Optimal design of line replaceable units

Joni P.C. Driessen, Joost T. de Kruijff, Joachim J. Arts (Corresponding author), Geert-Jan J.A.N. van Houtum

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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.
Original languageEnglish
Pages (from-to)189-209
Number of pages21
JournalNaval Research Logistics
Issue number2
Early online date29 Aug 2023
Publication statusPublished - 1 Mar 2024


  • Column generation
  • Graph theory
  • Integer programming
  • Line replaceable units
  • integer programming
  • graph theory
  • line replaceable units
  • column generation


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