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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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    Cited by:

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    4. Li, Feng & Xu, Shifu & Xu, Zhou, 2023. "New exact and approximation algorithms for integrated production and transportation scheduling with committed delivery due dates and order acceptance," European Journal of Operational Research, Elsevier, vol. 306(1), pages 127-140.
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    6. 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.
    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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