8. Consider the inventory situation in which the stock is replenished uniformly (rather than instantaneously) at the rate

a. Consumption occurs at the constant rate D. Because 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 y is the order size and no shortage is allowed, show that

(a) The maximum inventory level is y(1 - ~).

(b) TIle total cost per unit time given y is rCU(y) = KyO + ~(l - ~)y

(c) The economic order quantity is

~. 2KD y* = ( D)' D < a hl--;;

(d) Show that the EOQ under instantaneous replenishment can be derived from the formula in (c).