Jointly Optimal Deterministic Inventory and Replacement Policies

A deterministic, continuous time, nonstationary inventory and replacement system model is formulated to find the number of orders, the order quantities, the times at which orders should be placed, and the replacement intervals which minimize the cost of operating, maintaining, and replacing a piece of equipment over a finite time horizon. Conditions are given for when the optimal policy is to buy equipments only when the last inventoried item is ready for replacement. A dynamic programming algorithm is presented for solving this problem. The structure of optimal policies is examined for the stationary case. Finally a computational procedure is given for solving the stationary, infinite horizon case.