Abstract
A MILP model for an extended version of the Flexible Job Shop Scheduling problem is proposed. The extension allows the precedences between operations of a job to be given by an arbitrary directed acyclic graph rather than a linear order. The goal is the minimization of the makespan. Theoretical and practical advantages of the proposed model are discussed. Numerical experiments show the performance of a commercial exact solver when applied to the proposed model. The new model is also compared with a simple extension of the model described by Özgüven et al. (Appl Math Modell 34:1539–1548, 2010), using instances from the literature and instances inspired by real data from the printing industry.
Similar content being viewed by others
References
Alvarez-Valdés, R., Fuertes, A., Tamarit, J.M., Giménez, G., Ramos, R.: A heuristic to schedule flexible job-shop in a glass factory. Eur. J. Oper. Res. 165(2), 525–534 (2005)
Brandimarte, P.: Routing and scheduling in a flexible job shop by tabu search. Ann. Oper. Res. 41(3), 157–183 (1993)
Chan, F.T.S., Wong, T.C., Chan, L.Y.: Flexible job-shop scheduling problem under resource constraints. Int. J. Prod. Res. 44(11), 2071–2089 (2006)
Fattahi, P., Mehrabad, M., Jolai, F.: Mathematical modeling and heuristic approaches to flexible job shop scheduling problems. J. Intell. Manuf. 18, 331–342 (2007)
Gutiérrez, C., García-Magariño, I.: Modular design of a hybrid genetic algorithm for a flexible job-shop scheduling problem. Knowl. Sys. 24(1), 102–112 (2011)
Garey, M., Johnson, D., Sethi, R.: The complexity of flowshop and jobshop scheduling. Math. Oper. Res. 1(2), 117–129 (1976)
Lawler, E., Lenstra, J., Rinnooy Kan, A., Shmoys, D.: Sequencing and scheduling: algorithms and complexity. In: Rinnooy Kan, A.H.G., Graves, S.C., Zipkin, P.H. (eds.) Logistics of Production and Inventory, volume 4, Chapter 9, pp. 445–522. Elsevier, Amsterdam (1993)
Manne, A.: On the job-shop scheduling problem. Oper. Res. 8, 219–223 (1960)
Mishra, P.K., Pandey, P.C.: Simulation modeling of batch job shop type flexible manufacturing systems. J. Mech. Work. Technol. 20, 441–450 (1989)
Özgüven, C., Özbakır, L., Yavuz, Y.: Mathematical models for job-shop scheduling problems with routing and process plan flexibility. Appl. Math. Model. 34, 1539–1548 (2010)
Vilcot, G., Billaut, J.-C.: A tabu search and a genetic algorithm for solving a bicriteria general job shop scheduling problem. Eur. J. Oper. Res. 190(2), 398–411 (2008)
Zeng, J., Jackson, S., Lin, I.-J., Gustafson, M., Hoarau, E., Mitchell, R.: On-demand digital print operations: A simulation based case study. Technical report, Hewlett-Packard (2010)
Zhang, G., Shao, X., Li, P., Gao, L.: An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem. Comput. Ind. Eng. 56(4), 1309–1318 (2009)
Acknowledgments
We thank Jun Zeng for several suggestions and discussions. This work was partially funded by CAPES, CNPq, FAPESP, and Hewlett-Packard GOLD advanced research grant, through HP Labs and HP Brazil.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Birgin, E.G., Feofiloff, P., Fernandes, C.G. et al. A MILP model for an extended version of the Flexible Job Shop Problem. Optim Lett 8, 1417–1431 (2014). https://doi.org/10.1007/s11590-013-0669-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-013-0669-7