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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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    3. Mohamadreza Dabiri & Mehdi Yazdani & Bahman Naderi & Hassan Haleh, 2022. "Modeling and solution methods for hybrid flow shop scheduling problem with job rejection," Operational Research, Springer, vol. 22(3), pages 2721-2765, July.
    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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