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Solution algorithms for the parallel replacement problem under economy of scale

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  • Zhi‐Long Chen

Abstract

We consider the parallel replacement problem in which machine investment costs exhibit economy of scale which is modeled through associating both fixed and variable costs with machine investment costs. Both finite‐ and infinite‐horizon cases are investigated. Under the three assumptions made in the literature on the problem parameters, we show that the finite‐horizon problem with time‐varying parameters is equivalent to a shortest path problem and hence can be solved very efficiently, and give a very simple and fast algorithm for the infinite‐horizon problem with time‐invariant parameters. For the general finite‐horizon problem without any assumption on the problem parameters, we formulate it as a zero‐one integer program and propose an algorithm for solving it exactly based on Benders' decomposition. Computational results show that this solution algorithm is efficient, i.e., it is capable of solving large scale problems within a reasonable cpu time, and robust, i.e., the number of iterations needed to solve a problem does not increase quickly with the problem size. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 279–295, 1998

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  • Zhi‐Long Chen, 1998. "Solution algorithms for the parallel replacement problem under economy of scale," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(3), pages 279-295, April.
    • Handle: RePEc:wly:navres:v:45:y:1998:i:3:p:279-295
    DOI: 10.1002/(SICI)1520-6750(199804)45:33.0.CO;2-4
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    1. Nejat Karabakal & Jack R. Lohmann & James C. Bean, 1994. "Parallel Replacement under Capital Rationing Constraints," Management Science, INFORMS, vol. 40(3), pages 305-319, March.
    2. Wallace J. Hopp & Suresh K. Nair, 1991. "Timing replacement decisions under discontinuous technological change," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 203-220, April.
    3. Suresh Sethi & Suresh Chand, 1979. "Planning Horizon Procedures for Machine Replacement Models," Management Science, INFORMS, vol. 25(2), pages 140-151, February.
    4. James C. Bean & Jack R. Lohmann & Robert L. Smith, 1994. "Equipment replacement under technological change," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 117-128, February.
    5. Sethi, Suresh P. & Taksar, Michael I. & Presman, Ernst L., 1995. "Erratum," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1297-1298.
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    1. Peiling Wu & Joseph C. Hartman & George R. Wilson, 2005. "An Integrated Model and Solution Approach for Fleet Sizing with Heterogeneous Assets," Transportation Science, INFORMS, vol. 39(1), pages 87-103, February.
    2. 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.
    3. 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.

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