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Bicriteria scheduling on a single batching machine with job transportation and deterioration considerations

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  • Lixin Tang
  • Hua Gong
  • Jiyin Liu
  • Feng Li

Abstract

We study a single batching machine scheduling problem with transportation and deterioration considerations arising from steel production. A set of jobs are transported, one at a time, by a vehicle from a holding area to the single batching machine. The machine can process several jobs simultaneously as a batch. The processing time of a job will increase if the duration from the time leaving the holding area to the start of its processing exceeds a given threshold. The time needed to process a batch is the longest of the job processing times in the batch. The problem is to determine the job sequence for transportation and the job batching for processing so as to minimize the makespan and the number of batches. We study four variations (P1, P2, P3, P4) of the problem with different treatments of the two criteria. We prove that all the four variations are strongly NP‐hard and further develop polynomial time algorithms for their special cases. For each of the first three variations, we propose a heuristic algorithm and analyze its worst‐case performance. For P4, which is to find the Pareto frontier, we provide a heuristic algorithm and an exact algorithm based on branch and bound. Computational experiments show that all the heuristic algorithms perform well on randomly generated problem instances, and the exact algorithm for P4 can obtain Pareto optimal schedules for small‐scale instances. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 269–285, 2014

Suggested Citation

  • Lixin Tang & Hua Gong & Jiyin Liu & Feng Li, 2014. "Bicriteria scheduling on a single batching machine with job transportation and deterioration considerations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(4), pages 269-285, June.
    • Handle: RePEc:wly:navres:v:61:y:2014:i:4:p:269-285
    DOI: 10.1002/nav.21582
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    References listed on IDEAS

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    2. Leung, Joseph Y.-T. & Ng, C.T. & Cheng, T.C. Edwin, 2008. "Minimizing sum of completion times for batch scheduling of jobs with deteriorating processing times," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1090-1099, June.
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    6. Potts, Chris N. & Kovalyov, Mikhail Y., 2000. "Scheduling with batching: A review," European Journal of Operational Research, Elsevier, vol. 120(2), pages 228-249, January.
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    Cited by:

    1. Zhou, Shengchao & Jin, Mingzhou & Du, Ni, 2020. "Energy-efficient scheduling of a single batch processing machine with dynamic job arrival times," Energy, Elsevier, vol. 209(C).
    2. Zhang, Hongbin & Yang, Yu & Wu, Feng, 2024. "Scheduling a set of jobs with convex piecewise linear cost functions on a single-batch-processing machine," Omega, Elsevier, vol. 122(C).
    3. Sun, X.T. & Chung, S.H. & Chan, Felix T.S. & Wang, Zheng, 2018. "The impact of liner shipping unreliability on the production–distribution scheduling of a decentralized manufacturing system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 242-269.
    4. Hua Gong & Lixin Tang & Joseph Y.T. Leung, 2016. "Parallel machine scheduling with batch deliveries to minimize total flow time and delivery cost," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(6), pages 492-502, September.
    5. Florian Jaehn & Sergey Kovalev & Mikhail Y. Kovalyov & Erwin Pesch, 2014. "Multiproduct batching and scheduling with buffered rework: The case of a car paint shop," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(6), pages 458-471, September.

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