inventory management, supply contracts and risk pooling
DESCRIPTION
suppy chain managementTRANSCRIPT
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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
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SupplySources:plantsvendorsportsRegionalWarehouses:stocking pointsField Warehouses:stockingpointsCustomers,demandcenterssinksProduction/purchase costsInventory &warehousing costsTransportation costsInventory &warehousing costsTransportation costs
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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
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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
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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)
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Understanding Inventory The inventory policy is affected by:Demand CharacteristicsLead TimeNumber of ProductsObjectivesService levelMinimize costsCost Structure
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Cost StructureOrder costs FixedVariableHolding CostsInsuranceMaintenance and HandlingTaxesOpportunity CostsObsolescence
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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?
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EOQ: A View of Inventory*TimeInventoryOrderSizeNote: No Stockouts Order when no inventory Order Size determines policyAvg. Inven
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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:
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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
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
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
Sheet1
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Order Quantity
Cost
Sheet2
Sheet3
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EOQ: Optimal Order Quantity*Optimal Quantity = (2*Demand*Setup Cost)/holding cost
So for our problem, the optimal quantity is 316
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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%
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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
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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
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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.
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Supply Chain Time Lines
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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
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
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Order Quantity
Cost
Sheet2
0.11
0.11
0.28
0.22
0.18
0.1
Sales
Probability
Demand Scenarios
Sheet3
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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
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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
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SnowTime Best SolutionFind order quantity that maximizes weighted average profit.Question: Will this quantity be less than, equal to, or greater than average demand?
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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
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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 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
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
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
0.11
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
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
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
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
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90138.666666666711.25149.9166666667
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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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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
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49025.469387755161.2586.7193877551
50024.9662.587.46
51024.470588235363.7588.2205882353
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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
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67018.626865671683.75102.3768656716
68018.352941176585103.3529411765
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93013.4193548387116.25129.6693548387
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97012.8659793814121.25134.1159793814
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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