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Non-permutation flow shop scheduling with order acceptance and weighted tardiness

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  • Xiao, Yiyong
  • Yuan, Yingying
  • Zhang, Ren-Qian
  • Konak, Abdullah

Abstract

This paper studies the non-permutation solution for the problem of flow shop scheduling with order acceptance and weighted tardiness (FSS-OAWT). We formulate the problem as a linear mixed integer programming (LMIP) model that can be optimally solved by AMPL/CPLEX for small-sized problems. In addition, a non-linear integer programming (NIP) model is presented to design heuristic algorithms. A two-phase genetic algorithm (TP-GA) is developed to solve the problem of medium and large sizes based on the NIP model. The properties of FSS-OAWT are investigated and several theorems for permutation and non-permutation optimum are provided. The performance of the TP-GA is studied through rigorous computational experiments using a large number of numeric instances. The LMIP model is used to demonstrate the differences between permutation and non-permutation solutions to the FSS-OAWT problem. The results show that a considerably large portion of the instances have only an optimal non-permutation schedule (e.g., 43.3% for small-sized), and the proposed TP-GA algorithms are effective in solving the FSS-OAWT problems of various scales (small, medium, and large) with both permutation and non-permutation solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:312-333
    DOI: 10.1016/j.amc.2015.08.011
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    1. Jianzhong Du & Joseph Y.-T. Leung, 1990. "Minimizing Total Tardiness on One Machine is NP-Hard," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 483-495, August.
    2. 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.
    3. Li, Gang & Wang, Xiao-Yuan & Wang, Ji-Bo & Sun, Lin-Yan, 2013. "Worst case analysis of flow shop scheduling problems with a time-dependent learning effect," International Journal of Production Economics, Elsevier, vol. 142(1), pages 98-104.
    4. Raaymakers, W. H. M. & Hoogeveen, J. A., 2000. "Scheduling multipurpose batch process industries with no-wait restrictions by simulated annealing," European Journal of Operational Research, Elsevier, vol. 126(1), pages 131-151, October.
    5. De, Prabuddha & Ghosh, Jay B. & Wells, Charles E., 1993. "Job selection and sequencing on a single machine in a random environment," European Journal of Operational Research, Elsevier, vol. 70(3), pages 425-431, November.
    6. Mehravaran, Yasaman & Logendran, Rasaratnam, 2012. "Non-permutation flowshop scheduling in a supply chain with sequence-dependent setup times," International Journal of Production Economics, Elsevier, vol. 135(2), pages 953-963.
    7. B. J. Lageweg & J. K. Lenstra & A. H. G. Rinnooy Kan, 1978. "A General Bounding Scheme for the Permutation Flow-Shop Problem," Operations Research, INFORMS, vol. 26(1), pages 53-67, February.
    8. 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.
    9. Koulamas, Christos, 1998. "A new constructive heuristic for the flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 105(1), pages 66-71, February.
    10. Sun, Lin-Hui & Sun, Lin-Yan & Wang, Ming-Zheng & Wang, Ji-Bo, 2012. "Flow shop makespan minimization scheduling with deteriorating jobs under dominating machines," International Journal of Production Economics, Elsevier, vol. 138(1), pages 195-200.
    11. Pourbabai, Behnam, 1989. "A short term production planning and scheduling model," Engineering Costs and Production Economics, Elsevier, vol. 18(2), pages 159-167, December.
    12. Cheng, T. C. E. & Ding, Q. & Lin, B. M. T., 2004. "A concise survey of scheduling with time-dependent processing times," European Journal of Operational Research, Elsevier, vol. 152(1), pages 1-13, January.
    13. Zhang, Yi & Li, Xiaoping & Wang, Qian, 2009. "Hybrid genetic algorithm for permutation flowshop scheduling problems with total flowtime minimization," European Journal of Operational Research, Elsevier, vol. 196(3), pages 869-876, August.
    14. 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.
    15. Sushil K. Gupta & Jerzy Kyparisis & Chi-Ming Ip, 1992. "Note---Project Selection and Sequencing to Maximize Net Present Value of the Total Return," Management Science, INFORMS, vol. 38(5), pages 751-752, May.
    16. 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.
    17. Cheng, Yushao & Sun, Shijie, 2009. "Scheduling linear deteriorating jobs with rejection on a single machine," European Journal of Operational Research, Elsevier, vol. 194(1), pages 18-27, April.
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    3. Xiao, Yiyong & Zhang, Siyue & Yang, Pei & You, Meng & Huang, Jiaoying, 2019. "A two-stage flow-shop scheme for the multi-satellite observation and data-downlink scheduling problem considering weather uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 263-275.
    4. 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).

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