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Machine scheduling with an availability constraint and job delivery coordination

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  • Xiuli Wang
  • T. C. Edwin Cheng

Abstract

In this paper we study the scheduling problem that considers both production and job delivery at the same time with machine availability considerations. Only one vehicle is available to deliver jobs in a fixed transportation time to a distribution center. The vehicle can load at most K jobs as a delivery batch in one shipment due to the vehicle capacity constraint. The objective is to minimize the arrival time of the last delivery batch to the distribution center. Since machines may not always be available over the production period in real life due to preventive maintenance, we incorporate machine availability into the models. Three scenarios of the problem are studied. For the problem in which the jobs are processed on a single machine and the jobs interrupted by the unavailable machine interval are resumable, we provide a polynomial algorithm to solve the problem optimally. For the problem in which the jobs are processed on a single machine and the interrupted jobs are nonresumable, we first show that the problem is NP‐hard. We then propose a heuristic with a worst‐case error bound of 1/2 and show that the bound is tight. For the problem in which the jobs are processed on either one of two parallel machines, where only one machine has an unavailable interval and the interrupted jobs are resumable, we propose a heuristic with a worst‐case error bound of 2/3. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007

Suggested Citation

  • Xiuli Wang & T. C. Edwin Cheng, 2007. "Machine scheduling with an availability constraint and job delivery coordination," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 11-20, February.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:1:p:11-20
    DOI: 10.1002/nav.20175
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    References listed on IDEAS

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    1. Liao, Ching-Jong & Shyur, Der-Lin & Lin, Chien-Hung, 2005. "Makespan minimization for two parallel machines with an availability constraint," European Journal of Operational Research, Elsevier, vol. 160(2), pages 445-456, January.
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    Cited by:

    1. Jason Pan & Chi-Shiang Su, 2015. "Two parallel machines problem with job delivery coordination and availability constraint," Annals of Operations Research, Springer, vol. 235(1), pages 653-664, December.
    2. Söhnke Maecker & Liji Shen, 2020. "Solving parallel machine problems with delivery times and tardiness objectives," Annals of Operations Research, Springer, vol. 285(1), pages 315-334, February.
    3. B.‐Y. Cheng & J.Y.‐T. Leung & K. Li & S.‐L. Yang, 2015. "Single batch machine scheduling with deliveries," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 470-482, September.
    4. Chagas, Guilherme O. & Coelho, Leandro C. & Darvish, Maryam & Renaud, Jacques, 2023. "Modeling and solving the waste valorization production and distribution scheduling problem," European Journal of Operational Research, Elsevier, vol. 306(1), pages 400-417.
    5. Jing Fan & Xiwen Lu, 2015. "Supply chain scheduling problem in the hospital with periodic working time on a single machine," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 892-905, November.

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