HallReorder Point CurveQ*ROP(units)Inventorylevel(units)Time (days)Figure 12.5Lead time = LSlope = units/day = dResupply takes place as order arrives
47. 47. 12 - 47© 2011 Pearson Education, Inc. publishing as Prentice HallReorder Point ExampleDemand = 8,000 iPods per year250 working day yearLead time for orders is 3 working daysROP = d x Ld =DNumber of working days in a year= 8,000/250 = 32 units= 32 units per day x 3 days = 96 units
48. 48. 12 - 48© 2011 Pearson Education, Inc. publishing as Prentice HallProduction Order QuantityModel Used when inventory builds upover a period of time after anorder is placed Used when units are producedand sold simultaneously
49. 49. 12 - 49© 2011 Pearson Education, Inc. publishing as Prentice HallProduction Order QuantityModelInventorylevelTimeDemand part of cyclewith no productionPart of inventory cycle duringwhich production (and usage)is taking placetMaximuminventoryFigure 12.6
50. 50. 12 - 50© 2011 Pearson Education, Inc. publishing as Prentice HallProduction Order QuantityModelQ = Number of pieces per order p = Daily production rateH = Holding cost per unit per year d = Daily demand/usage ratet = Length of the production run in days= (Average inventory level) xAnnual inventoryholding costHolding costper unit per year= (Maximum inventory level)/2Annual inventorylevel= –Maximuminventory levelTotal produced duringthe production runTotal used duringthe production run= pt – dt
51. 51. 12 - 51© 2011 Pearson Education, Inc. publishing as Prentice HallProduction Order QuantityModelQ = Number of pieces per order p = Daily production rateH = Holding cost per unit per year d = Daily demand/usage ratet = Length of the production run in days= –Maximuminventory levelTotal produced duringthe production runTotal used duringthe production run= pt – dtHowever, Q = total produced = pt ; thus t = Q/pMaximuminventory level = p – d = Q 1 –QpQpdpHolding cost = (H) = 1 – HdpQ2Maximum inventory level2
52. 52. 12 - 52© 2011 Pearson Education, Inc. publishing as Prentice HallProduction Order QuantityModelQ = Number of pieces per order p = Daily production rateH = Holding cost per unit per year d = Daily demand/usage rateD = Annual demandQ2 =2DSH[1 - (d/p)]Q* =2DSH[1 - (d/p)]pSetup cost = (D/Q)SHolding cost = HQ[1 - (d/p)]12(D/Q)S = HQ[1 - (d/p)]12
53. 53. 12 - 53© 2011 Pearson Education, Inc. publishing as Prentice HallProduction Order QuantityExampleD = 1,000 units p = 8 units per dayS = \$10 d = 4 units per dayH = \$0.50 per unit per yearQ* =2DSH[1 - (d/p)]= 282.8 or 283 hubcapsQ* = = 80,0002(1,000)(10)0.50[1 - (4/8)]
54. 54. 12 - 54© 2011 Pearson Education, Inc. publishing as Prentice HallProduction Order QuantityModelWhen annual data are used the equation becomesQ* =2DSannual demand rateannual production rateH 1 –Note:d = 4 = =DNumber of days the plant is in operation1,000250
55. 55. 12 - 55© 2011 Pearson Education, Inc. publishing as Prentice HallQuantity Discount Models Reduced prices are often available whenlarger quantities are purchased Trade-off is between reduced product costand increased holding costTotal cost = Setup cost + Holding cost + Product costTC = S + H + PDDQQ2
56. 56. 12 - 56© 2011 Pearson Education, Inc. publishing as Prentice HallQuantity Discount ModelsDiscountNumber Discount Quantity Discount (%)DiscountPrice (P)1 0 to 999 no discount \$5.002 1,000 to 1,999 4 \$4.803 2,000 and over 5 \$4.75Table 12.2A typical quantity discount schedule
57. 57. 12 - 57© 2011 Pearson Education, Inc. publishing as Prentice HallQuantity Discount Models1. For each discount, calculate Q*2. If Q* for a discount doesn’t qualify,choose the smallest possible order sizeto get the discount3. Compute the total cost for each Q* oradjusted value from Step 24. Select the Q* that gives the lowest totalcostSteps in analyzing a quantity discount
58. 58. 12 - 58© 2011 Pearson Education, Inc. publishing as Prentice HallQuantity Discount Models1,000 2,000Totalcost\$0Order quantityQ* for discount 2 is below the allowable range at point aand must be adjusted upward to 1,000 units at point bab1st pricebreak2nd pricebreakTotal costcurve fordiscount 1Total cost curve for discount 2Total cost curve for discount 3Figure 12.7
