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

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

Research output: Contribution to journalArticle

9 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)312-333
Number of pages22
JournalApplied Mathematics and Computation
Volume270
DOIs
StatePublished - Nov 1 2015

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Tardiness
Flow Shop Scheduling
Integer programming
Scheduling
Programming Model
Genetic algorithms
Nonlinear Integer Programming
Permutation
Genetic Algorithm
Heuristic algorithms
Integer
Numerics
Computational Experiments
Heuristic algorithm
Schedule
Experiments
Theorem
Demonstrate

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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title = "Non-permutation flow shop scheduling with order acceptance and weighted tardiness",
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.",
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Non-permutation flow shop scheduling with order acceptance and weighted tardiness. / Xiao, Yiyong; Yuan, Yingying; Zhang, Ren Qian; Konak, Abdullah.

In: Applied Mathematics and Computation, Vol. 270, 01.11.2015, p. 312-333.

Research output: Contribution to journalArticle

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