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A Branch-Bound Solution to the General Scheduling Problem

Author

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  • Harold H. Greenberg

    (General Electric Company, Denver, Colorado)

Abstract

A mixed integer formulation is presented for the general n job, m machine scheduling problem. This formulation is shown to reduce to a series of noninteger L.P. problems of moderate proportions when applying the branch-bound technique. Solutions are presented for the two problems: minimize make-span and minimize idle time. An example and some computational experience for the “minimize idle time” problem are given.

Suggested Citation

  • Harold H. Greenberg, 1968. "A Branch-Bound Solution to the General Scheduling Problem," Operations Research, INFORMS, vol. 16(2), pages 353-361, April.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:2:p:353-361
    DOI: 10.1287/opre.16.2.353
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    Citations

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    Cited by:

    1. George L. Vairaktarakis, 2003. "The Value of Resource Flexibility in the Resource-Constrained Job Assignment Problem," Management Science, INFORMS, vol. 49(6), pages 718-732, June.
    2. Pongcharoen, P. & Hicks, C. & Braiden, P. M. & Stewardson, D. J., 2002. "Determining optimum Genetic Algorithm parameters for scheduling the manufacturing and assembly of complex products," International Journal of Production Economics, Elsevier, vol. 78(3), pages 311-322, August.
    3. Pongcharoen, P. & Hicks, C. & Braiden, P. M., 2004. "The development of genetic algorithms for the finite capacity scheduling of complex products, with multiple levels of product structure," European Journal of Operational Research, Elsevier, vol. 152(1), pages 215-225, January.
    4. Yang, Lixing & Qi, Jianguo & Li, Shukai & Gao, Yuan, 2016. "Collaborative optimization for train scheduling and train stop planning on high-speed railways," Omega, Elsevier, vol. 64(C), pages 57-76.
    5. Roslof, Janne & Harjunkoski, Iiro & Westerlund, Tapio & Isaksson, Johnny, 2002. "Solving a large-scale industrial scheduling problem using MILP combined with a heuristic procedure," European Journal of Operational Research, Elsevier, vol. 138(1), pages 29-42, April.
    6. Zhou, Xuesong & Zhong, Ming, 2005. "Bicriteria train scheduling for high-speed passenger railroad planning applications," European Journal of Operational Research, Elsevier, vol. 167(3), pages 752-771, December.
    7. Blazewicz, Jacek & Domschke, Wolfgang & Pesch, Erwin, 1996. "The job shop scheduling problem: Conventional and new solution techniques," European Journal of Operational Research, Elsevier, vol. 93(1), pages 1-33, August.
    8. Michael Schachtebeck & Anita Schöbel, 2010. "To Wait or Not to Wait---And Who Goes First? Delay Management with Priority Decisions," Transportation Science, INFORMS, vol. 44(3), pages 307-321, August.
    9. Jain, A. S. & Meeran, S., 1999. "Deterministic job-shop scheduling: Past, present and future," European Journal of Operational Research, Elsevier, vol. 113(2), pages 390-434, March.
    10. Zhou, Xuesong & Zhong, Ming, 2007. "Single-track train timetabling with guaranteed optimality: Branch-and-bound algorithms with enhanced lower bounds," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 320-341, March.
    11. Nagar, Amit & Haddock, Jorge & Heragu, Sunderesh, 1995. "Multiple and bicriteria scheduling: A literature survey," European Journal of Operational Research, Elsevier, vol. 81(1), pages 88-104, February.

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