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Outsourcing and scheduling for two-machine ordered flow shop scheduling problems

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  • Chung, Dae-Young
  • Choi, Byung-Cheon

Abstract

This paper considers a two-machine ordered flow shop problem, where each job is processed through the in-house system or outsourced to a subcontractor. For in-house jobs, a schedule is constructed and its performance is measured by the makespan. Jobs processed by subcontractors require paying an outsourcing cost. The objective is to minimize the sum of the makespan and the total outsourcing cost. Since this problem is NP-hard, we present an approximation algorithm. Furthermore, we consider three special cases in which job j has a processing time requirement pj, and machine i a characteristic qi. The first case assumes the time job j occupies machine i is equal to the processing requirement divided by a characteristic value of machine i, that is, pj/qi. The second (third) case assumes that the time job j occupies machine i is equal to the maximum (minimum) of its processing requirement and a characteristic value of the machine, that is, max{pj,qi} (min{pj,qi}). We show that the first and the second cases are NP-hard and the third case is polynomially solvable.

Suggested Citation

  • Chung, Dae-Young & Choi, Byung-Cheon, 2013. "Outsourcing and scheduling for two-machine ordered flow shop scheduling problems," European Journal of Operational Research, Elsevier, vol. 226(1), pages 46-52.
    • Handle: RePEc:eee:ejores:v:226:y:2013:i:1:p:46-52
    DOI: 10.1016/j.ejor.2012.10.048
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    References listed on IDEAS

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    1. M. L. Smith & S. S. Panwalkar & R. A. Dudek, 1975. "Flowshop Sequencing Problem with Ordered Processing Time Matrices," Management Science, INFORMS, vol. 21(5), pages 544-549, January.
    2. Peng Si Ow, 1985. "Focused Scheduling in Proportionate Flowshops," Management Science, INFORMS, vol. 31(7), pages 852-869, July.
    3. Lee, Kangbok & Choi, Byung-Cheon, 2011. "Two-stage production scheduling with an outsourcing option," European Journal of Operational Research, Elsevier, vol. 213(3), pages 489-497, September.
    4. Qi, Xiangtong, 2011. "Outsourcing and production scheduling for a two-stage flow shop," International Journal of Production Economics, Elsevier, vol. 129(1), pages 43-50, January.
    5. Lee, Ik Sun & Sung, C.S., 2008. "Minimizing due date related measures for a single machine scheduling problem with outsourcing allowed," European Journal of Operational Research, Elsevier, vol. 186(3), pages 931-952, May.
    6. Chung, Daeyoung & Lee, Kichang & Shin, Kitae & Park, Jinwoo, 2005. "A new approach to job shop scheduling problems with due date constraints considering operation subcontracts," International Journal of Production Economics, Elsevier, vol. 98(2), pages 238-250, November.
    7. Gérard P. Cachon & Patrick T. Harker, 2002. "Competition and Outsourcing with Scale Economies," Management Science, INFORMS, vol. 48(10), pages 1314-1333, October.
    8. Koulamas, Christos & Kyparisis, George J., 2009. "A note on the proportionate flow shop with a bottleneck machine," European Journal of Operational Research, Elsevier, vol. 193(2), pages 644-645, March.
    9. Byung-Cheon Choi & Joseph Y.-T. Leung & Michael L. Pinedo, 2011. "Minimizing makespan in an ordered flow shop with machine-dependent processing times," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 797-818, November.
    10. Lee, Ik Sun & Sung, C.S., 2008. "Single machine scheduling with outsourcing allowed," International Journal of Production Economics, Elsevier, vol. 111(2), pages 623-634, February.
    11. Choi, Byung-Cheon & Chung, Jibok, 2011. "Two-machine flow shop scheduling problem with an outsourcing option," European Journal of Operational Research, Elsevier, vol. 213(1), pages 66-72, August.
    12. 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. Choi, Byung-Cheon & Chung, Kwanghun, 2016. "Min–max regret version of a scheduling problem with outsourcing decisions under processing time uncertainty," European Journal of Operational Research, Elsevier, vol. 252(2), pages 367-375.
    2. Mohammad Mohammadi, 2017. "The Tradeoff between Outsourcing and Using More Factories in a Distributed Flow Shop System," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(4), pages 279-295.
    3. Zhong, Xueling & Fan, Jie & Ou, Jinwen, 2022. "Coordinated scheduling of the outsourcing, in-house production and distribution operations," European Journal of Operational Research, Elsevier, vol. 302(2), pages 427-437.
    4. Thürer, Matthias & Stevenson, Mark & Qu, Ting & Godinho Filho, Moacir, 2014. "The design of simple subcontracting rules for make-to-order shops: An assessment by simulation," European Journal of Operational Research, Elsevier, vol. 239(3), pages 854-864.

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