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

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

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)312-333
Number of pages22
JournalApplied Mathematics and Computation
StatePublished - Nov 1 2015

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics


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