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On the minimum number of resources for a perfect schedule

Author

Listed:
  • Rachid Benmansour

    (Institut National de Statistique et d’Économie Appliquée)

  • Oliver Braun

    (Trier University of Applied Sciences, Environmental Campus Birkenfeld)

Abstract

In the single-processor scheduling problem with time restrictions there is one main processor and B resources that are used to execute the jobs. A perfect schedule has no idle times or gaps on the main processor and the makespan is therefore equal to the sum of the processing times. In general, more resources result in smaller makespans, and as it is in practical applications often more economic not to mobilize resources that will be unnecessary and expensive, we investigate in this paper the problem to find the smallest number B of resources that make a perfect schedule possible. We show that the decision version of this problem is NP-complete, derive new structural properties of perfect schedules, and we describe a Mixed Integer Linear Programming (MIP) formulation to solve the problem. A large number of computational tests show that (for our randomly chosen problem instances) only $$B=3$$ B = 3 or $$B=4$$ B = 4 resources are sufficient for a perfect schedule.

Suggested Citation

  • Rachid Benmansour & Oliver Braun, 2023. "On the minimum number of resources for a perfect schedule," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(1), pages 191-204, March.
    • Handle: RePEc:spr:cejnor:v:31:y:2023:i:1:d:10.1007_s10100-022-00803-7
    DOI: 10.1007/s10100-022-00803-7
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    References listed on IDEAS

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    1. Kabir Rustogi & Vitaly A. Strusevich, 2013. "Parallel Machine Scheduling: Impact of Adding Extra Machines," Operations Research, INFORMS, vol. 61(5), pages 1243-1257, October.
    2. Oliver Braun & Fan Chung & Ron Graham, 2016. "Worst-case analysis of the LPT algorithm for single processor scheduling with time restrictions," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(2), pages 531-540, March.
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