Abstract
In this paper we propose a heuristic approach based on column generation (CG) and a general purpose integer programming (GPIP) solver to address a scheduling problem. The problem consists in scheduling independent jobs with given processing times on unrelated parallel machines with sequence-dependent setup times. The objective is to minimize the total weighted tardiness. The proposed matheuristic (MH) takes advantage of the efficiency of CG to define a (restricted) search space which is explored by a GPIP solver. In different iterations, different additional constraints are introduced in CG, allowing the definition of several (restricted) search spaces to be explored by the GPIP solver. Computational results show that the proposed MH can be used to tackle very large instances (e.g. 100 machines and 400 jobs) obtaining better solutions in less time than a state-of-the-art branch-and-price algorithm from the literature.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Allahverdi, A., Soroush, H.M.: The significance of reducing setup times/setup costs. Eur. J. Oper. Res. 187(3), 978–984 (2008)
Allahverdi, A., Ng, C., Cheng, T., Kovalyov, M.: A survey of scheduling problems with setup times or costs. Eur. J. Oper. Res. 187(3), 985–1032 (2008)
Alvelos, F., Sousa, A., Santos, D.: Combining column generation and metaheuristics. In: Talbi, E.G. (ed.) Hybrid Metaheuristics. Studies in Computational Intelligence, vol. 434, pp. 285–334. Springer, Berlin/Heidelberg (2013)
Graham, R.L., Lawler, E.L., Lenstra, J.K., Kan, A.R.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discret. Math. 5(2), 287–326 (1979)
ILOG: IBM ILOG CPLEX Optimization Studio V12.4 (2012)
Lenstra, J.K., Rinnooy Kan, A.H.G., Brucker, P.: Complexity of machine scheduling problems. Ann. Discret. Math. 1, 343–362 (1977)
Lopes, M.J.P., de Carvalho, J.M.V.: A branch-and-price algorithm for scheduling parallel machines with sequence dependent setup times. Eur. J. Oper. Res. 176(3), 1508–1527 (2007)
Lopes, M., Alvelos, F., Lopes, H.: Improving branch-and-price for parallel machine scheduling. Lect. Notes Comput. Sci. 8580, 290–300 (2014)
Mokotoff, E.: Parallel machine scheduling problems: a survey. Asia-Pacific J. Oper. Res. 18(2), 193–243 (2001)
SearchCol++: http://searchcol.dps.uminho.pt/ (2014)
Acknowledgements
This work is financed by Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) within projects “SearchCol: Metaheuristic search by column generation” (PTDC/EIAEIA/100645/2008) and PEst-OE/EEI/UI0319/2014.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Alvelos, F., Lopes, M., Lopes, H. (2016). A Matheuristic Based on Column Generation for Parallel Machine Scheduling with Sequence Dependent Setup Times. In: Fonseca, R., Weber, GW., Telhada, J. (eds) Computational Management Science. Lecture Notes in Economics and Mathematical Systems, vol 682. Springer, Cham. https://doi.org/10.1007/978-3-319-20430-7_30
Download citation
DOI: https://doi.org/10.1007/978-3-319-20430-7_30
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-20429-1
Online ISBN: 978-3-319-20430-7
eBook Packages: Business and ManagementBusiness and Management (R0)