PROBLEM: A company can either produce a commodity or purchase it from a contractor. If it produces it, it will cost $20 each time the machines are set up. The production rate is 100 units per day. If purchased from the contractor, it will cost $15 each time an order is placed. The cost of keeping the goods in stock, whether purchased or produced, is $0.02 per unit per day. The company's use of the merchandise is estimated to be 26,000 units annually. Assuming no shortages are allowed, should the company buy it or produce it?

Hint: Consider the inventory situation in which stocks are replenished uniformly (rather than instantaneously) at a rate a . Consumption occurs at constant rate D. Since consumption also occurs during the replenishment period, it is necessary that a>D. The setup cost is K per order, and the holding cost is h per unit, per unit time. If Q is the order size and no shortage is allowed, then:

(a) the maximum inventory level is: Q(1-Da).

b) the total cost per unit time: kDQ+h2(1-Da)Q

c) the economic order quantity is: Q=2kDh(1-Da)----------, D

(d) assume that shortages are allowed to occur at a penalty cost of p per unit per unit time. If w is the maximum shortage during the inventory cycle.