Each year, Comfy Shoes faces demands (which must be met on time) for pairs of sh

Question

Each year, Comfy Shoes faces demands (which must be met on time) for pairs of shoes as shown in the table below. Workers work three consecutive quarters and then receive one quarter off. For example, a worker might work during Quarters 3 and 4 of one year and Quarter 1 of the next year. During a quarter in which a worker works, he or she can produce 600 pairs of shoes. Each worker is paid $20,000 for each quarter worked. At the end of each quarter, a holding cost of $30 per pair of shoes is assessed. Determine how to minimize the cost per year (labor plus holding cost) of meeting the demand for shoes. To simplify matters, assume that at the end of the year, the ending inventory will be zero. (Hint: you may assume that a given worker will get the same quarter off during each year.) Quarter Demand Quarter 1 7000 Quarter 2 4500 Quarter 3 8500 Quarter 4 10000

Explanation / Answer

The most closest optimal solution is

Qtr Demand Labor at work Labor on off Production Closing inventory Holding cost Labor cost 1 7000 12 5 7200 200 6000 240000 2 4500 8 9 4800 500 15000 160000 3 8500 13 4 7800 -200 0 260000 4 10000 17 0 10200 0 0 340000 50 18 21000 1000000 Total Cost = 1021000

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