dolution

In the basic EOQ model, suppose the stock is replenished uniformly (rather than instantaneously) at the rate of b items per unit time until the order quantity Q is fulfilled. Withdrawals from the inventory are made at the rate of a items per unit time, where a ≤ b. Replenishments and withdrawals of the inventory are made simultaneously. For example, if Q is 60, b is 3 per day, and a is 2 per day, then 3 units of stock arrive each day for days 1 to 20, 31 to 50, and so on, whereas units are withdrawn at the rate of 2 per day every day. The diagram of inventory level versus time is given below for this example.

(a) Find the total cost per unit time in terms of the setup cost K, production quantity Q, unit cost c, holding cost h, withdrawal rate a, and replenishment rate b.

(b) Determine the economic order quantity Q*.