lect14 - Single Period Inventory Models Yossi Sheffi Mass...

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Single Period Inventory Models Yossi Sheffi Mass Inst of Tech Cambridge, MA
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Outline ± Single period inventory decisions ± Calculating the optimal order size ² Numerically ± Using spreadsheet ± Using simulation ² Analytically ± The profit function ² For specific distributions ± Level of Service ± Extensions: ² Fixed costs ² Risks ² Initial inventory ² Elastic demand
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Single Period Ordering ± ± ± ± ± ±
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Selling Magazines ± Weekly demand: 90 48 87 78 58 71 102 87 66 79 97 75 89 57 86 95 67 89 70 113 52 84 62 91 71 66 99 73 92 66 67 89 87 64 70 54 67 88 62 79 79 105 76 73 78 50 107 80 78 51 79 80 ² Total: 4023 magazines ² Average: 77.4 Mag/week ² Min: 51; max: 113 Mag/week
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Detailed Histogram 0 1 2 3 4 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 Demand (Mag/Wk) Frequency (Wks/Yr) 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Cumm Freq. (Wks/Yr) Average=77.4 Mag/wk
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Histogram 0 2 4 6 8 10 12 14 16 40 50 60 70 8 0 9 100 11 1 3 Mo r e Demand (Mag/week) Frequency (Wks/Yr) 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Cummulative Frequency
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The Ordering Decision (Spreadsheet) ± Assume: each magazine sells for: $15 ± Cost of each magazine: $8 Order: 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 d/wk Prob. 40 0.00 $140 $210 $280 $200 $120 $40 -$40 -$120 -$200 -$280 -$360 -$440 -$520 -$600 -$680 50 0.04 $140 $210 $280 $350 $270 $190 $110 $30 -$50 -$130 -$210 -$290 -$370 -$450 -$530 60 0.10 $140 $210 $280 $350 $420 $340 $260 $180 $100 $20 -$60 -$140 -$220 -$300 -$380 70 0.21 $140 $210 $280 $350 $420 $490 $410 $330 $250 $170 $90 $10 -$70 -$150 -$230 80 0.29 $140 $210 $280 $350 $420 $490 $560 $480 $400 $320 $240 $160 $80 $0 -$80 90 0.19 $140 $210 $280 $350 $420 $490 $560 $630 $550 $470 $390 $310 $230 $150 $70 100 0.10 $140 $210 $280 $350 $420 $490 $560 $630 $700 $620 $540 $460 $380 $300 $220 110 0.06 $140 $210 $280 $350 $420 $490 $560 $630
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lect14 - Single Period Inventory Models Yossi Sheffi Mass...

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