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A Branch-and-Bound Algorithm for Computing Optimal Replacement Policies in K -Out-of- N Systems

Author

Listed:
  • Chia-Shin Chung
  • James Flynn

    (Cleveland State University, Cleveland, Ohio)

Abstract

We study a discrete time, infinite-horizon, dynamic programming model for the replacement of components in a binary coherent system with n components. Costs are incurred when the system fails and when failed components are replaced. The objective is to minimize the expected discounted infinite-horizon cost or the long-run expected average undiscounted cost per period. An earlier paper found general conditions under which it is optimal to follow a critical component policy (CCP), i.e., a policy specified by a critical component set and the rule: Replace a component if and only if it is failed and in the critical component set. Computing an optimal CCP is a binary nonlinear programming problem in n variables. This paper specializes to k -out-of- n systems and develops a branch-and-bound algorithm for finding an optimal decision. Its memory storage requirement is O((n+1)(n-k+1)) , and the number of nodes examined is under O(n k ) . Extensive computational experiments with n ranging from 10 to 100 find it to be effective when k is small or near n . In our 120,000 test problems with k=n (parallel systems), the average computation time on a 20Mhz 386 microcomputer is 0.106 seconds.

Suggested Citation

  • Chia-Shin Chung & James Flynn, 1995. "A Branch-and-Bound Algorithm for Computing Optimal Replacement Policies in K -Out-of- N Systems," Operations Research, INFORMS, vol. 43(5), pages 826-837, October.
    • Handle: RePEc:inm:oropre:v:43:y:1995:i:5:p:826-837
    DOI: 10.1287/opre.43.5.826
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    Cited by:

    1. James Flynn & Chia‐Shin Chung, 2002. "A branch and bound algorithm for computing optimal replacement policies in consecutive k‐out‐of‐n‐systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 288-302, April.
    2. Chia‐Shin Chung & James Flynn, 1997. "A heuristic algorithm for determining replacement policies in k‐out‐of‐n systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(3), pages 273-286, April.

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