inventory management, supply contracts and risk pooling

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Inventory Management, Supply Contracts and Risk Pooling Phil Kaminsky [email protected] David Simchi-Levi Philip Kaminsky Edith Simchi-Levi

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  • Outline of the PresentationIntroduction to Inventory Management

    The Effect of Demand Uncertainty(s,S) PolicyPeriodic Review PolicySupply ContractsRisk Pooling

    Centralized vs. Decentralized Systems

    Practical Issues in Inventory Management

  • SupplySources:plantsvendorsportsRegionalWarehouses:stocking pointsField Warehouses:stockingpointsCustomers,demandcenterssinksProduction/purchase costsInventory &warehousing costsTransportation costsInventory &warehousing costsTransportation costs

  • InventoryWhere do we hold inventory?Suppliers and manufacturerswarehouses and distribution centersretailersTypes of InventoryWIPraw materialsfinished goodsWhy do we hold inventory?Economies of scaleUncertainty in supply and demandLead Time, Capacity limitations

  • Goals: Reduce Cost, Improve ServiceBy effectively managing inventory:Xerox eliminated $700 million inventory from its supply chainWal-Mart became the largest retail company utilizing efficient inventory managementGM has reduced parts inventory and transportation costs by 26% annually

  • Goals: Reduce Cost, Improve ServiceBy not managing inventory successfullyIn 1994, IBM continues to struggle with shortages in their ThinkPad line (WSJ, Oct 7, 1994)In 1993, Liz Claiborne said its unexpected earning decline is the consequence of higher than anticipated excess inventory (WSJ, July 15, 1993)In 1993, Dell Computers predicts a loss; Stock plunges. Dell acknowledged that the company was sharply off in its forecast of demand, resulting in inventory write downs (WSJ, August 1993)

  • Understanding Inventory The inventory policy is affected by:Demand CharacteristicsLead TimeNumber of ProductsObjectivesService levelMinimize costsCost Structure

  • Cost StructureOrder costs FixedVariableHolding CostsInsuranceMaintenance and HandlingTaxesOpportunity CostsObsolescence

  • EOQ: A Simple Model*Book Store Mug SalesDemand is constant, at 20 units a weekFixed order cost of $12.00, no lead timeHolding cost of 25% of inventory value annuallyMugs cost $1.00, sell for $5.00QuestionHow many, when to order?

  • EOQ: A View of Inventory*TimeInventoryOrderSizeNote: No Stockouts Order when no inventory Order Size determines policyAvg. Inven

  • EOQ: Calculating Total Cost*Purchase Cost ConstantHolding Cost: (Avg. Inven) * (Holding Cost)Ordering (Setup Cost): Number of Orders * Order CostGoal: Find the Order Quantity that Minimizes These Costs:

  • EOQ:Total Cost*Total CostOrder CostHolding Cost

    Chart1

    73.411764705921.2594.6617647059

    69.333333333322.591.8333333333

    65.684210526323.7589.4342105263

    62.42587.4

    59.428571428626.2585.6785714286

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    54.260869565228.7583.0108695652

    523082

    49.9231.2581.17

    4832.580.5

    46.222222222233.7579.9722222222

    44.57142857143579.5714285714

    43.034482758636.2579.2844827586

    41.637.579.1

    40.258064516138.7579.0080645161

    394079

    37.818181818241.2579.0681818182

    36.705882352942.579.2058823529

    35.657142857143.7579.4071428571

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    33.729729729746.2579.9797297297

    32.842105263247.580.3421052632

    3248.7580.75

    31.25081.2

    30.439024390251.2581.6890243902

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    23.547169811366.2589.7971698113

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    22.28571428577092.2857142857

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    21.152542372973.7594.9025423729

    20.87595.8

    20.459016393476.2596.7090163934

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    16.6493.75110.39

    16.421052631695111.4210526316

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    1697.5113.5

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    15.6100115.6

    15.4074074074101.25116.6574074074

    15.2195121951102.5117.7195121951

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    14.8571428571105119.8571428571

    14.6823529412106.25120.9323529412

    14.511627907107.5122.011627907

    14.3448275862108.75123.0948275862

    14.1818181818110124.1818181818

    14.0224719101111.25125.2724719101

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    13.7142857143113.75127.4642857143

    13.5652173913115128.5652173913

    13.4193548387116.25129.6693548387

    13.2765957447117.5130.7765957447

    13.1368421053118.75131.8868421053

    13120133

    12.8659793814121.25134.1159793814

    12.7346938776122.5135.2346938776

    12.6060606061123.75136.3560606061

    12.48125137.48

    Order Quantity

    Cost

    Sheet1

    Amount to Order:(each time inventory hits 0)

    Order Cost:12

    Weekly Demand:20

    Annual Demand:1040

    Annual Orders:(Annual Demand / Amount to Order)

    Holding Cost:0.25(25% of .02)

    Avg. Annual Inven:(Half of Order Amount Times Number of Orders)

    Total Annual Cost:(Avg. Annual Inven)*Holding Cost + Number of Orders * Order Cost

    QOrder CostHolding CostTC

    1012481.251249.25

    206242.5626.5

    304163.75419.75

    403125317

    50249.66.25255.85

    602087.5215.5

    70178.28571428578.75187.0357142857

    8015610166

    90138.666666666711.25149.9166666667

    100124.812.5137.3

    110113.454545454513.75127.2045454545

    12010415119

    1309616.25112.25

    14089.142857142917.5106.6428571429

    15083.218.75101.95

    160782098

    17073.411764705921.2594.6617647059

    18069.333333333322.591.8333333333

    19065.684210526323.7589.4342105263

    20062.42587.4

    21059.428571428626.2585.6785714286

    22056.727272727327.584.2272727273

    23054.260869565228.7583.0108695652

    240523082

    25049.9231.2581.17

    2604832.580.5

    27046.222222222233.7579.9722222222

    28044.57142857143579.5714285714

    29043.034482758636.2579.2844827586

    30041.637.579.1

    31040.258064516138.7579.0080645161

    320394079

    33037.818181818241.2579.0681818182

    34036.705882352942.579.2058823529

    35035.657142857143.7579.4071428571

    36034.66666666674579.6666666667

    37033.729729729746.2579.9797297297

    38032.842105263247.580.3421052632

    3903248.7580.75

    40031.25081.2

    41030.439024390251.2581.6890243902

    42029.714285714352.582.2142857143

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    44028.36363636365583.3636363636

    45027.733333333356.2583.9833333333

    46027.130434782657.584.6304347826

    47026.553191489458.7585.3031914894

    480266086

    49025.469387755161.2586.7193877551

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    520246589

    53023.547169811366.2589.7971698113

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    56022.28571428577092.2857142857

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    58021.517241379372.594.0172413793

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    80015.6100115.6

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    82015.2195121951102.5117.7195121951

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    84014.8571428571105119.8571428571

    85014.6823529412106.25120.9323529412

    86014.511627907107.5122.011627907

    87014.3448275862108.75123.0948275862

    88014.1818181818110124.1818181818

    89014.0224719101111.25125.2724719101

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    91013.7142857143113.75127.4642857143

    92013.5652173913115128.5652173913

    93013.4193548387116.25129.6693548387

    94013.2765957447117.5130.7765957447

    95013.1368421053118.75131.8868421053

    96013120133

    97012.8659793814121.25134.1159793814

    98012.7346938776122.5135.2346938776

    99012.6060606061123.75136.3560606061

    100012.48125137.48

    Sheet1

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    Order Quantity

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    Sheet2

    Sheet3

  • EOQ: Optimal Order Quantity*Optimal Quantity = (2*Demand*Setup Cost)/holding cost

    So for our problem, the optimal quantity is 316

  • EOQ: Important Observations*Tradeoff between set-up costs and holding costs when determining order quantity. In fact, we order so that these costs are equal per unit timeTotal Cost is not particularly sensitive to the optimal order quantity

    Order Quantity

    50%

    80%

    90%

    100%

    110%

    120%

    150%

    200%

    Cost Increase

    125%

    103%

    101%

    100%

    101%

    102%

    108%

    125%

  • The Effect of Demand UncertaintyMost companies treat the world as if it were predictable:Production and inventory planning are based on forecasts of demand made far in advance of the selling seasonCompanies are aware of demand uncertainty when they create a forecast, but they design their planning process as if the forecast truly represents realityRecent technological advances have increased the level of demand uncertainty:Short product life cycles Increasing product variety

  • Demand ForecastThe three principles of all forecasting techniques:

    Forecasting is always wrongThe longer the forecast horizon the worst is the forecast Aggregate forecasts are more accurate

  • SnowTime Sporting GoodsFashion items have short life cycles, high variety of competitorsSnowTime Sporting Goods New designs are completedOne production opportunityBased on past sales, knowledge of the industry, and economic conditions, the marketing department has a probabilistic forecastThe forecast averages about 13,000, but there is a chance that demand will be greater or less than this.

