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Two-machine flow shop scheduling problem with an outsourcing option

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  • Choi, Byung-Cheon
  • Chung, Jibok

Abstract

We consider a two-machine flow shop problem in which each job is processed through an in-house system or outsourced to a subcontractor. A schedule is established for the in-house jobs, and 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 total outsourcing costs. We show that the problem is NP-hard in the ordinary sense. We consider a special case in which each job has a processing requirement, and each machine a characteristic value. In this case, the time a job occupies a machine is equal to the job's processing requirement plus a setup time equal to the characteristic value of that machine. We introduce some optimality conditions and present a polynomial-time algorithm to solve the special case.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:213:y:2011:i:1:p:66-72
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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. 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.
    3. 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.
    4. 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.
    5. Peng Si Ow, 1985. "Focused Scheduling in Proportionate Flowshops," Management Science, INFORMS, vol. 31(7), pages 852-869, July.
    6. 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.
    7. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    8. 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.
    9. Gérard P. Cachon & Patrick T. Harker, 2002. "Competition and Outsourcing with Scale Economies," Management Science, INFORMS, vol. 48(10), pages 1314-1333, October.
    10. 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. Liqi Zhang & Lingfa Lu & Shisheng Li, 2016. "New results on two-machine flow-shop scheduling with rejection," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1493-1504, May.
    3. Shi-Sheng Li & De-Liang Qian & Ren-Xia Chen, 2017. "Proportionate Flow Shop Scheduling with Rejection," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-13, August.
    4. Della Croce, Federico & Koulamas, Christos & T'kindt, Vincent, 2017. "A constraint generation approach for two-machine shop problems with jobs selection," European Journal of Operational Research, Elsevier, vol. 259(3), pages 898-905.
    5. Lingfa Lu & Liqi Zhang & Jie Zhang & Lili Zuo, 2020. "Single Machine Scheduling with Outsourcing Under Different Fill Rates or Quantity Discount Rates," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(01), pages 1-15, January.
    6. 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.
    7. 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.
    8. Lingfa Lu & Liqi Zhang & Jinwen Ou, 2021. "In-house production and outsourcing under different discount schemes on the total outsourcing cost," Annals of Operations Research, Springer, vol. 298(1), pages 361-374, March.
    9. S.S. Panwalkar & Milton L. Smith & Christos Koulamas, 2013. "Review of the ordered and proportionate flow shop scheduling research," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 46-55, February.
    10. 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.

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