Optimal Design of Lines Replaceable Units

TL;DR

This paper introduces a new model for designing Line Replaceable Units (LRUs) that minimizes total costs by considering system connectivity, disassembly, and repair costs, with proven optimality properties and computational comparisons.

Contribution

It formalizes a novel optimization model for LRU design, including a set partitioning formulation with guaranteed integer solutions and a binary linear program, along with computational analysis.

Findings

Optimal solutions are integer in the set partitioning model.

The binary linear program provides a practical alternative.

Parameter variations significantly affect LRU design outcomes.

Abstract

A Line Replaceable Unit (LRU) is a collection of connected parts in a system that is replaced when any part of the LRU fails. Companies use LRUs as a mechanism to reduce downtime of systems following a failure. The design of LRUs determines how fast a replacement is performed, so a smart design reduces replacement and downtime cost. A firm must purchase/repair a LRU upon failure, and large LRUs are more expensive to purchase/repair. Hence, a firm seeks to design LRUs such that the average costs per time unit are minimized. We formalize this problem in a new model that captures how parts in a system are connected, and how they are disassembled from the system. Our model optimizes the design of LRUs such that the replacement (and downtime) costs and LRU purchase/repair costs are minimized. We present a set partitioning formulation for which we prove a rare result: the optimal solution is integer, despite a non--integral feasible polyhedron. Secondly, we formulate our problem as a binary linear program. The paper concludes by numerically comparing the computation times of both formulations and illustrates the effects of various parameters on the model's outcome.