  • Supply Chain Time Lines

  • SnowTime Demand Scenarios

    Chart1

    0.11

    0.11

    0.28

    0.22

    0.18

    0.1

    Sales

    Probability

    Demand Scenarios

    Sheet1

    Amount to Order:(each time inventory hits 0)

    Order Cost:12

    Weekly Demand:20

    Annual Demand:1040

    Annual Orders:(Annual Demand / Amount to Order)

    Holding Cost:0.25(25% of .02)

    Avg. Annual Inven:(Half of Order Amount Times Number of Orders)

    Total Annual Cost:(Avg. Annual Inven)*Holding Cost + Number of Orders * Order Cost

    QOrder CostHolding CostTC

    1012481.251249.25

    206242.5626.5

    304163.75419.75

    403125317

    50249.66.25255.85

    602087.5215.5

    70178.28571428578.75187.0357142857

    8015610166

    90138.666666666711.25149.9166666667

    100124.812.5137.3

    110113.454545454513.75127.2045454545

    12010415119

    1309616.25112.25

    14089.142857142917.5106.6428571429

    15083.218.75101.95

    160782098

    17073.411764705921.2594.6617647059

    18069.333333333322.591.8333333333

    19065.684210526323.7589.4342105263

    20062.42587.4

    21059.428571428626.2585.6785714286

    22056.727272727327.584.2272727273

    23054.260869565228.7583.0108695652

    240523082

    25049.9231.2581.17

    2604832.580.5

    27046.222222222233.7579.9722222222

    28044.57142857143579.5714285714

    29043.034482758636.2579.2844827586

    30041.637.579.1

    31040.258064516138.7579.0080645161

    320394079

    33037.818181818241.2579.0681818182

    34036.705882352942.579.2058823529

    35035.657142857143.7579.4071428571

    36034.66666666674579.6666666667

    37033.729729729746.2579.9797297297

    38032.842105263247.580.3421052632

    3903248.7580.75

    40031.25081.2

    41030.439024390251.2581.6890243902

    42029.714285714352.582.2142857143

    43029.02325581453.7582.773255814

    44028.36363636365583.3636363636

    45027.733333333356.2583.9833333333

    46027.130434782657.584.6304347826

    47026.553191489458.7585.3031914894

    480266086

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    520246589

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    54023.111111111167.590.6111111111

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    57021.894736842171.2593.1447368421

    58021.517241379372.594.0172413793

    59021.152542372973.7594.9025423729

    60020.87595.8

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    63019.809523809578.7598.5595238095

    64019.58099.5

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    68018.352941176585103.3529411765

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    71017.577464788788.75106.3274647887

    72017.333333333390107.3333333333

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    77016.207792207896.25112.4577922078

    7801697.5113.5

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    82015.2195121951102.5117.7195121951

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    84014.8571428571105119.8571428571

    85014.6823529412106.25120.9323529412

    86014.511627907107.5122.011627907

    87014.3448275862108.75123.0948275862

    88014.1818181818110124.1818181818

    89014.0224719101111.25125.2724719101

    90013.8666666667112.5126.3666666667

    91013.7142857143113.75127.4642857143

    92013.5652173913115128.5652173913

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    95013.1368421053118.75131.8868421053

    96013120133

    97012.8659793814121.25134.1159793814

    98012.7346938776122.5135.2346938776

    99012.6060606061123.75136.3560606061

    100012.48125137.48

    80000.11

    100000.11

    120000.28

    140000.22

    160000.18

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    Order Quantity

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    Sheet2

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    Sales

    Probability

    Demand Scenarios

    Sheet3

  • SnowTime CostsProduction cost per unit (C): $80Selling price per unit (S): $125Salvage value per unit (V): $20Fixed production cost (F): $100,000Q is production quantity, D demand

    Profit = Revenue - Variable Cost - Fixed Cost + Salvage

  • SnowTime ScenariosScenario One:Suppose you make 12,000 jackets and demand ends up being 13,000 jackets.Profit = 125(12,000) - 80(12,000) - 100,000 = $440,000Scenario Two:Suppose you make 12,000 jackets and demand ends up being 11,000 jackets.Profit = 125(11,000) - 80(12,000) - 100,000 + 20(1000) = $ 335,000

  • SnowTime Best SolutionFind order quantity that maximizes weighted average profit.Question: Will this quantity be less than, equal to, or greater than average demand?

  • What to Make?Question: Will this quantity be less than, equal to, or greater than average demand?Average demand is 13,100Look at marginal cost Vs. marginal profitif extra jacket sold, profit is 125-80 = 45if not sold, cost is 80-20 = 60So we will make less than average

  • SnowTime Expected Profit

    Chart2

    260000

    276725

    293450

    310175

    326900

    348800

    359750

    370700

    366950

    363200

    359450

    355700

    340400

    325100

    309800

    294500

    269750

    245000

    220250

    195500

    165500

    135500

    105500

    75500

    Order Quantity

    Profit

    Expected Profit

    Sheet1

    Amount to Order:(each time inventory hits 0)

    Order Cost:12

    Weekly Demand:20

    Annual Demand:1040

    Annual Orders:(Annual Demand / Amount to Order)

    Holding Cost:0.25(25% of .02)

    Avg. Annual Inven:(Half of Order Amount Times Number of Orders)

    Total Annual Cost:(Avg. Annual Inven)*Holding Cost + Number of Orders * Order Cost

    QOrder CostHolding CostTC

    1012481.251249.25

    206242.5626.5

    304163.75419.75

    403125317

    50249.66.25255.85

    602087.5215.5

    70178.28571428578.75187.0357142857

    8015610166

    90138.666666666711.25149.9166666667

    100124.812.5137.3

    110113.454545454513.75127.2045454545

    12010415119

    1309616.25112.25

    14089.142857142917.5106.6428571429

    15083.218.75101.95

    160782098

    17073.411764705921.2594.6617647059

    18069.333333333322.591.8333333333

    19065.684210526323.7589.4342105263

    20062.42587.4

    21059.428571428626.2585.6785714286

    22056.727272727327.584.2272727273

    23054.260869565228.7583.0108695652

    240523082

    25049.9231.2581.17

    2604832.580.5

    27046.222222222233.7579.9722222222

    28044.57142857143579.5714285714

    29043.034482758636.2579.2844827586

    30041.637.579.1

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    320394079

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    34036.705882352942.579.2058823529

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    37033.729729729746.2579.9797297297

    38032.842105263247.580.3421052632

    3903248.7580.75

    40031.25081.2

    41030.439024390251.2581.6890243902

    42029.714285714352.582.2142857143

    43029.02325581453.7582.773255814

    44028.36363636365583.3636363636

    45027.733333333356.2583.9833333333

    46027.130434782657.584.6304347826

    47026.553191489458.7585.3031914894

    480266086

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    50024.9662.587.46

    51024.470588235363.7588.2205882353

    520246589

    53023.547169811366.2589.7971698113

    54023.111111111167.590.6111111111

    55022.690909090968.7591.4409090909

    56022.28571428577092.2857142857

    57021.894736842171.2593.1447368421

    58021.517241379372.594.0172413793

    59021.152542372973.7594.9025423729

    60020.87595.8

    61020.459016393476.2596.7090163934

    62020.129032258177.597.6290322581

    63019.809523809578.7598.5595238095

    64019.58099.5

    65019.281.25100.45

    66018.909090909182.5101.4090909091

    67018.626865671683.75102.3768656716

    68018.352941176585103.3529411765

    69018.086956521786.25104.3369565217

    70017.828571428687.5105.3285714286

    71017.577464788788.75106.3274647887

    72017.333333333390107.3333333333

    73017.09589041191.25108.345890411

    74016.864864864992.5109.3648648649

    75016.6493.75110.39

    76016.421052631695111.4210526316

    77016.207792207896.25112.4577922078

    7801697.5113.5

    79015.797468354498.75114.5474683544

    80015.6100115.6

    81015.4074074074101.25116.6574074074

    82015.2195121951102.5117.7195121951

    83015.0361445783103.75118.7861445783

    84014.8571428571105119.8571428571

    85014.6823529412106.25120.9323529412

    86014.511627907107.5122.011627907

    87014.3448275862108.75123.0948275862

    88014.1818181818110124.1818181818

    89014.0224719101111.25125.2724719101

    90013.8666666667112.5126.3666666667

    91013.7142857143113.75127.4642857143

    92013.5652173913115128.5652173913

    93013.4193548387116.25129.6693548387

    94013.2765957447117.5130.7765957447

    95013.1368421053118.75131.8868421053

    96013120133

    97012.8659793814121.25134.1159793814

    98012.7346938776122.5135.2346938776

    99012.6060606061123.75136.3560606061

    100012.48125137.48

    8000850090009500100001100011,5001200012500130001350014000145001500015500160001650017000175001800018500190001950020000

    DemandProbWeighted Demand

    80000.11880260000230000200000170000140000800005000020000-10000-40000-70000-100000-130000-160000-190000-220000-250000-280000-310000-340000-370000-400000-430000-460000

    100000.111100260000282500305000327500350000290000260000230000200000170000140000110000800005000020000-10000-40000-70000-100000-130000-160000-190000-220000-250000

    120000.283360260000282500305000327500350000395000417500440000410000380000350000320000290000260000230000200000170000140000110000800005000020000-10000-40000

    140000.223080260000282500305000327500350000395000417500440000462500485000507500530000500000470000440000410000380000350000320000290000260000230000200000170000

    160000.182880260000282500305000327500350000395000417500440000462500485000507500530000552500575000597500620000590000560000530000500000470000440000410000380000

    180000.11800260000282500305000327500350000395000417500440000462500485000507500530000552500575000597500620000642500665000687500710000680000650000620000590000

    8000850090009500100001100011,5001200012500130001350014000145001500015500160001650017000175001800018500190001950020000

    11310026000027672529345031017532690034880035975037070036695036320035945035570034040032510030980029450026975024500022025019550016550013550010550075500

