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The just-in-time scheduling problem in a flow-shop scheduling system

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  • Shabtay, Dvir

Abstract

We study the problem of maximizing the weighted number of just-in-time (JIT) jobs in a flow-shop scheduling system under four different scenarios. The first scenario is where the flow-shop includes only two machines and all the jobs have the same gain for being completed JIT. For this scenario, we provide an O(n3) time optimization algorithm which is faster than the best known algorithm in the literature. The second scenario is where the job processing times are machine-independent. For this scenario, the scheduling system is commonly referred to as a proportionate flow-shop. We show that in this case, the problem of maximizing the weighted number of JIT jobs is NP-hard in the ordinary sense for any arbitrary number of machines. Moreover, we provide a fully polynomial time approximation scheme (FPTAS) for its solution and a polynomial time algorithm to solve the special case for which all the jobs have the same gain for being completed JIT. The third scenario is where a set of identical jobs is to be produced for different customers. For this scenario, we provide an O(n3) time optimization algorithm which is independent of the number of machines. We also show that the time complexity can be reduced to O(nlogn) if all the jobs have the same gain for being completed JIT. In the last scenario, we study the JIT scheduling problem on m machines with a no-wait restriction and provide an O(mn2) time optimization algorithm.

Suggested Citation

  • Shabtay, Dvir, 2012. "The just-in-time scheduling problem in a flow-shop scheduling system," European Journal of Operational Research, Elsevier, vol. 216(3), pages 521-532.
    • Handle: RePEc:eee:ejores:v:216:y:2012:i:3:p:521-532
    DOI: 10.1016/j.ejor.2011.07.053
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    References listed on IDEAS

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    1. Mosheiov, Gur & Oron, Daniel, 2008. "Open-shop batch scheduling with identical jobs," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1282-1292, June.
    2. G Mosheiov, 2003. "Scheduling unit processing time jobs on an m-machine flow-shop," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(4), pages 437-441, April.
    3. Mosheiov, Gur & Oron, Daniel, 2005. "A note on flow-shop and job-shop batch scheduling with identical processing-time jobs," European Journal of Operational Research, Elsevier, vol. 161(1), pages 285-291, February.
    4. Kovalyov, Mikhail Y. & Ng, C.T. & Cheng, T.C. Edwin, 2007. "Fixed interval scheduling: Models, applications, computational complexity and algorithms," European Journal of Operational Research, Elsevier, vol. 178(2), pages 331-342, April.
    5. Mosheiov, Gur & Shadmon, Michal, 2001. "Minmax earliness-tardiness costs with unit processing time jobs," European Journal of Operational Research, Elsevier, vol. 130(3), pages 638-652, May.
    6. Choi, Byung-Cheon & Yoon, Suk-Hun & Chung, Sung-Jin, 2007. "Minimizing maximum completion time in a proportionate flow shop with one machine of different speed," European Journal of Operational Research, Elsevier, vol. 176(2), pages 964-974, January.
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    Cited by:

    1. Shabtay, Dvir & Gilenson, Miri, 2023. "A state-of-the-art survey on multi-scenario scheduling," European Journal of Operational Research, Elsevier, vol. 310(1), pages 3-23.
    2. Janiak, Adam & Janiak, Władysław A. & Krysiak, Tomasz & Kwiatkowski, Tomasz, 2015. "A survey on scheduling problems with due windows," European Journal of Operational Research, Elsevier, vol. 242(2), pages 347-357.
    3. Yin, Yunqiang & Cheng, Shuenn-Ren & Cheng, T.C.E. & Wang, Du-Juan & Wu, Chin-Chia, 2016. "Just-in-time scheduling with two competing agents on unrelated parallel machines," Omega, Elsevier, vol. 63(C), pages 41-47.
    4. Imen Hamdi & Imen Boujneh, 2022. "Particle swarm optimization based-algorithms to solve the two-machine cross-docking flow shop problem: just in time scheduling," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 947-969, September.
    5. Danny Hermelin & Dvir Shabtay & Nimrod Talmon, 2019. "On the parameterized tractability of the just-in-time flow-shop scheduling problem," Journal of Scheduling, Springer, vol. 22(6), pages 663-676, December.
    6. Koulamas, Christos, 2020. "The proportionate flow shop total tardiness problem," European Journal of Operational Research, Elsevier, vol. 284(2), pages 439-444.
    7. Yunqiang Yin & T. C. E. Cheng & Du-Juan Wang & Chin-Chia Wu, 2017. "Two-agent flowshop scheduling to maximize the weighted number of just-in-time jobs," Journal of Scheduling, Springer, vol. 20(4), pages 313-335, August.
    8. Enrique Gerstl & Gur Mosheiov, 2023. "A note: maximizing the weighted number of Just-in-Time jobs for a given job sequence," Journal of Scheduling, Springer, vol. 26(4), pages 403-409, August.

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