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Order acceptance and scheduling in a two-machine flowshop

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  • Wang, Xiuli
  • Xie, Xingzi
  • Cheng, T.C.E.

Abstract

We study the order acceptance and scheduling problem in a two-machine flowshop. The firm receives a pool of orders before a planning period, each of which is characterized by revenue, processing times on machines 1 and 2, a due date, and a tardiness penalty. The firm seeks to decide on the orders to accept and schedule the accepted orders so as to maximize the total net revenue. We formulate the problem as mixed-integer linear programming models, and develop a heuristic and a branch-and-bound (B&B) algorithm based on some derived dominance rules and relaxation techniques. We assess the performance of the B&B algorithm and the heuristic via computational experiments. The computational results show that the B&B algorithm can solve problem instances with up to 20 jobs within a reasonable time while the heuristic is efficient in approximately solving large instances of the problem.

Suggested Citation

  • Wang, Xiuli & Xie, Xingzi & Cheng, T.C.E., 2013. "Order acceptance and scheduling in a two-machine flowshop," International Journal of Production Economics, Elsevier, vol. 141(1), pages 366-376.
    • Handle: RePEc:eee:proeco:v:141:y:2013:i:1:p:366-376
    DOI: 10.1016/j.ijpe.2012.08.020
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    References listed on IDEAS

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    1. Chris N. Potts & Luk N. Van Wassenhove, 1985. "A Branch and Bound Algorithm for the Total Weighted Tardiness Problem," Operations Research, INFORMS, vol. 33(2), pages 363-377, April.
    2. Og[breve]uz, Ceyda & Sibel Salman, F. & Bilgintürk YalçIn, Zehra, 2010. "Order acceptance and scheduling decisions in make-to-order systems," International Journal of Production Economics, Elsevier, vol. 125(1), pages 200-211, May.
    3. Louis-Philippe Bigras & Michel Gamache & Gilles Savard, 2008. "Time-Indexed Formulations and the Total Weighted Tardiness Problem," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 133-142, February.
    4. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
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    Citations

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    Cited by:

    1. Wang, Xiuli & Cheng, T.C.E., 2015. "A heuristic for scheduling jobs on two identical parallel machines with a machine availability constraint," International Journal of Production Economics, Elsevier, vol. 161(C), pages 74-82.
    2. Shih-Hsin Chen & Yeong-Cheng Liou & Yi-Hui Chen & Kun-Ching Wang, 2019. "Order Acceptance and Scheduling Problem with Carbon Emission Reduction and Electricity Tariffs on a Single Machine," Sustainability, MDPI, vol. 11(19), pages 1-16, September.
    3. Carvalho, Andréa Nunes & Oliveira, Fabricio & Scavarda, Luiz Felipe, 2016. "Tactical capacity planning in a real-world ETO industry case: A robust optimization approach," International Journal of Production Economics, Elsevier, vol. 180(C), pages 158-171.
    4. Li, Xin & Ventura, Jose A., 2020. "Exact algorithms for a joint order acceptance and scheduling problem," International Journal of Production Economics, Elsevier, vol. 223(C).
    5. Lei, Deming & Guo, Xiuping, 2015. "A parallel neighborhood search for order acceptance and scheduling in flow shop environment," International Journal of Production Economics, Elsevier, vol. 165(C), pages 12-18.
    6. Esmaeilbeigi, Rasul & Charkhgard, Parisa & Charkhgard, Hadi, 2016. "Order acceptance and scheduling problems in two-machine flow shops: New mixed integer programming formulations," European Journal of Operational Research, Elsevier, vol. 251(2), pages 419-431.
    7. Hanane Krim & Nicolas Zufferey & Jean-Yves Potvin & Rachid Benmansour & David Duvivier, 2022. "Tabu search for a parallel-machine scheduling problem with periodic maintenance, job rejection and weighted sum of completion times," Journal of Scheduling, Springer, vol. 25(1), pages 89-105, February.
    8. Carvalho, Andréa Nunes & Oliveira, Fabricio & Scavarda, Luiz Felipe, 2015. "Tactical capacity planning in a real-world ETO industry case: An action research," International Journal of Production Economics, Elsevier, vol. 167(C), pages 187-203.
    9. Chen, Wenchong & Gong, Xuejian & Rahman, Humyun Fuad & Liu, Hongwei & Qi, Ershi, 2021. "Real-time order acceptance and scheduling for data-enabled permutation flow shops: Bilevel interactive optimization with nonlinear integer programming," Omega, Elsevier, vol. 105(C).
    10. Brachmann, Robert & Kolisch, Rainer, 2021. "The impact of flexibility on engineer-to-order production planning," International Journal of Production Economics, Elsevier, vol. 239(C).
    11. Wang, Xiuli & Zhu, Qianqian & Cheng, T.C.E., 2015. "Subcontracting price schemes for order acceptance and scheduling," Omega, Elsevier, vol. 54(C), pages 1-10.
    12. Xiao, Yiyong & Yuan, Yingying & Zhang, Ren-Qian & Konak, Abdullah, 2015. "Non-permutation flow shop scheduling with order acceptance and weighted tardiness," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 312-333.
    13. Naderi, Bahman & Roshanaei, Vahid, 2020. "Branch-Relax-and-Check: A tractable decomposition method for order acceptance and identical parallel machine scheduling," European Journal of Operational Research, Elsevier, vol. 286(3), pages 811-827.

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