Optimal design of line replaceable units

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 nonintegral feasible polyhedron. Second, we formulate our problem as a binary linear program (BLP). The article concludes by numerically comparing the computation times of both formulations and illustrates the effects of various parameters on the model's outcome.