Analysis of Greedy Solutions for a Replacement Part Sequencing Problem

Abstract

This paper considers the problem of sequencing the installation of replacement parts for the repeated repair of a machine consisting of two working parts. A finite inventory of spares is initially available for each type of part. Each spare has a known (deterministic) field life, and spares of each type may have different field lives. The inventories are eventually depleted since no replacement or repairs of parts occur. The primary objective is to obtain a sequencing policy which minimizes the total number of installations (replacements). This problem is a special case of many opportunistic replacement problems and is called a “build” problem. The motivation for this work is based on the maintenance of modular gas turbine aircraft engines used by domestic airlines and the U.S. Air Force. We show this build problem is NP-hard which indicates the necessity of efficient heuristic solution procedures. This paper considers several “greedy” type algorithms based on grouping parts according to exact matching of field lives. Then, a generalization is presented which allows approximate matches. The focus of the analysis is to obtain tight worst case bounds on the number of replacements obtained by each of the greedy algorithms.