Consider the following classical inventory problem. A retailer must decide the quantity Q to order periodically to minimize expected annual cost. The retailer faces demand of D units per year and every order that is placed incurs an order processing fee of K dollars and a unit purchase cost of c dollars. It is easily seen that the average inventory is Q/2 on which an inventory carrying cost of h dollars/unit/year is charged. The total annual cost function, T(Q) may be expressed as:
T(Q) = K·D/Q +h·Q/2 + c·D
a) Write an expression for the number of orders placed per year?
b) Write an expression for the time between orders?
c) Determine a formula for the optimal order quantity that minimizes costs.
d) What would be the formula for the optimal order quantity if the term h·Q/2 in T(Q) were replaced by h·Qm/2, where m is a positive integer.