    Sheet1

    73.411764705921.2594.6617647059

    69.333333333322.591.8333333333

    65.684210526323.7589.4342105263

    62.42587.4

    59.428571428626.2585.6785714286

    56.727272727327.584.2272727273

    54.260869565228.7583.0108695652

    523082

    49.9231.2581.17

    4832.580.5

    46.222222222233.7579.9722222222

    44.57142857143579.5714285714

    43.034482758636.2579.2844827586

    41.637.579.1

    40.258064516138.7579.0080645161

    394079

    37.818181818241.2579.0681818182

    36.705882352942.579.2058823529

    35.657142857143.7579.4071428571

    34.66666666674579.6666666667

    33.729729729746.2579.9797297297

    32.842105263247.580.3421052632

    3248.7580.75

    31.25081.2

    30.439024390251.2581.6890243902

    29.714285714352.582.2142857143

    29.02325581453.7582.773255814

    28.36363636365583.3636363636

    27.733333333356.2583.9833333333

    27.130434782657.584.6304347826

    26.553191489458.7585.3031914894

    266086

    25.469387755161.2586.7193877551

    24.9662.587.46

    24.470588235363.7588.2205882353

    246589

    23.547169811366.2589.7971698113

    23.111111111167.590.6111111111

    22.690909090968.7591.4409090909

    22.28571428577092.2857142857

    21.894736842171.2593.1447368421

    21.517241379372.594.0172413793

    21.152542372973.7594.9025423729

    20.87595.8

    20.459016393476.2596.7090163934

    20.129032258177.597.6290322581

    19.809523809578.7598.5595238095

    19.58099.5

    19.281.25100.45

    18.909090909182.5101.4090909091

    18.626865671683.75102.3768656716

    18.352941176585103.3529411765

    18.086956521786.25104.3369565217

    17.828571428687.5105.3285714286

    17.577464788788.75106.3274647887

    17.333333333390107.3333333333

    17.09589041191.25108.345890411

    16.864864864992.5109.3648648649

    16.6493.75110.39

    16.421052631695111.4210526316

    16.207792207896.25112.4577922078

    1697.5113.5

    15.797468354498.75114.5474683544

    15.6100115.6

    15.4074074074101.25116.6574074074

    15.2195121951102.5117.7195121951

    15.0361445783103.75118.7861445783

    14.8571428571105119.8571428571

    14.6823529412106.25120.9323529412

    14.511627907107.5122.011627907

    14.3448275862108.75123.0948275862

    14.1818181818110124.1818181818

    14.0224719101111.25125.2724719101

    13.8666666667112.5126.3666666667

    13.7142857143113.75127.4642857143

    13.5652173913115128.5652173913

    13.4193548387116.25129.6693548387

    13.2765957447117.5130.7765957447

    13.1368421053118.75131.8868421053

    13120133

    12.8659793814121.25134.1159793814

    12.7346938776122.5135.2346938776

    12.6060606061123.75136.3560606061

    12.48125137.48

    Order Quantity

    Cost

    Sheet2

    0

    0

    0

    0

    0

    0

    Sales

    Probability

    Demand Scenarios

    Sheet3

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Order Quantity

    Profit

    Expected Profit

  • SnowTime Expected Profit

    Chart2

    260000

    276725

    293450

    310175

    326900

    348800

    359750

    370700

    366950

    363200

    359450

    355700

    340400

    325100

    309800

    294500

    269750

    245000

    220250

    195500

    165500

    135500

    105500

    75500

    Order Quantity

    Profit

    Expected Profit

    Sheet1

    Amount to Order:(each time inventory hits 0)

    Order Cost:12

    Weekly Demand:20

    Annual Demand:1040

    Annual Orders:(Annual Demand / Amount to Order)

    Holding Cost:0.25(25% of .02)

    Avg. Annual Inven:(Half of Order Amount Times Number of Orders)

    Total Annual Cost:(Avg. Annual Inven)*Holding Cost + Number of Orders * Order Cost

    QOrder CostHolding CostTC

    1012481.251249.25

    206242.5626.5

    304163.75419.75

    403125317

    50249.66.25255.85

    602087.5215.5

    70178.28571428578.75187.0357142857

    8015610166

    90138.666666666711.25149.9166666667

    100124.812.5137.3

    110113.454545454513.75127.2045454545

    12010415119

    1309616.25112.25

    14089.142857142917.5106.6428571429

    15083.218.75101.95

    160782098

    17073.411764705921.2594.6617647059

    18069.333333333322.591.8333333333

    19065.684210526323.7589.4342105263

    20062.42587.4

    21059.428571428626.2585.6785714286

    22056.727272727327.584.2272727273

    23054.260869565228.7583.0108695652

    240523082

    25049.9231.2581.17

    2604832.580.5

    27046.222222222233.7579.9722222222

    28044.57142857143579.5714285714

    29043.034482758636.2579.2844827586

    30041.637.579.1

    31040.258064516138.7579.0080645161

    320394079

    33037.818181818241.2579.0681818182

    34036.705882352942.579.2058823529

    35035.657142857143.7579.4071428571

    36034.66666666674579.6666666667

    37033.729729729746.2579.9797297297

    38032.842105263247.580.3421052632

    3903248.7580.75

    40031.25081.2

    41030.439024390251.2581.6890243902

    42029.714285714352.582.2142857143

    43029.02325581453.7582.773255814

    44028.36363636365583.3636363636

    45027.733333333356.2583.9833333333

    46027.130434782657.584.6304347826

    47026.553191489458.7585.3031914894

    480266086

    49025.469387755161.2586.7193877551

    50024.9662.587.46

    51024.470588235363.7588.2205882353

    520246589

    53023.547169811366.2589.7971698113

    54023.111111111167.590.6111111111

    55022.690909090968.7591.4409090909

    56022.28571428577092.2857142857

    57021.894736842171.2593.1447368421

    58021.517241379372.594.0172413793

    59021.152542372973.7594.9025423729

    60020.87595.8

    61020.459016393476.2596.7090163934

    62020.129032258177.597.6290322581

    63019.809523809578.7598.5595238095

    64019.58099.5

    65019.281.25100.45

    66018.909090909182.5101.4090909091

    67018.626865671683.75102.3768656716

    68018.352941176585103.3529411765

    69018.086956521786.25104.3369565217

    70017.828571428687.5105.3285714286

    71017.577464788788.75106.3274647887

    72017.333333333390107.3333333333

    73017.09589041191.25108.345890411

    74016.864864864992.5109.3648648649

    75016.6493.75110.39

    76016.421052631695111.4210526316

    77016.207792207896.25112.4577922078

    7801697.5113.5

    79015.797468354498.75114.5474683544

    80015.6100115.6

    81015.4074074074101.25116.6574074074

    82015.2195121951102.5117.7195121951

    83015.0361445783103.75118.7861445783

    84014.8571428571105119.8571428571

    85014.6823529412106.25120.9323529412

    86014.511627907107.5122.011627907

    87014.3448275862108.75123.0948275862

    88014.1818181818110124.1818181818

    89014.0224719101111.25125.2724719101

    90013.8666666667112.5126.3666666667

    91013.7142857143113.75127.4642857143

    92013.5652173913115128.5652173913

    93013.4193548387116.25129.6693548387

    94013.2765957447117.5130.7765957447

    95013.1368421053118.75131.8868421053

    96013120133

    97012.8659793814121.25134.1159793814

    98012.7346938776122.5135.2346938776

    99012.6060606061123.75136.3560606061

    100012.48125137.48

    8000850090009500100001100011,5001200012500130001350014000145001500015500160001650017000175001800018500190001950020000

    DemandProbWeighted Demand

    80000.11880260000230000200000170000140000800005000020000-10000-40000-70000-100000-130000-160000-190000-220000-250000-280000-310000-340000-370000-400000-430000-460000

    100000.111100260000282500305000327500350000290000260000230000200000170000140000110000800005000020000-10000-40000-70000-100000-130000-160000-190000-220000-250000

    120000.283360260000282500305000327500350000395000417500440000410000380000350000320000290000260000230000200000170000140000110000800005000020000-10000-40000

    140000.223080260000282500305000327500350000395000417500440000462500485000507500530000500000470000440000410000380000350000320000290000260000230000200000170000

    160000.182880260000282500305000327500350000395000417500440000462500485000507500530000552500575000597500620000590000560000530000500000470000440000410000380000

    180000.11800260000282500305000327500350000395000417500440000462500485000507500530000552500575000597500620000642500665000687500710000680000650000620000590000

    8000850090009500100001100011,5001200012500130001350014000145001500015500160001650017000175001800018500190001950020000

    11310026000027672529345031017532690034880035975037070036695036320035945035570034040032510030980029450026975024500022025019550016550013550010550075500

    Sheet1

    73.411764705921.2594.6617647059

    69.333333333322.591.8333333333

    65.684210526323.7589.4342105263

    62.42587.4

    59.428571428626.2585.6785714286

    56.727272727327.584.2272727273

    54.260869565228.7583.0108695652

    523082

    49.9231.2581.17

    4832.580.5

    46.222222222233.7579.9722222222

    44.57142857143579.5714285714

    43.034482758636.2579.2844827586

    41.637.579.1

    40.258064516138.7579.0080645161

    394079

    37.818181818241.2579.0681818182

    36.705882352942.579.2058823529

    35.657142857143.7579.4071428571

    34.66666666674579.6666666667

    33.729729729746.2579.9797297297

    32.842105263247.580.3421052632

    3248.7580.75

    31.25081.2

    30.439024390251.2581.6890243902

    29.714285714352.582.2142857143

    29.02325581453.7582.773255814

    28.36363636365583.3636363636

    27.733333333356.2583.9833333333

    27.130434782657.584.6304347826

    26.553191489458.7585.3031914894

    266086

    25.469387755161.2586.7193877551

    24.9662.587.46

    24.470588235363.7588.2205882353

    246589

    23.547169811366.2589.7971698113

    23.111111111167.590.6111111111

    22.690909090968.7591.4409090909

    22.28571428577092.2857142857

    21.894736842171.2593.1447368421

    21.517241379372.594.0172413793

    21.152542372973.7594.9025423729

    20.87595.8

    20.459016393476.2596.7090163934

    20.129032258177.597.6290322581

    19.809523809578.7598.5595238095

    19.58099.5

    19.281.25100.45

    18.909090909182.5101.4090909091

    18.626865671683.75102.3768656716

    18.352941176585103.3529411765

    18.086956521786.25104.3369565217

    17.828571428687.5105.3285714286

    17.577464788788.75106.3274647887

    17.333333333390107.3333333333

    17.09589041191.25108.345890411

    16.864864864992.5109.3648648649

    16.6493.75110.39

    16.421052631695111.4210526316

    16.207792207896.25112.4577922078

    1697.5113.5

    15.797468354498.75114.5474683544

    15.6100115.6

    15.4074074074101.25116.6574074074

    15.2195121951102.5117.7195121951

    15.0361445783103.75118.7861445783

    14.8571428571105119.8571428571

    14.6823529412106.25120.9323529412

    14.511627907107.5122.011627907

    14.3448275862108.75123.0948275862

    14.1818181818110124.1818181818

    14.0224719101111.25125.2724719101

    13.8666666667112.5126.3666666667

    13.7142857143113.75127.4642857143

    13.5652173913115128.5652173913

    13.4193548387116.25129.6693548387

    13.2765957447117.5130.7765957447

    13.1368421053118.75131.8868421053

    13120133

    12.8659793814121.25134.1159793814

    12.7346938776122.5135.2346938776

    12.6060606061123.75136.3560606061

    12.48125137.48

    Order Quantity

    Cost

    Sheet2

    0

    0

    0

    0

    0

    0

    Sales

    Probability

    Demand Scenarios

    Sheet3

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Order Quantity

    Profit

    Expected Profit

  • SnowTime: Important ObservationsTradeoff between ordering enough to meet demand and ordering too muchSeveral quantities have the same average profitAverage profit does not tell the whole story

    Question: 9000 and 16000 units lead to about the same average profit, so which do we prefer?