59. 59. 12 - 59© 2011 Pearson Education, Inc. publishing as Prentice HallQuantity Discount ExampleCalculate Q* for every discount Q* =2DSIPQ1* = = 700 cars/order2(5,000)(49)(.2)(5.00)Q2* = = 714 cars/order2(5,000)(49)(.2)(4.80)Q3* = = 718 cars/order2(5,000)(49)(.2)(4.75)
60. 60. 12 - 60© 2011 Pearson Education, Inc. publishing as Prentice HallQuantity Discount ExampleCalculate Q* for every discount Q* =2DSIPQ1* = = 700 cars/order2(5,000)(49)(.2)(5.00)Q2* = = 714 cars/order2(5,000)(49)(.2)(4.80)Q3* = = 718 cars/order2(5,000)(49)(.2)(4.75)1,000 — adjusted2,000 — adjusted
61. 61. 12 - 61© 2011 Pearson Education, Inc. publishing as Prentice HallQuantity Discount ExampleDiscountNumberUnitPriceOrderQuantityAnnualProductCostAnnualOrderingCostAnnualHoldingCost Total1 \$5.00 700 \$25,000 \$350 \$350 \$25,7002 \$4.80 1,000 \$24,000 \$245 \$480 \$24,7253 \$4.75 2,000 \$23.750 \$122.50 \$950 \$24,822.50Table 12.3Choose the price and quantity that givesthe lowest total costBuy 1,000 units at \$4.80 per unit
62. 62. 12 - 62© 2011 Pearson Education, Inc. publishing as Prentice HallProbabilistic Models andSafety Stock Used when demand is not constantor certain Use safety stock to achieve a desiredservice level and avoid stockoutsROP = d x L + ssAnnual stockout costs = the sum of the units shortx the probability x the stockout cost/unitx the number of orders per year
63. 63. 12 - 63© 2011 Pearson Education, Inc. publishing as Prentice HallSafety Stock ExampleNumber of Units Probability30 .240 .2ROP  50 .360 .270 .11.0ROP = 50 units Stockout cost = \$40 per frameOrders per year = 6 Carrying cost = \$5 per frame per year
64. 64. 12 - 64© 2011 Pearson Education, Inc. publishing as Prentice HallSafety Stock ExampleROP = 50 units Stockout cost = \$40 per frameOrders per year = 6 Carrying cost = \$5 per frame per yearSafetyStockAdditionalHolding Cost Stockout CostTotalCost20 (20)(\$5) = \$100 \$0 \$10010 (10)(\$5) = \$ 50 (10)(.1)(\$40)(6) = \$240 \$2900 \$ 0 (10)(.2)(\$40)(6) + (20)(.1)(\$40)(6) = \$960 \$960A safety stock of 20 frames gives the lowest total costROP = 50 + 20 = 70 frames
65. 65. 12 - 65© 2011 Pearson Education, Inc. publishing as Prentice HallSafety stock 16.5 unitsROP PlaceorderProbabilistic DemandInventorylevelTime0Minimum demand during lead timeMaximum demand during lead timeMean demand during lead timeNormal distribution probability ofdemand during lead timeExpected demand during lead time (350 kits)ROP = 350 + safety stock of 16.5 = 366.5ReceiveorderLeadtimeFigure 12.8
66. 66. 12 - 66© 2011 Pearson Education, Inc. publishing as Prentice HallProbabilistic DemandUse prescribed service levels to set safetystock when the cost of stockouts cannot bedeterminedROP = demand during lead time + ZsdLTwhere Z = number of standard deviationssdLT = standard deviation of demandduring lead time
67. 67. 12 - 67© 2011 Pearson Education, Inc. publishing as Prentice HallProbabilistic DemandSafetystockProbability ofno stockout95% of the timeMeandemand350ROP = ? kits QuantityNumber ofstandard deviations0 zRisk of a stockout(5% of area ofnormal curve)
68. 68. 12 - 68© 2011 Pearson Education, Inc. publishing as Prentice HallProbabilistic ExampleAverage demand = m = 350 kitsStandard deviation of demand during lead time = sdLT = 10 kits5% stockout policy (service level = 95%)Using Appendix I, for an area under the curveof 95%, the Z = 1.65Safety stock = ZsdLT = 1.65(10) = 16.5 kitsReorder point = expected demand during lead time+ safety stock= 350 kits + 16.5 kits of safety stock= 366.5 or 367 kits
69. 69. 12 - 69© 2011 Pearson Education, Inc. publishing as Prentice HallOther Probabilistic Models1. When demand is variable and leadtime is constant2. When lead time is variable anddemand is constant3. When both demand and lead timeare variableWhen data on demand during lead time isnot available, there are other modelsavailable
70. 70. 12 - 70© 2011 Pearson Education, Inc. publishing as Prentice HallOther Probabilistic ModelsDemand is variable and lead time is constantROP = (average daily demandx lead time in days) + ZsdLTwhere sd = standard deviation of demand per daysdLT = sd lead time
