Optimal Ordering Policies for a Continuous Time, Deterministic Inventory Model

A deterministic, continuous time, nonstationary inventory model is formulated to find the number of orders, the order quantities, and the times at which orders should be placed which minimize the total cost over a finite time horizon of meeting a given requirements function. Both backlogging and no backlogging are considered. Conditions are given for the existence of an optimal policy with a regeneration point property which permits the order quantities to be calculated from the requirements function. The conditions for an optimal policy permit the use of a purchase cost function providing for quantity discounts. Two examples are considered.