Abstract
In this paper we present a hybrid exact-heuristic method to improve a branch-and-price algorithm to solve the unrelated parallel machines with sequence-dependent setup times scheduling problem. As most of the computational time in the column generation (CG) process is spent in subproblems, two new heuristics to solve the subproblems are embedded in the branch-and-price (BP) framework with the aim to improve the efficiency of the process in obtaining optimal solutions. Computational results show that the proposed method improves a state-of-the-art BP algorithm from the literature, providing optimal solutions for large instances (e.g. 50 machines and 180 jobs) of the parallel machine scheduling problem with sequence dependent setup times, in significantly less time. One of the proposed approaches reduces, in average, to a half the time spent in the root of the branch-and-price tree and to a quarter the time spent in the full branch-and-price algorithm.
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References
Mokotoff, E.: Parallel Machine Scheduling Problems: a survey. Asia-Pacific Journal of Operational Research 18, 193–243 (2001)
Allahverdi, A., Ng, C.T., Cheng, T.C.E., Kovalyov, M.Y.: A survey of scheduling problems with setup times or costs. European Journal of Operational Research 187, 985–1032 (2008)
Allahverdi, A., Soroush, H.M.: The significance of reducing setup times/setup costs. European Journal of Operational Research 187, 978–984 (2008)
Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 5, 287–326 (1979)
Lenstra, J.K., Rinnooy Kan, A.H.G., Brucker, P.: Complexity of Machine Scheduling Problems. Annals of Discrete Mathematics 1, 343–362 (1977)
Barnhart, C., Johnson, E.L., Nemhauser, G.L., Savelsbergh, M.W.P., Vance, P.H.: Branch-and-price: column generation for solving huge integer programs. Operations Research 46, 316–329 (1998)
Lopes, M.J.P., de Carvalho, J.M.V.: A branch-and-price algorithm for scheduling parallel machines with sequence dependent setup times. European Journal of Operational Research 176, 1508–1527 (2007)
Desaulniers, G., Desrosiers, J., Solomon, M.M.: Column generation. Springer (2005)
Wilhelm, W.E.: A technical review of column generation in integer programming. Optimization and Engineering 2, 159–200 (2001)
Lopes, M.: Resolução de Problemas de Programação de Máquinas Paralelas pelo Método de Partição e Geração de Colunas. PhD thesis, Universidade do Minho (2004) (in Portuguese)
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Lopes, M., Alvelos, F., Lopes, H. (2014). Improving Branch-and-Price for Parallel Machine Scheduling. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2014. ICCSA 2014. Lecture Notes in Computer Science, vol 8580. Springer, Cham. https://doi.org/10.1007/978-3-319-09129-7_22
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DOI: https://doi.org/10.1007/978-3-319-09129-7_22
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09128-0
Online ISBN: 978-3-319-09129-7
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