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# Inventory models:ROP, EOQ

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The problem is as follows:

The Goodstone Tire Company produces a brand of tire called the Rainpath. The demand at its distribution center is 1,035 tires per month. The transport and handling costs are \$2,600 each time a shipment of tires is ordered at the distribution center. The annual carrying cost is \$3.75 per tire, which represents the unit cost multiplied by the carrying rate.

(a) Determine the optimal ordering quantity and minimum total annual cost. How often will an order be placed?

(b) Suppose that the standard deviation of monthly demand is 500 tires, and lead time is ½ month. If Goodstone desires a 90% service level (assuming normal demand), what should their reorder point be? What is the impact on the total annual cost?

(c) The company is thinking of relocating its distribution center, which would reduce transport and handling costs to \$1900 per order and lead time to ¼ month. Carrying cost would increase to \$4.50 per tire per year. Should the company relocate based on inventory costs?

(d) Suppose that Goodstone decided to use a P system, rather than a Q system, because they can then schedule regular replenishment. What will the impact be on the safety stock? Why? No calculations are required, although you may do them.

In (a), I can not figure out unit cost, carrying rate or lot size. I know it's somewhere in the carrying costs calculation, but I'm not sure how to get at it. Hints with problems (b)-(c) would be appreciated.