Question

LaRue Shoe Co. produces and sells an​ excellent-quality walking shoe. After​ production, the shoes are distributed to 20 warehouses around the country. Each warehouse services approximately 100 stores in its region. LaRue uses an EOQ model to determine the number of pairs of shoes to order for each warehouse from the factory. Annual demand for Warehouse OR2 is approximately 120,000 pairs of shoes. The ordering cost is $250 per order. The annual carrying cost of a pair of shoes is $2.40 per pair.

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 OR2 reorder​ shoes?

3. Although​ OR2's average weekly demand is 2,500pairs of shoes

​(120,000​/ 12 months​ / 4​ weeks), demand each week may vary with the following probability​ distribution:

Total demand for 1 week	1,900 pairs	1,750 pairs	2,500 pairs	2,700 pairs	2,960 pairs
Probability (sums to 1.00)	0.03	0.30	0.34	0.30	0.03

If a store wants shoes and OR2 has none in​ stock, OR2 can​ "rush" them to the store at an additional cost of $3 per pair. How much safety stock should Warehouse OR2​ hold? How will this affect the reorder point and reorder​quantity?

The relevant total stockout and carrying costs are the________when a safety stock of________

pairs of shoes is maintained. Therefore, Warehouse OR2_______ hold that number as safety stock.

This will_____the reorder point to_______pairs of shoes. The reorder quantity will________

Answer 1

Part 1

EOQ = (2DP/C)^0.5

= ((2*120000*250)/2.40)^0.5 = 5000 air of shoes

Part 2

Monthly demand = annual demand / 12 = 120000/12 =10000

Weekly demand = monthly demand / 12 = 10000/4 = 2500 pairs

Purchase lead time (given) = 1 week

Reorder point = weekly demand * lead time = 2500 pairs * 1 week = 2500 pairs

Part 3

1. carrying cost are the lowest
2. stock of 250 pairs of shoes is
3. OR2 should hold
4. This will raise the
5. reorder point to 2750 pairs
6. reorder quantity will be unaffected