  • SnowTime Expected Profit

    Chart2

    260000

    276725

    293450

    310175

    326900

    348800

    359750

    370700

    366950

    363200

    359450

    355700

    340400

    325100

    309800

    294500

    269750

    245000

    220250

    195500

    165500

    135500

    105500

    75500

    Order Quantity

    Profit

    Expected Profit

    Sheet1

    Amount to Order:(each time inventory hits 0)

    Order Cost:12

    Weekly Demand:20

    Annual Demand:1040

    Annual Orders:(Annual Demand / Amount to Order)

    Holding Cost:0.25(25% of .02)

    Avg. Annual Inven:(Half of Order Amount Times Number of Orders)

    Total Annual Cost:(Avg. Annual Inven)*Holding Cost + Number of Orders * Order Cost

    QOrder CostHolding CostTC

    1012481.251249.25

    206242.5626.5

    304163.75419.75

    403125317

    50249.66.25255.85

    602087.5215.5

    70178.28571428578.75187.0357142857

    8015610166

    90138.666666666711.25149.9166666667

    100124.812.5137.3

    110113.454545454513.75127.2045454545

    12010415119

    1309616.25112.25

    14089.142857142917.5106.6428571429

    15083.218.75101.95

    160782098

    17073.411764705921.2594.6617647059

    18069.333333333322.591.8333333333

    19065.684210526323.7589.4342105263

    20062.42587.4

    21059.428571428626.2585.6785714286

    22056.727272727327.584.2272727273

    23054.260869565228.7583.0108695652

    240523082

    25049.9231.2581.17

    2604832.580.5

    27046.222222222233.7579.9722222222

    28044.57142857143579.5714285714

    29043.034482758636.2579.2844827586

    30041.637.579.1

    31040.258064516138.7579.0080645161

    320394079

    33037.818181818241.2579.0681818182

    34036.705882352942.579.2058823529

    35035.657142857143.7579.4071428571

    36034.66666666674579.6666666667

    37033.729729729746.2579.9797297297

    38032.842105263247.580.3421052632

    3903248.7580.75

    40031.25081.2

    41030.439024390251.2581.6890243902

    42029.714285714352.582.2142857143

    43029.02325581453.7582.773255814

    44028.36363636365583.3636363636

    45027.733333333356.2583.9833333333

    46027.130434782657.584.6304347826

    47026.553191489458.7585.3031914894

    480266086

    49025.469387755161.2586.7193877551

    50024.9662.587.46

    51024.470588235363.7588.2205882353

    520246589

    53023.547169811366.2589.7971698113

    54023.111111111167.590.6111111111

    55022.690909090968.7591.4409090909

    56022.28571428577092.2857142857

    57021.894736842171.2593.1447368421

    58021.517241379372.594.0172413793

    59021.152542372973.7594.9025423729

    60020.87595.8

    61020.459016393476.2596.7090163934

    62020.129032258177.597.6290322581

    63019.809523809578.7598.5595238095

    64019.58099.5

    65019.281.25100.45

    66018.909090909182.5101.4090909091

    67018.626865671683.75102.3768656716

    68018.352941176585103.3529411765

    69018.086956521786.25104.3369565217

    70017.828571428687.5105.3285714286

    71017.577464788788.75106.3274647887

    72017.333333333390107.3333333333

    73017.09589041191.25108.345890411

    74016.864864864992.5109.3648648649

    75016.6493.75110.39

    76016.421052631695111.4210526316

    77016.207792207896.25112.4577922078

    7801697.5113.5

    79015.797468354498.75114.5474683544

    80015.6100115.6

    81015.4074074074101.25116.6574074074

    82015.2195121951102.5117.7195121951

    83015.0361445783103.75118.7861445783

    84014.8571428571105119.8571428571

    85014.6823529412106.25120.9323529412

    86014.511627907107.5122.011627907

    87014.3448275862108.75123.0948275862

    88014.1818181818110124.1818181818

    89014.0224719101111.25125.2724719101

    90013.8666666667112.5126.3666666667

    91013.7142857143113.75127.4642857143

    92013.5652173913115128.5652173913

    93013.4193548387116.25129.6693548387

    94013.2765957447117.5130.7765957447

    95013.1368421053118.75131.8868421053

    96013120133

    97012.8659793814121.25134.1159793814

    98012.7346938776122.5135.2346938776

    99012.6060606061123.75136.3560606061

    100012.48125137.48

    8000850090009500100001100011,5001200012500130001350014000145001500015500160001650017000175001800018500190001950020000

    DemandProbWeighted Demand

    80000.11880260000230000200000170000140000800005000020000-10000-40000-70000-100000-130000-160000-190000-220000-250000-280000-310000-340000-370000-400000-430000-460000

    100000.111100260000282500305000327500350000290000260000230000200000170000140000110000800005000020000-10000-40000-70000-100000-130000-160000-190000-220000-250000

    120000.283360260000282500305000327500350000395000417500440000410000380000350000320000290000260000230000200000170000140000110000800005000020000-10000-40000

    140000.223080260000282500305000327500350000395000417500440000462500485000507500530000500000470000440000410000380000350000320000290000260000230000200000170000

    160000.182880260000282500305000327500350000395000417500440000462500485000507500530000552500575000597500620000590000560000530000500000470000440000410000380000

    180000.11800260000282500305000327500350000395000417500440000462500485000507500530000552500575000597500620000642500665000687500710000680000650000620000590000

    8000850090009500100001100011,5001200012500130001350014000145001500015500160001650017000175001800018500190001950020000

    11310026000027672529345031017532690034880035975037070036695036320035945035570034040032510030980029450026975024500022025019550016550013550010550075500

    Sheet1

    73.411764705921.2594.6617647059

    69.333333333322.591.8333333333

    65.684210526323.7589.4342105263

    62.42587.4

    59.428571428626.2585.6785714286

    56.727272727327.584.2272727273

    54.260869565228.7583.0108695652

    523082

    49.9231.2581.17

    4832.580.5

    46.222222222233.7579.9722222222

    44.57142857143579.5714285714

    43.034482758636.2579.2844827586

    41.637.579.1

    40.258064516138.7579.0080645161

    394079

    37.818181818241.2579.0681818182

    36.705882352942.579.2058823529

    35.657142857143.7579.4071428571

    34.66666666674579.6666666667

    33.729729729746.2579.9797297297

    32.842105263247.580.3421052632

    3248.7580.75

    31.25081.2

    30.439024390251.2581.6890243902

    29.714285714352.582.2142857143

    29.02325581453.7582.773255814

    28.36363636365583.3636363636

    27.733333333356.2583.9833333333

    27.130434782657.584.6304347826

    26.553191489458.7585.3031914894

    266086

    25.469387755161.2586.7193877551

    24.9662.587.46

    24.470588235363.7588.2205882353

    246589

    23.547169811366.2589.7971698113

    23.111111111167.590.6111111111

    22.690909090968.7591.4409090909

    22.28571428577092.2857142857

    21.894736842171.2593.1447368421

    21.517241379372.594.0172413793

    21.152542372973.7594.9025423729

    20.87595.8

    20.459016393476.2596.7090163934

    20.129032258177.597.6290322581

    19.809523809578.7598.5595238095

    19.58099.5

    19.281.25100.45

    18.909090909182.5101.4090909091

    18.626865671683.75102.3768656716

    18.352941176585103.3529411765

    18.086956521786.25104.3369565217

    17.828571428687.5105.3285714286

    17.577464788788.75106.3274647887

    17.333333333390107.3333333333

    17.09589041191.25108.345890411

    16.864864864992.5109.3648648649

    16.6493.75110.39

    16.421052631695111.4210526316

    16.207792207896.25112.4577922078

    1697.5113.5

    15.797468354498.75114.5474683544

    15.6100115.6

    15.4074074074101.25116.6574074074

    15.2195121951102.5117.7195121951

    15.0361445783103.75118.7861445783

    14.8571428571105119.8571428571

    14.6823529412106.25120.9323529412

    14.511627907107.5122.011627907

    14.3448275862108.75123.0948275862

    14.1818181818110124.1818181818

    14.0224719101111.25125.2724719101

    13.8666666667112.5126.3666666667

    13.7142857143113.75127.4642857143

    13.5652173913115128.5652173913

    13.4193548387116.25129.6693548387

    13.2765957447117.5130.7765957447

    13.1368421053118.75131.8868421053

    13120133

    12.8659793814121.25134.1159793814

    12.7346938776122.5135.2346938776

    12.6060606061123.75136.3560606061

    12.48125137.48

    Order Quantity

    Cost

    Sheet2

    0

    0

    0

    0

    0

    0

    Sales

    Probability

    Demand Scenarios

    Sheet3

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Order Quantity

    Profit

    Expected Profit

  • Probability of Outcomes

    Chart3

    00

    00.11

    00.11

    00

    00

    0.110.28

    0.890

    00.22

    00

    6000000.28

    Q=9000

    Q=16000

    Revenue

    Probability

    Sheet1

    Amount to Order:(each time inventory hits 0)

    Order Cost:12

    Weekly Demand:20

    Annual Demand:1040

    Annual Orders:(Annual Demand / Amount to Order)

    Holding Cost:0.25(25% of .02)

    Avg. Annual Inven:(Half of Order Amount Times Number of Orders)

    Total Annual Cost:(Avg. Annual Inven)*Holding Cost + Number of Orders * Order Cost

