Jointly Optimal Inventory and Maintenance Policies for Stochastically Failing Equipment

Abstract

A dynamic programming problem is formulated to find the inventory, x, of a spare component and a sequence of maintenance intervals r= (r1,…,rx + 1) that minimize the expected cost of operating an equipment for a finite planning horizon, T. It is assumed that the component fails according to a life distribution function, F(⋯), with an increasing hazard function and that it is cheaper to replace components prior to failure. An operating cost function is found to be strictly convex in the time remaining to the end of the period and that at any time there is a finite nonincreasing sequence of economical maintenance policies, each a continuous nondecreasing function of the time remaining. A procedure is given for calculating the optimal initial inventory and reorders when the procurement cost function is K + c ⋯ x.