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# pigskin - Pigskin has decided that they want to meet the...

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A "Dynamic" (Multi-Period) Production Problem: Footballs Page 37 The Pigskin Company will produce footballs over the next six months. Forecasted demand and production costs over this time period are: Month 1 2 3 4 5 6 Demand (Cases of 100) 100 150 300 350 250 100 Unit Production Cost \$ 12.50 \$ 12.55 \$ 12.70 \$ 12.80 \$ 12.85 \$ 12.95 Pigskin has a monthly production capacity of 300 cases. They currently have 50 cases of footballs in inventory, and have enough capacity to store up to 100 cases. The holding cost of keeping a football in inventory for a month is estimated to be 5% of the cost of producing in that month.

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Unformatted text preview: Pigskin has decided that they want to meet the entire demand for footballs over the 6-month period. How can they do that at minimum cost? P i = Number of Footballs cases produced in month i=1,2,…,6 I i = Number of Footballs cases in stock at end of month i=1,2,…,6 [HELPERS] Min: 12.5 P 1 + 0.625 I 1 +12.55 P 2 + 0.6275 I 2 + …+12.95 P 6 + 0.6475 I 6 S.T. 50+ P 1 = 100+ I 1 | I 1 = 50+ P 1-100 I 1 + P 2 = 150+ I 2 | I 2 = I 1 + P 2- 150 • • I 5 + P 6 = 100+ I 6 | I 6 = I 5 + P 6- 100 0≤P i ≤300, 0≤I i ≤100, i=1,2,…,6...
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