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Relocation Scheduling in a Two-Machine Flow Shop with Resource Recycling Operations

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  • Ting-Chun Lo

    (Institute of Information Management, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan)

  • Bertrand M. T. Lin

    (Institute of Information Management, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan)

Abstract

This paper considers a variant of the relocation problem, which is formulated from an urban renewal project. There is a set of jobs to be processed in a two-machine flow shop subject to a given initial resource level. Each job consumes some units of the resource to start its processing on machine 1 and will return some amount of the resource when it is completed on machine 2. The amount of resource released by a job is not necessarily equal to the amount of resource acquired by the job for starting the process. Subject to the resource constraint, the problem is to find a feasible schedule whose makespan is minimum. In this paper, we first prove the NP-hardness of two special cases. Two heuristic algorithms with different processing characteristics, permutation and non-permutation, are designed to construct feasible schedules. Ant colony optimization (ACO) algorithms are also proposed to produce approximate solutions. We design and conduct computational experiments to appraise the performances of the proposed algorithms.

Suggested Citation

  • Ting-Chun Lo & Bertrand M. T. Lin, 2021. "Relocation Scheduling in a Two-Machine Flow Shop with Resource Recycling Operations," Mathematics, MDPI, vol. 9(13), pages 1-35, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1527-:d:584782
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    References listed on IDEAS

    as
    1. Edward H. Kaplan & Oded Berman, 1988. "OR Hits the Heights: Relocation Planning at the Orient Heights Housing Project," Interfaces, INFORMS, vol. 18(6), pages 14-22, December.
    2. Brucker, Peter & Drexl, Andreas & Mohring, Rolf & Neumann, Klaus & Pesch, Erwin, 1999. "Resource-constrained project scheduling: Notation, classification, models, and methods," European Journal of Operational Research, Elsevier, vol. 112(1), pages 3-41, January.
    3. Kaplan, Edward H. & Amir, Amihood, 1988. "A fast feasibility test for relocation problems," European Journal of Operational Research, Elsevier, vol. 35(2), pages 201-206, May.
    4. Lin, B. M. T. & Cheng, T. C. E., 1999. "Minimizing the weighted number of tardy jobs and maximum tardiness in relocation problem with due date constraints," European Journal of Operational Research, Elsevier, vol. 116(1), pages 183-193, July.
    5. Lin, B.M.T. & Liu, S.T., 2008. "Maximizing the reward in the relocation problem with generalized due dates," International Journal of Production Economics, Elsevier, vol. 115(1), pages 55-63, September.
    6. Y.M. Shafransky & V.A. Strusevich, 1998. "The open shop scheduling problem with a given sequence of jobs on one machine," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(7), pages 705-731, October.
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    Cited by:

    1. Jian-You Xu & Win-Chin Lin & Yu-Wei Chang & Yu-Hsiang Chung & Juin-Han Chen & Chin-Chia Wu, 2023. "A Two-Machine Learning Date Flow-Shop Scheduling Problem with Heuristics and Population-Based GA to Minimize the Makespan," Mathematics, MDPI, vol. 11(19), pages 1-21, September.

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