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Integrated production and delivery on parallel batching machines

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  • Li, Kai
  • Jia, Zhao-hong
  • Leung, Joseph Y.-T.

Abstract

We consider the problem of scheduling a set of n jobs on m identical and parallel batching machines. The machines have identical capacities equal to K and the jobs have identical processing times equal to p. Job j has a size sj, a due date dj and a profit Rj. Several jobs can be batched together and processed by a machine, provided that the total size of the jobs in the batch does not exceed the machine capacity K. The company will earn a profit of Rj dollars if job j is delivered by time dj; otherwise, it earns nothing. A third party logistic (3PL) provider will be used to deliver the jobs. The 3PL provider picks up the jobs at times T1 < T2 < ⋅⋅⋅ < Tz, and vk (1 ≤ k ≤ z) vehicles will be provided for delivery at time Tk. The vehicles have identical capacities equal to C. The objective is to find a production and delivery schedule so as to maximize the total profit that the company can earn. We show that the problem is solvable in polynomial time if the jobs have identical sizes, but it becomes unary NP-hard if the jobs have different sizes. We propose heuristics for various NP-hard cases and analyze their performances.

Suggested Citation

  • Li, Kai & Jia, Zhao-hong & Leung, Joseph Y.-T., 2015. "Integrated production and delivery on parallel batching machines," European Journal of Operational Research, Elsevier, vol. 247(3), pages 755-763.
    • Handle: RePEc:eee:ejores:v:247:y:2015:i:3:p:755-763
    DOI: 10.1016/j.ejor.2015.06.051
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    References listed on IDEAS

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    1. Agnetis, Alessandro & Aloulou, Mohamed Ali & Fu, Liang-Liang, 2014. "Coordination of production and interstage batch delivery with outsourced distribution," European Journal of Operational Research, Elsevier, vol. 238(1), pages 130-142.
    2. Wang, Jun-Qiang & Leung, Joseph Y.-T., 2014. "Scheduling jobs with equal-processing-time on parallel machines with non-identical capacities to minimize makespan," International Journal of Production Economics, Elsevier, vol. 156(C), pages 325-331.
    3. Dorit S. Hochbaum & Dan Landy, 1997. "Scheduling Semiconductor Burn-In Operations to Minimize Total Flowtime," Operations Research, INFORMS, vol. 45(6), pages 874-885, December.
    4. Kathryn E. Stecke & Xuying Zhao, 2007. "Production and Transportation Integration for a Make-to-Order Manufacturing Company with a Commit-to-Delivery Business Mode," Manufacturing & Service Operations Management, INFORMS, vol. 9(2), pages 206-224, September.
    5. Jia, Zhao-hong & Leung, Joseph Y.-T., 2015. "A meta-heuristic to minimize makespan for parallel batch machines with arbitrary job sizes," European Journal of Operational Research, Elsevier, vol. 240(3), pages 649-665.
    6. Chung-Yee Lee & Reha Uzsoy & Louis A. Martin-Vega, 1992. "Efficient Algorithms for Scheduling Semiconductor Burn-In Operations," Operations Research, INFORMS, vol. 40(4), pages 764-775, August.
    7. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    8. Zhi-Long Chen, 2010. "Integrated Production and Outbound Distribution Scheduling: Review and Extensions," Operations Research, INFORMS, vol. 58(1), pages 130-148, February.
    9. Agnetis, Alessandro & Aloulou, Mohamed Ali & Fu, Liang-Liang & Kovalyov, Mikhail Y., 2015. "Two faster algorithms for coordination of production and batch delivery: A note," European Journal of Operational Research, Elsevier, vol. 241(3), pages 927-930.
    10. 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:

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    3. Liang-Liang Fu & Mohamed Ali Aloulou & Christian Artigues, 2018. "Integrated production and outbound distribution scheduling problems with job release dates and deadlines," Journal of Scheduling, Springer, vol. 21(4), pages 443-460, August.
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    5. 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.
    6. Chen, Jian & Huang, George Q. & Wang, Jun-Qiang & Yang, Chen, 2019. "A cooperative approach to service booking and scheduling in cloud manufacturing," European Journal of Operational Research, Elsevier, vol. 273(3), pages 861-873.
    7. Berghman, Lotte & Kergosien, Yannick & Billaut, Jean-Charles, 2023. "A review on integrated scheduling and outbound vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 1-23.
    8. 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.
    9. Yong-Jae Kim & Byung-Soo Kim, 2022. "Population-Based Meta-Heuristic Algorithms for Integrated Batch Manufacturing and Delivery Scheduling Problem," Mathematics, MDPI, vol. 10(21), pages 1-22, November.

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