    QOrder CostHolding CostTC

    1012481.251249.25

    206242.5626.5

    304163.75419.75

    403125317

    50249.66.25255.85

    602087.5215.5

    70178.28571428578.75187.0357142857

    8015610166

    90138.666666666711.25149.9166666667

    100124.812.5137.3

    110113.454545454513.75127.2045454545

    12010415119

    1309616.25112.25

    14089.142857142917.5106.6428571429

    15083.218.75101.95

    160782098

    17073.411764705921.2594.6617647059

    18069.333333333322.591.8333333333

    19065.684210526323.7589.4342105263

    20062.42587.4

    21059.428571428626.2585.6785714286

    22056.727272727327.584.2272727273

    23054.260869565228.7583.0108695652

    240523082

    25049.9231.2581.17

    2604832.580.5

    27046.222222222233.7579.9722222222

    28044.57142857143579.5714285714

    29043.034482758636.2579.2844827586

    30041.637.579.1

    31040.258064516138.7579.0080645161

    320394079

    33037.818181818241.2579.0681818182

    34036.705882352942.579.2058823529

    35035.657142857143.7579.4071428571

    36034.66666666674579.6666666667

    37033.729729729746.2579.9797297297

    38032.842105263247.580.3421052632

    3903248.7580.75

    40031.25081.2

    41030.439024390251.2581.6890243902

    42029.714285714352.582.2142857143

    43029.02325581453.7582.773255814

    44028.36363636365583.3636363636

    45027.733333333356.2583.9833333333

    46027.130434782657.584.6304347826

    47026.553191489458.7585.3031914894

    480266086

    49025.469387755161.2586.7193877551

    50024.9662.587.46

    51024.470588235363.7588.2205882353

    520246589

    53023.547169811366.2589.7971698113

    54023.111111111167.590.6111111111

    55022.690909090968.7591.4409090909

    56022.28571428577092.2857142857

    57021.894736842171.2593.1447368421

    58021.517241379372.594.0172413793

    59021.152542372973.7594.9025423729

    60020.87595.8

    61020.459016393476.2596.7090163934

    62020.129032258177.597.6290322581

    63019.809523809578.7598.5595238095

    64019.58099.5

    65019.281.25100.45

    66018.909090909182.5101.4090909091

    67018.626865671683.75102.3768656716

    68018.352941176585103.3529411765

    69018.086956521786.25104.3369565217

    70017.828571428687.5105.3285714286

    71017.577464788788.75106.3274647887

    72017.333333333390107.3333333333

    73017.09589041191.25108.345890411

    74016.864864864992.5109.3648648649

    75016.6493.75110.39

    76016.421052631695111.4210526316

    77016.207792207896.25112.4577922078

    7801697.5113.5

    79015.797468354498.75114.5474683544

    80015.6100115.6

    81015.4074074074101.25116.6574074074

    82015.2195121951102.5117.7195121951

    83015.0361445783103.75118.7861445783

    84014.8571428571105119.8571428571

    85014.6823529412106.25120.9323529412

    86014.511627907107.5122.011627907

    87014.3448275862108.75123.0948275862

    88014.1818181818110124.1818181818

    89014.0224719101111.25125.2724719101

    90013.8666666667112.5126.3666666667

    91013.7142857143113.75127.4642857143

    92013.5652173913115128.5652173913

    93013.4193548387116.25129.6693548387

    94013.2765957447117.5130.7765957447

    95013.1368421053118.75131.8868421053

    96013120133

    97012.8659793814121.25134.1159793814

    98012.7346938776122.5135.2346938776

    99012.6060606061123.75136.3560606061

    100012.48125137.48

    8000850090009500100001100011,5001200012500130001350014000145001500015500160001650017000175001800018500190001950020000

    DemandProbWeighted Demand

    80000.11880260000230000200000170000140000800005000020000-10000-40000-70000-100000-130000-160000-190000-220000-250000-280000-310000-340000-370000-400000-430000-460000

    100000.111100260000282500305000327500350000290000260000230000200000170000140000110000800005000020000-10000-40000-70000-100000-130000-160000-190000-220000-250000

    120000.283360260000282500305000327500350000395000417500440000410000380000350000320000290000260000230000200000170000140000110000800005000020000-10000-40000

    140000.223080260000282500305000327500350000395000417500440000462500485000507500530000500000470000440000410000380000350000320000290000260000230000200000170000

    160000.182880260000282500305000327500350000395000417500440000462500485000507500530000552500575000597500620000590000560000530000500000470000440000410000380000

    180000.11800260000282500305000327500350000395000417500440000462500485000507500530000552500575000597500620000642500665000687500710000680000650000620000590000

    8000850090009500100001100011,5001200012500130001350014000145001500015500160001650017000175001800018500190001950020000

    11310026000027672529345031017532690034880035975037070036695036320035945035570034040032510030980029450026975024500022025019550016550013550010550075500

    900016000900016000

    0.11200000-220000-30000000

    0.11305000-10000-20000000.11

    0.28305000200000-10000000.11

    0.22305000410000000

    0.1830500062000010000000

    0.13050006200002000000.110.28

    3000000.890

    90001600040000000.22

    29345029450050000000

    6000000.28

    Sheet1

    73.411764705921.2594.6617647059

    69.333333333322.591.8333333333

    65.684210526323.7589.4342105263

    62.42587.4

    59.428571428626.2585.6785714286

    56.727272727327.584.2272727273

    54.260869565228.7583.0108695652

    523082

    49.9231.2581.17

    4832.580.5

    46.222222222233.7579.9722222222

    44.57142857143579.5714285714

    43.034482758636.2579.2844827586

    41.637.579.1

    40.258064516138.7579.0080645161

    394079

    37.818181818241.2579.0681818182

    36.705882352942.579.2058823529

    35.657142857143.7579.4071428571

    34.66666666674579.6666666667

    33.729729729746.2579.9797297297

    32.842105263247.580.3421052632

    3248.7580.75

    31.25081.2

    30.439024390251.2581.6890243902

    29.714285714352.582.2142857143

    29.02325581453.7582.773255814

    28.36363636365583.3636363636

    27.733333333356.2583.9833333333

    27.130434782657.584.6304347826

    26.553191489458.7585.3031914894

    266086

    25.469387755161.2586.7193877551

    24.9662.587.46

    24.470588235363.7588.2205882353

    246589

    23.547169811366.2589.7971698113

    23.111111111167.590.6111111111

    22.690909090968.7591.4409090909

    22.28571428577092.2857142857

    21.894736842171.2593.1447368421

    21.517241379372.594.0172413793

    21.152542372973.7594.9025423729

    20.87595.8

    20.459016393476.2596.7090163934

    20.129032258177.597.6290322581

    19.809523809578.7598.5595238095

    19.58099.5

    19.281.25100.45

    18.909090909182.5101.4090909091

    18.626865671683.75102.3768656716

    18.352941176585103.3529411765

    18.086956521786.25104.3369565217

    17.828571428687.5105.3285714286

    17.577464788788.75106.3274647887

    17.333333333390107.3333333333

    17.09589041191.25108.345890411

    16.864864864992.5109.3648648649

    16.6493.75110.39

    16.421052631695111.4210526316

    16.207792207896.25112.4577922078

    1697.5113.5

    15.797468354498.75114.5474683544

    15.6100115.6

    15.4074074074101.25116.6574074074

    15.2195121951102.5117.7195121951

    15.0361445783103.75118.7861445783

    14.8571428571105119.8571428571

    14.6823529412106.25120.9323529412

    14.511627907107.5122.011627907

    14.3448275862108.75123.0948275862

    14.1818181818110124.1818181818

    14.0224719101111.25125.2724719101

    13.8666666667112.5126.3666666667

    13.7142857143113.75127.4642857143

    13.5652173913115128.5652173913

    13.4193548387116.25129.6693548387

    13.2765957447117.5130.7765957447

    13.1368421053118.75131.8868421053

    13120133

    12.8659793814121.25134.1159793814

    12.7346938776122.5135.2346938776

    12.6060606061123.75136.3560606061

    12.48125137.48

    Order Quantity

    Cost

    Sheet2

    0

    0

    0

    0

    0

    0

    Sales

    Probability

    Demand Scenarios

    Sheet3

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Order Quantity

    Profit

    Expected Profit

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    Q=9000

    Q=1600

    Cost

    Probability

  • Key Insights from this ModelThe optimal order quantity is not necessarily equal to average forecast demandThe optimal quantity depends on the relationship between marginal profit and marginal costAs order quantity increases, average profit first increases and then decreasesAs production quantity increases, risk increases. In other words, the probability of large gains and of large losses increases

  • Supply ContractsWholesale Price =$80

  • Demand Scenarios

    Chart1

    0.11

    0.11

    0.28

    0.22

    0.18

    0.1

    Sales

    Probability

    Demand Scenarios

    Sheet1

    Amount to Order:(each time inventory hits 0)

    Order Cost:12

    Weekly Demand:20

    Annual Demand:1040

    Annual Orders:(Annual Demand / Amount to Order)

    Holding Cost:0.25(25% of .02)

    Avg. Annual Inven:(Half of Order Amount Times Number of Orders)

    Total Annual Cost:(Avg. Annual Inven)*Holding Cost + Number of Orders * Order Cost

