FootLove Shoe Co. produces and sells excellent quality walking shoes. After production, these shoes are distributed to 30 warehouses around the country. Each warehouse services approximately 120 stores in its region. FootLove uses an EOQ model to determine the number of pairs of shoes to order for each warehouse from the factory. Annual demand for warehouse WH1 is approximately 180,000 pairs of shoes. The ordering cost is $200 per order. The annual carrying cost of a pair of shoes is $3.20 per pair.

Required

1. Use the EOQ model to determine the optimal number of pairs of shoes per order.

2. Assume each month consists of approximately 4 weeks. If it takes 1 week to receive an order, at what point should warehouse WH1 reorder shoes?

3. Although WH1’s average weekly demand is 3,750 pairs of shoes (180,000 ÷ 12 months ÷ 4 weeks), demand each week may vary with the following probability distribution:

If a store wants shoes and WH1 has none in stock, WH1 can “rush” them to the store at an additional cost of $3.00 per pair. How much safety stock should warehouse WH1 hold? How will this affect the reorder point and reorder quantity?

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Total demand for 1 week Probability (sums to 1.00) 3,250 pairs 0.05 3,500 pairs 0.15 3,750 pairs 0.55 4,000 pairs 0.20 4,250 pairs 0.05