71. 71. 12 - 71© 2011 Pearson Education, Inc. publishing as Prentice HallProbabilistic ExampleAverage daily demand (normally distributed) = 15Standard deviation = 5Lead time is constant at 2 days90% service level desiredZ for 90% = 1.28From Appendix IROP = (15 units x 2 days) + ZsdLT= 30 + 1.28(5)( 2)= 30 + 9.02 = 39.02 ≈ 39Safety stock is about 9 iPods
72. 72. 12 - 72© 2011 Pearson Education, Inc. publishing as Prentice HallOther Probabilistic ModelsLead time is variable and demand is constantROP = (daily demand x average leadtime in days)= Z x (daily demand) x sLTwhere sLT = standard deviation of lead time in days
73. 73. 12 - 73© 2011 Pearson Education, Inc. publishing as Prentice HallProbabilistic ExampleDaily demand (constant) = 10Average lead time = 6 daysStandard deviation of lead time = sLT = 398% service level desiredZ for 98% = 2.055From Appendix IROP = (10 units x 6 days) + 2.055(10 units)(3)= 60 + 61.65 = 121.65Reorder point is about 122 cameras
74. 74. 12 - 74© 2011 Pearson Education, Inc. publishing as Prentice HallOther Probabilistic ModelsBoth demand and lead time are variableROP = (average daily demandx average lead time) + ZsdLTwhere sd = standard deviation of demand per daysLT = standard deviation of lead time in dayssdLT = (average lead time x sd2)+ (average daily demand)2 x sLT2
75. 75. 12 - 75© 2011 Pearson Education, Inc. publishing as Prentice HallProbabilistic ExampleAverage daily demand (normally distributed) = 150Standard deviation = sd = 16Average lead time 5 days (normally distributed)Standard deviation = sLT = 1 day95% service level desired Z for 95% = 1.65From Appendix IROP = (150 packs x 5 days) + 1.65sdLT= (150 x 5) + 1.65 (5 days x 162) + (1502 x 12)= 750 + 1.65(154) = 1,004 packs
76. 76. 12 - 76© 2011 Pearson Education, Inc. publishing as Prentice HallSingle Period Model Only one order is placed for a product Units have little or no value at the end ofthe sales periodCs = Cost of shortage = Sales price/unit – Cost/unitCo = Cost of overage = Cost/unit – Salvage valueService level =CsCs + Co
77. 77. 12 - 77© 2011 Pearson Education, Inc. publishing as Prentice HallSingle Period ExampleAverage demand = m = 120 papers/dayStandard deviation = s = 15 papersCs = cost of shortage = \$1.25 - \$.70 = \$.55Co = cost of overage = \$.70 - \$.30 = \$.40Service level =CsCs + Co.55.55 + .40.55.95== = .578Servicelevel57.8%Optimal stocking levelm = 120
78. 78. 12 - 78© 2011 Pearson Education, Inc. publishing as Prentice HallSingle Period ExampleFrom Appendix I, for the area .578, Z  .20The optimal stocking level= 120 copies + (.20)(s)= 120 + (.20)(15) = 120 + 3 = 123 papersThe stockout risk = 1 – service level= 1 – .578 = .422 = 42.2%
79. 79. 12 - 79© 2011 Pearson Education, Inc. publishing as Prentice HallFixed-Period (P) Systems Orders placed at the end of a fixed period Inventory counted only at end of period Order brings inventory up to target level Only relevant costs are ordering and holding Lead times are known and constant Items are independent from one another
80. 80. 12 - 80© 2011 Pearson Education, Inc. publishing as Prentice HallFixed-Period (P) SystemsOn-handinventoryTimeQ1Q2Target quantity (T)PQ3Q4PPFigure 12.9
81. 81. 12 - 81© 2011 Pearson Education, Inc. publishing as Prentice HallFixed-Period (P) ExampleOrder amount (Q) = Target (T) - On-hand inventory - Earlier orders not yetreceived + Back ordersQ = 50 - 0 - 0 + 3 = 53 jackets3 jackets are back ordered No jackets are in stockIt is time to place an order Target value = 50
82. 82. 12 - 82© 2011 Pearson Education, Inc. publishing as Prentice HallFixed-Period Systems Inventory is only counted at eachreview period May be scheduled at convenient times Appropriate in routine situations May result in stockouts betweenperiods May require increased safety stock
83. 83. 12 - 83© 2011 Pearson Education, Inc. publishing as Prentice HallAll rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem, or transmitted, in any form or by any means, electronic, mechanical, photocopying,recording, or otherwise, without the prior written permission of the publisher.Printed in the United States of America.
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