    QOrder CostHolding CostTC

    1012481.251249.25

    206242.5626.5

    304163.75419.75

    403125317

    50249.66.25255.85

    602087.5215.5

    70178.28571428578.75187.0357142857

    8015610166

    90138.666666666711.25149.9166666667

    100124.812.5137.3

    110113.454545454513.75127.2045454545

    12010415119

    1309616.25112.25

    14089.142857142917.5106.6428571429

    15083.218.75101.95

    160782098

    17073.411764705921.2594.6617647059

    18069.333333333322.591.8333333333

    19065.684210526323.7589.4342105263

    20062.42587.4

    21059.428571428626.2585.6785714286

    22056.727272727327.584.2272727273

    23054.260869565228.7583.0108695652

    240523082

    25049.9231.2581.17

    2604832.580.5

    27046.222222222233.7579.9722222222

    28044.57142857143579.5714285714

    29043.034482758636.2579.2844827586

    30041.637.579.1

    31040.258064516138.7579.0080645161

    320394079

    33037.818181818241.2579.0681818182

    34036.705882352942.579.2058823529

    35035.657142857143.7579.4071428571

    36034.66666666674579.6666666667

    37033.729729729746.2579.9797297297

    38032.842105263247.580.3421052632

    3903248.7580.75

    40031.25081.2

    41030.439024390251.2581.6890243902

    42029.714285714352.582.2142857143

    43029.02325581453.7582.773255814

    44028.36363636365583.3636363636

    45027.733333333356.2583.9833333333

    46027.130434782657.584.6304347826

    47026.553191489458.7585.3031914894

    480266086

    49025.469387755161.2586.7193877551

    50024.9662.587.46

    51024.470588235363.7588.2205882353

    520246589

    53023.547169811366.2589.7971698113

    54023.111111111167.590.6111111111

    55022.690909090968.7591.4409090909

    56022.28571428577092.2857142857

    57021.894736842171.2593.1447368421

    58021.517241379372.594.0172413793

    59021.152542372973.7594.9025423729

    60020.87595.8

    61020.459016393476.2596.7090163934

    62020.129032258177.597.6290322581

    63019.809523809578.7598.5595238095

    64019.58099.5

    65019.281.25100.45

    66018.909090909182.5101.4090909091

    67018.626865671683.75102.3768656716

    68018.352941176585103.3529411765

    69018.086956521786.25104.3369565217

    70017.828571428687.5105.3285714286

    71017.577464788788.75106.3274647887

    72017.333333333390107.3333333333

    73017.09589041191.25108.345890411

    74016.864864864992.5109.3648648649

    75016.6493.75110.39

    76016.421052631695111.4210526316

    77016.207792207896.25112.4577922078

    7801697.5113.5

    79015.797468354498.75114.5474683544

    80015.6100115.6

    81015.4074074074101.25116.6574074074

    82015.2195121951102.5117.7195121951

    83015.0361445783103.75118.7861445783

    84014.8571428571105119.8571428571

    85014.6823529412106.25120.9323529412

    86014.511627907107.5122.011627907

    87014.3448275862108.75123.0948275862

    88014.1818181818110124.1818181818

    89014.0224719101111.25125.2724719101

    90013.8666666667112.5126.3666666667

    91013.7142857143113.75127.4642857143

    92013.5652173913115128.5652173913

    93013.4193548387116.25129.6693548387

    94013.2765957447117.5130.7765957447

    95013.1368421053118.75131.8868421053

    96013120133

    97012.8659793814121.25134.1159793814

    98012.7346938776122.5135.2346938776

    99012.6060606061123.75136.3560606061

    100012.48125137.48

    80000.11

    100000.11

    120000.28

    140000.22

    160000.18

    180000.1

    1

    Sheet1

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

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    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

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    000

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    000

    000

    000

    000

    000

    000

    000

    000

    000

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    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    Order Quantity

    Cost

    Sheet2

    0.11

    0.11

    0.28

    0.22

    0.18

    0.1

    Sales

    Probability

    Demand Scenarios

    Sheet3

  • Distributor Expected Profit

  • Distributor Expected Profit

  • Supply Contracts (cont.)Distributor optimal order quantity is 12,000 unitsDistributor expected profit is $470,000Manufacturer profit is $440,000Supply Chain Profit is $910,000

    Is there anything that the distributor and manufacturer can do to increase the profit of both?

  • Supply ContractsWholesale Price =$80

  • Retailer Profit (Buy Back=$55)

    Chart3

    270000

    315000

    360000

    397300

    434600

    464200

    493800

    503800

    513800

    508400

    503000

    485000

    467000

    Order Quantity

    Retailer Profit

    Sheet1

    Amount to Order:(each time inventory hits 0)

    Order Cost:12

    Weekly Demand:20

    Annual Demand:1040

    Annual Orders:(Annual Demand / Amount to Order)

    Holding Cost:0.25(25% of .02)

    Avg. Annual Inven:(Half of Order Amount Times Number of Orders)

    Total Annual Cost:(Avg. Annual Inven)*Holding Cost + Number of Orders * Order Cost

    QOrder CostHolding CostTC

    1012481.251249.25

    206242.5626.5

    304163.75419.75

    403125317

    50249.66.25255.85

    602087.5215.5

    70178.28571428578.75187.0357142857

    8015610166

    90138.666666666711.25149.9166666667

    100124.812.5137.3

    110113.454545454513.75127.2045454545

    12010415119

    1309616.25112.25

    14089.142857142917.5106.6428571429

    15083.218.75101.95

    160782098

    17073.411764705921.2594.6617647059

    18069.333333333322.591.8333333333

    19065.684210526323.7589.4342105263

    20062.42587.4

    21059.428571428626.2585.6785714286

    22056.727272727327.584.2272727273

    23054.260869565228.7583.0108695652

    240523082

    25049.9231.2581.17

    2604832.580.5

    27046.222222222233.7579.9722222222

    28044.57142857143579.5714285714

    29043.034482758636.2579.2844827586

    30041.637.579.1

    31040.258064516138.7579.0080645161

    320394079

    33037.818181818241.2579.0681818182

    34036.705882352942.579.2058823529

    35035.657142857143.7579.4071428571

    36034.66666666674579.6666666667

    37033.729729729746.2579.9797297297

    38032.842105263247.580.3421052632

    3903248.7580.75

    40031.25081.2

    41030.439024390251.2581.6890243902

    42029.714285714352.582.2142857143

    43029.02325581453.7582.773255814

    44028.36363636365583.3636363636

    45027.733333333356.2583.9833333333

    46027.130434782657.584.6304347826

    47026.553191489458.7585.3031914894

    480266086

    49025.469387755161.2586.7193877551

    50024.9662.587.46

    51024.470588235363.7588.2205882353

    520246589

    53023.547169811366.2589.7971698113

    54023.111111111167.590.6111111111

    55022.690909090968.7591.4409090909

    56022.28571428577092.2857142857

    57021.894736842171.2593.1447368421

    58021.517241379372.594.0172413793

    59021.152542372973.7594.9025423729

    60020.87595.8

    61020.459016393476.2596.7090163934

    62020.129032258177.597.6290322581

    63019.809523809578.7598.5595238095

    64019.58099.5

    65019.281.25100.45

    66018.909090909182.5101.4090909091

    67018.626865671683.75102.3768656716

    68018.352941176585103.3529411765

    69018.086956521786.25104.3369565217

    70017.828571428687.5105.3285714286

    71017.577464788788.75106.3274647887

    72017.333333333390107.3333333333

    73017.09589041191.25108.345890411

    74016.864864864992.5109.3648648649

    75016.6493.75110.39

    76016.421052631695111.4210526316

    77016.207792207896.25112.4577922078

    7801697.5113.5

    79015.797468354498.75114.5474683544

    80015.6100115.6

    81015.4074074074101.25116.6574074074

    82015.2195121951102.5117.7195121951

    83015.0361445783103.75118.7861445783

    84014.8571428571105119.8571428571

    85014.6823529412106.25120.9323529412

    86014.511627907107.5122.011627907

    87014.3448275862108.75123.0948275862

    88014.1818181818110124.1818181818

    89014.0224719101111.25125.2724719101

    90013.8666666667112.5126.3666666667

    91013.7142857143113.75127.4642857143

    92013.5652173913115128.5652173913

    93013.4193548387116.25129.6693548387

    94013.2765957447117.5130.7765957447

    95013.1368421053118.75131.8868421053

    96013120133

    97012.8659793814121.25134.1159793814

    98012.7346938776122.5135.2346938776

    99012.6060606061123.75136.3560606061

    100012.48125137.48

    starting inven60007000800090001000011000120001300014000150001600017000180001900020000210002200023000240002500026000270002800029000300003100032000330003400035000360003700038000

    101700002150002600002934503269003488003707003632003557003251002945002450001955001355007550015500-44500-104500-164500-224500-284500-344500-404500-464500

    160007500006950007400007734508069008288008507008432008357008051007745007250006755006155005555004955004355003755003155002555001955001355007550015500

    1700087500082000085345088690090880093070092320091570088510085450080500075550069550063550057550051550045550039550033550027550021550015550095500

    18000100000093345096690098880010107001003200995700965100934500885000835500775500715500655500595500535500475500415500355500295500235500175500

    1900011134501046900106880010907001083200107570010451001014500965000915500855500795500735500675500615500555500495500435500375500315500255500

    11000012269001148800117070011632001155700112510010945001045000995500935500875500815500755500695500635500575500515500455500395500335500

    80008000800080008000800080008000800080008000800080008000800080008000800080008000800080008000800080008000800080008000800080008000800080008000

    800060007000800090001000011000120001300014000150001600017000180001900020000210002200023000240002500026000270002800029000300003100032000330003400035000360003700038000

    DemandProbWeighted Demand

    80000.118809100009550001000000840000780000720000660000600000540000480000420000360000300000240000180000120000600000-60000-120000-180000-240000-300000-360000-420000-480000-540000-600000-660000-720000-780000-840000-900000164000016400001000000

    100000.11110091000095500010000009450009900009300008700008100007500006900006300005700005100004500003900003300002700002100001500009000030000-30000-90000-150000-210000-270000-330000-390000-450000-510000-570000-630000-690000189000018900001250000

    120000.2833609100009550001000000945000990000103500010800001020000960000900000840000780000720000660000600000540000480000420000360000300000240000180000120000600000-60000-120000-180000-240000-300000-360000-420000-480000214000021400001500000

    140000.22308091000095500010000009450009900001035000108000011250001170000111000010500009900009300008700008100007500006900006300005700005100004500003900003300002700002100001500009000030000-30000-90000-150000-210000-270000239000023900001750000

    160000.18288091000095500010000009450009900001035000108000011250001170000121500012600001200000114000010800001020000960000900000840000780000720000660000600000540000480000420000360000300000240000180000120000600000-60000264000026400002000000

    180000.1180091000095500010000009450009900001035000108000011250001170000121500012600001305000135000012900001230000117000011100001050000990000930000870000810000750000690000630000570000510000450000390000330000270000210000150000289000028900002250000

    60007000800090001000011000120001300014000150001600017000180001900020000210002200023000240002500026000270002800029000300003100032000330003400035000360003700038000

