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The parallel replacement problem with demand and capital budgeting constraints

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  • Joseph C. Hartman

Abstract

A generalized parallel replacement problem is considered with both fixed and variable replacement costs, capital budgeting, and demand constraints. The demand constraints specify that a number of assets, which may vary over time, are required each period over a finite horizon. A deterministic, integer programming formulation is presented as replacement decisions must be integer. However, the linear programming relaxation is shown to have integer extreme points if the economies of scale binary variables are fixed. This allows for the efficient computation of large parallel replacement problems as only a limited number of 0–1 variables are required. Examples are presented to provide insight into replacement rules, such as the “no‐splitting‐rule” from previous research, under various demand scenarios. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 40–56, 2000

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  • 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.
    • Handle: RePEc:wly:navres:v:47:y:2000:i:1:p:40-56
    DOI: 10.1002/(SICI)1520-6750(200002)47:13.0.CO;2-T
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    References listed on IDEAS

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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. Philip C. Jones & James L. Zydiak & Wallace J. Hopp, 1991. "Parallel machine replacement," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(3), pages 351-365, June.
    3. 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.
    4. Robert E. Bixby & William H. Cunningham, 1980. "Converting Linear Programs to Network Problems," Mathematics of Operations Research, INFORMS, vol. 5(3), pages 321-357, August.
    5. Gordon H. Bradley & Gerald G. Brown & Glenn W. Graves, 1977. "Exceptional Paper--Design and Implementation of Large Scale Primal Transshipment Algorithms," Management Science, INFORMS, vol. 24(1), pages 1-34, September.
    6. 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.
    7. S. Rajagopalan, 1998. "Capacity Expansion and Equipment Replacement: A Unified Approach," Operations Research, INFORMS, vol. 46(6), pages 846-857, December.
    8. 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.
    9. 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.
    10. 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.
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    Cited by:

    1. Metin Çakanyıldırım & Robin O. Roundy & Samuel C. Wood, 2004. "Optimal machine capacity expansions with nested limitations under stochastic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(2), pages 217-241, March.
    2. Paul R. Kleindorfer & Andrei Neboian & Alain Roset & Stefan Spinler, 2012. "Fleet Renewal with Electric Vehicles at La Poste," Interfaces, INFORMS, vol. 42(5), pages 465-477, October.
    3. Natali Hritonenko & Yuri Yatsenko, 2012. "Fleet replacement under technological shocks," Annals of Operations Research, Springer, vol. 196(1), pages 311-331, July.

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