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A note on parallel machine replacement

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  • Jen Tang
  • Kwei Tang

Abstract

Jones, Zydiak, and Hopp [1] consider the parallel machine replacement problem (PMRP), in which there are both fixed and variable costs associated with replacing machines. Increasing maintenance cost motivates replacements, and a fixed replacement cost provides incentive for replacing machines of the same age in clusters. They prove two intuitive but important results for finite‐ or infinite‐horizon PMRPs, which significantly reduce the size of the linear programming (LP) formulation of the problem and computing efforts required to obtain an optimal replacement policy. Their results are the no‐splitting rule (NSR) and the older cluster replacement rule (OCRR). Under a slightly weaker set of assumptions, we prove a third rule, the all‐or‐none rule (AONR), which states that in any period, an optimal policy is to keep or to replace all the machines regardless of age. This result further reduces the size of the LP formulation of the PMRP. © 1993 John Wiley & Sons, Inc.

Suggested Citation

  • Jen Tang & Kwei Tang, 1993. "A note on parallel machine replacement," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(4), pages 569-573, June.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:4:p:569-573
    DOI: 10.1002/1520-6750(199306)40:43.0.CO;2-F
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    Cited by:

    1. Tim McClurg & Suresh Chand, 2002. "A parallel machine replacement model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(3), pages 275-287, April.
    2. Wallace J. Hopp & Philip C. Jones & James L. Zydiak, 1993. "A further note on parallel machine replacement," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(4), pages 575-579, June.
    3. Zhang, Le & Gu, Weihua & Fu, Liangliang & Mei, Yu & Hu, Yaohua, 2021. "A two-stage heuristic approach for fleet management optimization under time-varying demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    4. Joseph C. Hartman, 2000. "The parallel replacement problem with demand and capital budgeting constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(1), pages 40-56, February.
    5. Shields, Brett A. & Seif, Javad & Yu, Andrew Junfang, 2019. "Parallel machine replacement with shipping decisions," International Journal of Production Economics, Elsevier, vol. 218(C), pages 62-71.
    6. Suzanne Childress & Pablo Durango‐Cohen, 2005. "On parallel machine replacement problems with general replacement cost functions and stochastic deterioration," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(5), pages 409-419, August.
    7. Chand, Suresh & McClurg, Tim & Ward, Jim, 2000. "A model for parallel machine replacement with capacity expansion," European Journal of Operational Research, Elsevier, vol. 121(3), pages 519-531, March.
    8. Bollapragada, Srinivas & Gupta, Aparna & Lawsirirat, Chaipat, 2007. "Managing a portfolio of long term service agreements," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1399-1411, November.

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