    113100910000955000100000093345096690098880010107001003200995700965100934500885000835500775500715500655500595500535500475500415500355500295500235500175500

    900016000900016000

    0.11200000-220000-30000000

    0.11305000-10000-20000000.11

    0.28305000200000-10000000.11

    0.22305000410000000

    0.1830500062000010000000

    0.13050006200002000000.110.28

    3000000.890

    90001600040000000.22

    29345029450050000000

    6000000.28

    Sheet1

    000

    000

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    000

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    000

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    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

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    000

    000

    000

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    000

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    000

    000

    000

    000

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    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    Order Quantity

    Cost

    Sheet2

    0

    0

    0

    0

    0

    0

    Sales

    Probability

    Demand Scenarios

    Sheet3

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Order Quantity

    Profit

    Expected Profit

    Sheet5

    00

    00

    00

    00

    00

    00

    00

    00

    00

    00

    Q=9000

    Q=1600

    Cost

    Probability

    Sheet4

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    000000

    0

    6000

    7000

    8000

    9000

    10000

    Total Inventory

    Profit

    DemandProbWeighted Demand

    80000.11880

    100000.111100

    120000.283360

    140000.223080

    160000.182880

    180000.11800

    113100

    Dist sells for:125

    Mfg sells for:80

    Dist salvage:20

    Mfg buys back:55

    Fixed Prod Cost100,000

    Var Prod Cost35

    Distributor

    Order Q6000700080009000100001100012000130001400015000160001700018000

    DemandProb

    80000.11270,000315,000360,000335,000310,000285,000260,000235,000210,000185,000160,000135,000110,000

    100000.11270,000315,000360,000405,000450,000425,000400,000375,000350,000325,000300,000275,000250,000

    120000.28270,000315,000360,000405,000450,000495,000540,000515,000490,000465,000440,000415,000390,000

    140000.22270,000315,000360,000405,000450,000495,000540,000585,000630,000605,000580,000555,000530,000

    160000.18270,000315,000360,000405,000450,000495,000540,000585,000630,000675,000720,000695,000670,000

    180000.1270,000315,000360,000405,000450,000495,000540,000585,000630,000675,000720,000765,000810,000

    Expected P:270,000315,000360,000397,300434,600464,200493,800503,800513,800508,400503,000485,000467,000

    Maximum00000000513,8000000

    Manufacturer

    Order Q6000700080009000100001100012000130001400015000160001700018000

    DemandProb

    80000.11170,000215,000260,000270,000280,000290,000300,000310,000320,000330,000340,000350,000360,000

    100000.11170,000215,000260,000305,000350,000360,000370,000380,000390,000400,000410,000420,000430,000

    120000.28170,000215,000260,000305,000350,000395,000440,000450,000460,000470,000480,000490,000500,000

    140000.22170,000215,000260,000305,000350,000395,000440,000485,000530,000540,000550,000560,000570,000

    160000.18170,000215,000260,000305,000350,000395,000440,000485,000530,000575,000620,000630,000640,000

    180000.1170,000215,000260,000305,000350,000395,000440,000485,000530,000575,000620,000665,000710,000

    Expected P:170,000215,000260,000301,150342,300379,600416,900444,400471,900491,700511,500525,000538,500

    Exp. Total P:440,000530,000620,000698,450776,900843,800910,700948,200985,7001,000,1001,014,5001,010,0001,005,500

    73.411764705921.2594.6617647059

    69.333333333322.591.8333333333

    65.684210526323.7589.4342105263

    62.42587.4

    59.428571428626.2585.6785714286

    56.727272727327.584.2272727273

    54.260869565228.7583.0108695652

    523082

    49.9231.2581.17

    4832.580.5

    46.222222222233.7579.9722222222

    44.57142857143579.5714285714

    43.034482758636.2579.2844827586

    41.637.579.1

    40.258064516138.7579.0080645161

    394079

    37.818181818241.2579.0681818182

    36.705882352942.579.2058823529

    35.657142857143.7579.4071428571

    34.66666666674579.6666666667

    33.729729729746.2579.9797297297

    32.842105263247.580.3421052632

    3248.7580.75

    31.25081.2

    30.439024390251.2581.6890243902

    29.714285714352.582.2142857143

    29.02325581453.7582.773255814

    28.36363636365583.3636363636

    27.733333333356.2583.9833333333

    27.130434782657.584.6304347826

    26.553191489458.7585.3031914894

    266086

    25.469387755161.2586.7193877551

    24.9662.587.46

    24.470588235363.7588.2205882353

    246589

    23.547169811366.2589.7971698113

    23.111111111167.590.6111111111

    22.690909090968.7591.4409090909

    22.28571428577092.2857142857

    21.894736842171.2593.1447368421

    21.517241379372.594.0172413793

    21.152542372973.7594.9025423729

    20.87595.8

    20.459016393476.2596.7090163934

    20.129032258177.597.6290322581

    19.809523809578.7598.5595238095

    19.58099.5

    19.281.25100.45

    18.909090909182.5101.4090909091

    18.626865671683.75102.3768656716

    18.352941176585103.3529411765

    18.086956521786.25104.3369565217

    17.828571428687.5105.3285714286

    17.577464788788.75106.3274647887

    17.333333333390107.3333333333

    17.09589041191.25108.345890411

    16.864864864992.5109.3648648649

    16.6493.75110.39

    16.421052631695111.4210526316

    16.207792207896.25112.4577922078

    1697.5113.5

    15.797468354498.75114.5474683544

    15.6100115.6

    15.4074074074101.25116.6574074074

    15.2195121951102.5117.7195121951

    15.0361445783103.75118.7861445783

    14.8571428571105119.8571428571

    14.6823529412106.25120.9323529412

    14.511627907107.5122.011627907

    14.3448275862108.75123.0948275862

    14.1818181818110124.1818181818

    14.0224719101111.25125.2724719101

    13.8666666667112.5126.3666666667

    13.7142857143113.75127.4642857143

    13.5652173913115128.5652173913

    13.4193548387116.25129.6693548387

    13.2765957447117.5130.7765957447

    13.1368421053118.75131.8868421053

    13120133

    12.8659793814121.25134.1159793814

    12.7346938776122.5135.2346938776

    12.6060606061123.75136.3560606061

    12.48125137.48

    Order Quantity

    Cost

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    Dist. P

    Mfg. P

    Total P.

    Quantity

    Profit ($)

    Profit vs Order Quantity

    0

    0

    0

    0

    0

    0

    Quantity

    Probability

    Demand Scenario

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Production Quantity

    Manufacturer Profit

    DemandProbWeighted Demand

    80000.11880

    100000.111100

    120000.283360

    140000.223080

    160000.182880

    180000.11800

    113100

    Dist sells for:125

    Mfg sells for:80

    Dist salvage:20

    Mfg buys back:20

    Fixed Prod Cost100,000

    Var Prod Cost35

    Distributor

    Order Q6000700080009000100001100012000130001400015000160001700018000

    DemandProb

    8,0000.11270,000315,000360,000300,000240,000180,000120,00060,0000-60,000-120,000-180,000-240,000

    10,0000.11270,000315,000360,000405,000450,000390,000330,000270,000210,000150,00090,00030,000-30,000

    12,0000.28270,000315,000360,000405,000450,000495,000540,000480,000420,000360,000300,000240,000180,000

    14,0000.22270,000315,000360,000405,000450,000495,000540,000585,000630,000570,000510,000450,000390,000

    16,0000.18270,000315,000360,000405,000450,000495,000540,000585,000630,000675,000720,000660,000600,000

    18,0000.10270,000315,000360,000405,000450,000495,000540,000585,000630,000675,000720,000765,000810,000

    Expected P:270,000315,000360,000393,450426,900448,800470,700463,200455,700425,100394,500345,000295,500

    Maximum000000470,700000000

    CoV:0.000.000.000.000.000.000.370.000.000.000.000.000.00

    StdDev0.00.00.00.00.00.0175,6990.00.00.00.00.00.0

    Manufacturer

    Order Q6000700080009000100001100012000130001400015000160001700018000

    DemandProb

    8,0000.11170,000215,000260,000305,000350,000395,000440,000485,000530,000575,000620,000665,000710,000

    10,0000.11170,000215,000260,000305,000350,000395,000440,000485,000530,000575,000620,000665,000710,000

    12,0000.28170,000215,000260,000305,000350,000395,000440,000485,000530,000575,000620,000665,000710,000

    14,0000.22170,000215,000260,000305,000350,000395,000440,000485,000530,000575,000620,000665,000710,000

    16,0000.18170,000215,000260,000305,000350,000395,000440,000485,000530,000575,000620,000665,000710,000

    18,0000.10170,000215,000260,000305,000350,000395,000440,000485,000530,000575,000620,000665,000710,000

    Expected P:170,000215,000260,000305,000350,000395,000440,000485,000530,000575,000620,000665,000710,000

    CoV:0.000.000.000.000.000.000.000.000.000.000.000.000.00

    StdDev:0.00.00.00.00.00.00.00.00.00.00.00.00.0

    Exp. Total P:440,000530,000620,000698,450776,900843,800910,700948,200985,7001,000,1001,014,5001,010,0001,005,500

