23. You manage inventory for your company and use a continuous review inventory system to control reordering items for stock. Your company is open for business 300 days per year. One of your most important items experiences demand of 20 units per day, normally distributed with a standard deviation of 3 units per day. You experience a lead time on orders from your supplier of six days with a standard deviation of two days. If you order 1,000 units or less, you pay the supplier $5.00 per unit. Orders of 1,000 or more can be bought at a unit price of $4.75. Your ordering cost is $50. Your inventory carrying cost is 20 percent. You have established a service level policy of 97.5 percent on this item.
a. What is your optimal order quantity?
b. What is your reorder point?
c. How much safety stock do you carry?
d. What is your average inventory?
24. Suppose in problem 23, you were able to reduce your order cost to $10. What is the impact of this change on the other variables?
25. After you reduce your order cost, as described in problem 24, the supplier in problem 23 changes its pricing policy to a standard $4.75 per unit, regardless of the order quantity. What is the impact of this policy change on the other variables?
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