### Inventory system to control reordering items for stock

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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 6 days with a standard deviation of 2 days. If you order less than 1,000 units, 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%. You have established a service level policy of 97.5% 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?

e. Suppose you reduced your ordering cost from \$50 to \$10, what is the impact on all other variables? (increase or decrease, change to how much?)

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