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Proportionate flow-shop scheduling with rejection

Author

Listed:
  • Dvir Shabtay

    (Ben-Gurion University of the Negev, Beer-Sheva, Israel)

  • Daniel Oron

    (The University of Sydney, Sydney, Australia)

Abstract

In many heavily loaded manufacturing systems, managers routinely make use of outsourcing options in order to maintain reasonable Quality of Service for customers. Thus, there is a strong need to provide tools for managers to economically coordinate sourcing and scheduling decisions. Our main aim is to provide such tools for an important set of flow-shop scheduling problems where rejection (outsourcing) is allowed and processing times are machine-independent. Our scheduling problems are essentially bicriteria problems, which combine a scheduling objective and the total outsourcing cost. We study several problems which differ according to the scheduling criterion considered. Moreover, each problem is divided into four different variations depending on the way the two criteria are dealt with. For example, in one variation the two criteria are aggregated into a single objective function; in two other variations the aim consists of minimizing one criterion subject to ensuring that the value of the other criterion will not exceed a predefined threshold. From a theoretical point of view, a computational complexity classification is provided for all variations of the problems under consideration. Moreover, optimization algorithms have been constructed to solve all problem variations, and approximation schemes have been developed for solving hard variations. Those schemes enable managers to solve large instances of hard variations while controlling the maximal gap between the obtained solution and the (unknown) optimal solution.

Suggested Citation

  • Dvir Shabtay & Daniel Oron, 2016. "Proportionate flow-shop scheduling with rejection," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(5), pages 752-769, May.
    • Handle: RePEc:pal:jorsoc:v:67:y:2016:i:5:p:752-769
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    Citations

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    Cited by:

    1. Mohamadreza Dabiri & Mehdi Yazdani & Bahman Naderi & Hassan Haleh, 2022. "Modeling and solution methods for hybrid flow shop scheduling problem with job rejection," Operational Research, Springer, vol. 22(3), pages 2721-2765, July.
    2. Danny Hermelin & Dvir Shabtay & Chen Zelig & Michael Pinedo, 2022. "A general scheme for solving a large set of scheduling problems with rejection in FPT time," Journal of Scheduling, Springer, vol. 25(2), pages 229-255, April.
    3. Shabtay, Dvir & Gerstl, Enrique, 2024. "Coordinating scheduling and rejection decisions in a two-machine flow shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 316(3), pages 887-898.
    4. Oron, Daniel, 2021. "Two-agent scheduling problems under rejection budget constraints," Omega, Elsevier, vol. 102(C).
    5. Mosheiov, Gur & Oron, Daniel & Shabtay, Dvir, 2021. "Minimizing total late work on a single machine with generalized due-dates," European Journal of Operational Research, Elsevier, vol. 293(3), pages 837-846.
    6. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.

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