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Solving the multiperiod assignment problem with start‐up costs using dual ascent

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  • Ishwar Murthy

Abstract

In this article we consider a multiperiod assignment problem where the assignment cost of assigning job i to machine j varies from one time period to the next. A start‐up cost is incurred whenever the job processed by a machine in the current time period is different from the one processed in the previous time period. This problem is modeled as an integer programming problem for which a dual ascent approximate procedure is developed. Our computational results show that our procedure outperforms the more common Lagrangian‐relaxation‐based subgradient procedure by a significant margin. It is also found to be faster than MPSX/370 by many orders of magnitude. © 1993 John Wiley & Sons, Inc.

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  • Ishwar Murthy, 1993. "Solving the multiperiod assignment problem with start‐up costs using dual ascent," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(3), pages 325-344, April.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:3:p:325-344
    DOI: 10.1002/1520-6750(199304)40:33.0.CO;2-W
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    References listed on IDEAS

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    1. Burkard, Rainer E., 1984. "Quadratic assignment problems," European Journal of Operational Research, Elsevier, vol. 15(3), pages 283-289, March.
    2. Ming S. Hung & Walter O. Rom, 1980. "Solving the Assignment Problem by Relaxation," Operations Research, INFORMS, vol. 28(4), pages 969-982, August.
    3. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    4. Uday S. Karmarkar & Sham Kekre & Sunder Kekre, 1987. "The Dynamic Lot-Sizing Problem with Startup and Reservation Costs," Operations Research, INFORMS, vol. 35(3), pages 389-398, June.
    5. T. C. Hu & Y. S. Kuo & F. Ruskey, 1987. "Some Optimum Algorithms for Scheduling Problems with Changeover Costs," Operations Research, INFORMS, vol. 35(1), pages 94-99, February.
    6. Donald Erlenkotter, 1978. "A Dual-Based Procedure for Uncapacitated Facility Location," Operations Research, INFORMS, vol. 26(6), pages 992-1009, December.
    7. Aronson, Jay E., 1986. "The multiperiod assignment problem: A multicommodity network flow model and specialized branch and bound algorithm," European Journal of Operational Research, Elsevier, vol. 23(3), pages 367-381, March.
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    Cited by:

    1. Reza Farahani & Zvi Drezner & Nasrin Asgari, 2009. "Single facility location and relocation problem with time dependent weights and discrete planning horizon," Annals of Operations Research, Springer, vol. 167(1), pages 353-368, March.

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