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Optimal arrangement of systems

Author

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  • Philip J. Boland
  • Frank Proschan

Abstract

To location Li we are to allocate a “generator” and ni “machines” for i = 1, …,k, where n1 … n1 ≧ … ≧ nk. Although the generators and machines function independently of one another, a machine is operable only if it and the generator at its location are functioning. The problem we consider is that of finding the arrangement or allocation optimizing the number of operable machines. We show that if the objective is to maximize the expected number of operable machines at some future time, then it is best to allocate the best generator and the n1 best machines to location L1, the second‐best generator and the n2‐next‐best machines to location L2, etc. However, this arrangement is not always stochastically optimal. For the case of two generators we give a necessary and sufficient condition that this arrangement is stochastically best, and illustrate the result with several examples.

Suggested Citation

  • Philip J. Boland & Frank Proschan, 1984. "Optimal arrangement of systems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(3), pages 399-407, September.
    • Handle: RePEc:wly:navlog:v:31:y:1984:i:3:p:399-407
    DOI: 10.1002/nav.3800310306
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    Cited by:

    1. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.

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