    73.411764705921.2594.6617647059

    69.333333333322.591.8333333333

    65.684210526323.7589.4342105263

    62.42587.4

    59.428571428626.2585.6785714286

    56.727272727327.584.2272727273

    54.260869565228.7583.0108695652

    523082

    49.9231.2581.17

    4832.580.5

    46.222222222233.7579.9722222222

    44.57142857143579.5714285714

    43.034482758636.2579.2844827586

    41.637.579.1

    40.258064516138.7579.0080645161

    394079

    37.818181818241.2579.0681818182

    36.705882352942.579.2058823529

    35.657142857143.7579.4071428571

    34.66666666674579.6666666667

    33.729729729746.2579.9797297297

    32.842105263247.580.3421052632

    3248.7580.75

    31.25081.2

    30.439024390251.2581.6890243902

    29.714285714352.582.2142857143

    29.02325581453.7582.773255814

    28.36363636365583.3636363636

    27.733333333356.2583.9833333333

    27.130434782657.584.6304347826

    26.553191489458.7585.3031914894

    266086

    25.469387755161.2586.7193877551

    24.9662.587.46

    24.470588235363.7588.2205882353

    246589

    23.547169811366.2589.7971698113

    23.111111111167.590.6111111111

    22.690909090968.7591.4409090909

    22.28571428577092.2857142857

    21.894736842171.2593.1447368421

    21.517241379372.594.0172413793

    21.152542372973.7594.9025423729

    20.87595.8

    20.459016393476.2596.7090163934

    20.129032258177.597.6290322581

    19.809523809578.7598.5595238095

    19.58099.5

    19.281.25100.45

    18.909090909182.5101.4090909091

    18.626865671683.75102.3768656716

    18.352941176585103.3529411765

    18.086956521786.25104.3369565217

    17.828571428687.5105.3285714286

    17.577464788788.75106.3274647887

    17.333333333390107.3333333333

    17.09589041191.25108.345890411

    16.864864864992.5109.3648648649

    16.6493.75110.39

    16.421052631695111.4210526316

    16.207792207896.25112.4577922078

    1697.5113.5

    15.797468354498.75114.5474683544

    15.6100115.6

    15.4074074074101.25116.6574074074

    15.2195121951102.5117.7195121951

    15.0361445783103.75118.7861445783

    14.8571428571105119.8571428571

    14.6823529412106.25120.9323529412

    14.511627907107.5122.011627907

    14.3448275862108.75123.0948275862

    14.1818181818110124.1818181818

    14.0224719101111.25125.2724719101

    13.8666666667112.5126.3666666667

    13.7142857143113.75127.4642857143

    13.5652173913115128.5652173913

    13.4193548387116.25129.6693548387

    13.2765957447117.5130.7765957447

    13.1368421053118.75131.8868421053

    13120133

    12.8659793814121.25134.1159793814

    12.7346938776122.5135.2346938776

    12.6060606061123.75136.3560606061

    12.48125137.48

    Order Quantity

    Cost

    270000170000440000

    315000215000530000

    360000260000620000

    393450305000698450

    426900350000776900

    448800395000843800

    470700440000910700

    463200485000948200

    455700530000985700

    4251005750001000100

    3945006200001014500

    3450006650001010000

    2955007100001005500

    Dist. P

    Mfg. P

    Total P.

    Quantity

    Profit ($)

    Profit vs Order Quantity

    0.11

    0.11

    0.28

    0.22

    0.18

    0.1

    Quantity

    Probability

    Demand Scenario

    270000

    315000

    360000

    397300

    434600

    464200

    493800

    503800

    513800

    508400

    503000

    485000

    467000

    Order Quantity

    Retailer Profit

    170000

    215000

    260000

    301150

    342300

    379600

    416900

    444400

    471900

    491700

    511500

    525000

    538500

    Production Quantity

    Manufacturer Profit

    6000270000

    7000315000

    8000360000

    9000393450

    10000426900

    11000448800

    12000470700

    13000463200

    14000455700

    15000425100

    16000394500

    17000345000

    18000295500

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Order Quantity

    Expected Profit

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

  • Retailer Profit (Buy Back=$55)$513,800

    Chart3

    270000

    315000

    360000

    397300

    434600

    464200

    493800

    503800

    513800

    508400

    503000

    485000

    467000

    Order Quantity

    Retailer Profit

    Sheet1

    Amount to Order:(each time inventory hits 0)

    Order Cost:12

    Weekly Demand:20

    Annual Demand:1040

    Annual Orders:(Annual Demand / Amount to Order)

    Holding Cost:0.25(25% of .02)

    Avg. Annual Inven:(Half of Order Amount Times Number of Orders)

    Total Annual Cost:(Avg. Annual Inven)*Holding Cost + Number of Orders * Order Cost

    QOrder CostHolding CostTC

    1012481.251249.25

    206242.5626.5

    304163.75419.75

    403125317

    50249.66.25255.85

    602087.5215.5

    70178.28571428578.75187.0357142857

    8015610166

    90138.666666666711.25149.9166666667

    100124.812.5137.3

    110113.454545454513.75127.2045454545

    12010415119

    1309616.25112.25

    14089.142857142917.5106.6428571429

    15083.218.75101.95

    160782098

    17073.411764705921.2594.6617647059

    18069.333333333322.591.8333333333

    19065.684210526323.7589.4342105263

    20062.42587.4

    21059.428571428626.2585.6785714286

    22056.727272727327.584.2272727273

    23054.260869565228.7583.0108695652

    240523082

    25049.9231.2581.17

    2604832.580.5

    27046.222222222233.7579.9722222222

    28044.57142857143579.5714285714

    29043.034482758636.2579.2844827586

    30041.637.579.1

    31040.258064516138.7579.0080645161

    320394079

    33037.818181818241.2579.0681818182

    34036.705882352942.579.2058823529

    35035.657142857143.7579.4071428571

    36034.66666666674579.6666666667

    37033.729729729746.2579.9797297297

    38032.842105263247.580.3421052632

    3903248.7580.75

    40031.25081.2

    41030.439024390251.2581.6890243902

    42029.714285714352.582.2142857143

    43029.02325581453.7582.773255814

    44028.36363636365583.3636363636

    45027.733333333356.2583.9833333333

    46027.130434782657.584.6304347826

    47026.553191489458.7585.3031914894

    480266086

    49025.469387755161.2586.7193877551

    50024.9662.587.46

    51024.470588235363.7588.2205882353

    520246589

    53023.547169811366.2589.7971698113

    54023.111111111167.590.6111111111

    55022.690909090968.7591.4409090909

    56022.28571428577092.2857142857

    57021.894736842171.2593.1447368421

    58021.517241379372.594.0172413793

    59021.152542372973.7594.9025423729

    60020.87595.8

    61020.459016393476.2596.7090163934

    62020.129032258177.597.6290322581

    63019.809523809578.7598.5595238095

    64019.58099.5

    65019.281.25100.45

    66018.909090909182.5101.4090909091

    67018.626865671683.75102.3768656716

    68018.352941176585103.3529411765

    69018.086956521786.25104.3369565217

    70017.828571428687.5105.3285714286

    71017.577464788788.75106.3274647887

    72017.333333333390107.3333333333

    73017.09589041191.25108.345890411

    74016.864864864992.5109.3648648649

    75016.6493.75110.39

    76016.421052631695111.4210526316

    77016.207792207896.25112.4577922078

    7801697.5113.5

    79015.797468354498.75114.5474683544

    80015.6100115.6

    81015.4074074074101.25116.6574074074

    82015.2195121951102.5117.7195121951

    83015.0361445783103.75118.7861445783

    84014.8571428571105119.8571428571

    85014.6823529412106.25120.9323529412

    86014.511627907107.5122.011627907

    87014.3448275862108.75123.0948275862

    88014.1818181818110124.1818181818

    89014.0224719101111.25125.2724719101

    90013.8666666667112.5126.3666666667

    91013.7142857143113.75127.4642857143

    92013.5652173913115128.5652173913

    93013.4193548387116.25129.6693548387

    94013.2765957447117.5130.7765957447

    95013.1368421053118.75131.8868421053

    96013120133

    97012.8659793814121.25134.1159793814

    98012.7346938776122.5135.2346938776

    99012.6060606061123.75136.3560606061

    100012.48125137.48

    starting inven60007000800090001000011000120001300014000150001600017000180001900020000210002200023000240002500026000270002800029000300003100032000330003400035000360003700038000

    101700002150002600002934503269003488003707003632003557003251002945002450001955001355007550015500-44500-104500-164500-224500-284500-344500-404500-464500

    160007500006950007400007734508069008288008507008432008357008051007745007250006755006155005555004955004355003755003155002555001955001355007550015500

    1700087500082000085345088690090880093070092320091570088510085450080500075550069550063550057550051550045550039550033550027550021550015550095500

    18000100000093345096690098880010107001003200995700965100934500885000835500775500715500655500595500535500475500415500355500295500235500175500

    1900011134501046900106880010907001083200107570010451001014500965000915500855500795500735500675500615500555500495500435500375500315500255500

    11000012269001148800117070011632001155700112510010945001045000995500935500875500815500755500695500635500575500515500455500395500335500

    80008000800080008000800080008000800080008000800080008000800080008000800080008000800080008000800080008000800080008000800080008000800080008000

    800060007000800090001000011000120001300014000150001600017000180001900020000210002200023000240002500026000270002800029000300003100032000330003400035000360003700038000

    DemandProbWeighted Demand

    80000.118809100009550001000000840000780000720000660000600000540000480000420000360000300000240000180000120000600000-60000-120000-180000-240000-300000-360000-420000-480000-540000-600000-660000-720000-780000-840000-900000164000016400001000000

    100000.11110091000095500010000009450009900009300008700008100007500006900006300005700005100004500003900003300002700002100001500009000030000-30000-90000-150000-210000-270000-330000-390000-450000-510000-570000-630000-690000189000018900001250000

    120000.2833609100009550001000000945000990000103500010800001020000960000900000840000780000720000660000600000540000480000420000360000300000240000180000120000600000-60000-120000-180000-240000-300000-360000-420000-480000214000021400001500000

    140000.22308091000095500010000009450009900001035000108000011250001170000111000010500009900009300008700008100007500006900006300005700005100004500003900003300002700002100001500009000030000-30000-90000-150000-210000-270000239000023900001750000

    160000.18288091000095500010000009450009900001035000108000011250001170000121500012600001200000114000010800001020000960000900000840000780000720000660000600000540000480000420000360000300000240000180000120000600000-60000264000026400002000000

    180000.1180091000095500010000009450009900001035000108000011250001170000121500012600001305000135000012900001230000117000011100001050000990000930000870000810000750000690000630000570000510000450000390000330000270000210000150000289000028900002250000

    60007000800090001000011000120001300014000150001600017000180001900020000210002200023000240002500026000270002800029000300003100032000330003400035000360003700038000

    113100910000955000100000093345096690098880010107001003200995700965100934500885000835500775500715500655500595500535500475500