Abstract
The NP-hard problem of scheduling jobs on unrelated parallel machines, in the presence of machine-dependent and sequence-dependent setup times, with the objective of minimizing the makespan, is considered. A variable neighborhood descent search algorithm, hybridized with mathematical programming elements, is presented and its performance is evaluated on a large set of benchmark problem instances. The extensive computational experiments show that the proposed algorithm outperforms previously proposed methods in terms of solution quality as well as computation time.
Similar content being viewed by others
References
Ahuja R. K., Ergun O., Orlin J. B., Punnen A. P. (2002) A survey of very large-scale neighborhood search techniques. Discrete Applied Mathematics 123: 75–102
Ahuja R. K., Orlin J. B., Sharma D. (2001) New neighborhood search structures for the capacitated minimum spanning tree problem. Mathematical Programming 91: 71–97
Al-Salem A. (2004) Scheduling to minimize makespan on unrelated parallel machines with sequence dependent setup times. Engineering Journal of the University of Qatar 17: 177–187
Archetti C., Speranza M. G., Savelsbergh M. W. P. (2008) An optimization-based heuristic for the split delivery vehicle routing problem. Transportation Science 42(1): 22–31
Arnaout J. P., Rabadi G., Musa R. (2010) A two-stage ant colony optimization algorithm to minimize the makespan on unrelated parallel machines with sequence-dependent setup times. Journal of Intelligent Manufacturing 21(6): 693–701
Blazewicz J., Ecker K. H., Pesch E., Schmidt G., Weglarz J. (1996) Scheduling computer and manufacturing processes. Springer, Berlin
Brucker P. (2004) Scheduling algorithms. Springer, Berlin
De Franceschi R., Fischetti M., Toth P. (2006) A new ILP-based refinement heuristic for vehicle routing problems. Mathematical Programming 105(2–3): 471–499
Ergun Ö., Orlin J. B., Steele-Feldman A. (2006) Creating very large scale neighborhoods out of smaller ones by compounding moves. Journal of Heuristics 12(1–2): 115–140
Espinoza D., Garcia R., Goycoolea M., Nemhauser G.L., Savelsbergh M.W.P. (2008) Per-seat, on-demand air transportation part I: problem description and an integer multicommodity flow model. Transportation Science 42(3): 263–278
Fleszar K., Hindi K.S. (2008) An effective VNS for the capacitated p-median problem. European Journal of Operational Research 191(3): 612–622
Fleszar K., Hindi K.S. (2009) Fast, effective heuristics for the 0–1 multi-dimensional knapsack problem. Computers and Operations Research 36(5): 1602–1607
Frangioni A., Necciari E., Scutella M. G. (2004) A multi-exchange neighborhood for minimum makespan parallel machine scheduling problems. Journal of Combinatorial Optimization 8: 195–220
Ghirardi M., Potts C. N. (2005) Makespan minimization for scheduling unrelated parallel machines: A recovering beam search approach. European Journal of Operational Research 165(2): 457–467
Glover F., Gutin G., Yeo A., Zverovich A. (2001) Construction heuristics for the asymmetric TSP. European Journal of Operational Research 129: 555–568
Hansen P., Mladenović M., Perez-Britos D. (2001) Variable neighborhood decomposition search. Journal of Heuristics 7(4): 335–350
Helal M., Rabadi G., Al-Salem A. (2006) A tabu search algorithm to minimize the makespan for the unrelated parallel machines scheduling problem with setup times. International Journal of Operations Research 3(3): 182–192
Hoogeveen, J., Lenstra, J. K., & van de Velde, S. L (1997). Sequencing and scheduling: An annotated bibliography. Eindhoven University of Technology, Department of Mathematics and Computing Science.
Jonker R., Volgenant A. (1987) A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing 38: 325–340
Kim D.-W., Na D.-G., Chen F. F. (2003) Unrelated parallel machine scheduling with setup times and a total weighted tardiness objective. Robotics and Computer Integrated Manufacturing 19: 173–181
Lee, C-Y., & Pinedo, M. (2002). Optimization and heuristics of scheduling. In P.M. Pardalos, & M.G.C. Resende, Handbook of applied optimization. New York: Oxford University Press.
Liaw C. F., Lin Y. K., Chen C. Y., Chen M. (2003) Scheduling unrelated parallel machines to minimize total weighted tardiness. Computers and Operations Research 30: 1777–1789
Logendran R., McDonell B., Smucker B. (2007) Scheduling unrelated parallel machines with sequence-dependent setups. Computers and Operations Research 34(11): 3420–3438
Martello S., Soumis F., Toth P. (1997) Exact and approximation algorithms for makespan minimization on unrelated parallel machines. Discrete Applied Mathematics 75: 169–188
Mokotoff E. (2001) Parallel machine scheduling problems: A survey. Asia-Pacific Journal of Operational Research 18(2): 193–242
Mokotoff E., Chretienne P. (2002) A cutting plane algorithm for the unrelated parallel machine scheduling problem. European Journal of Operational Research 141(3): 515–525
Mokotoff E., Jimeno J. L. (2002) Heuristics based on partial enumeration for the unrelated parallel processor scheduling problem. Annals of Operations Research 117(1–4): 133–150
Pereira Lopes M. J., de Carvalho J. M. V. (2007) A branch-and-price algorithm for scheduling parallel machines with sequence dependent setup times. European Journal of Operational Research 176(3): 1508–1527
Pinedo M. (2002) Scheduling: theory, algorithms, and systems. Prentice Hall, New Jersey
Rabadi G., Moraga R. J., Al-Salem A. (2006) Heuristics for the unrelated parallel machine scheduling problem with setup times. Journal of Intelligent Manufacturing 17: 85–97
Ravetti M. G., Mateus G. R., Rocha P. L., Pardalos P. M. (2007) A scheduling problem with unrelated parallel machines and sequence dependent setups. International Journal of Operational Research 2(4): 380–399
Rocha P. L., Ravetti M. G., Mateus G. R., Pardalos P. M. (2008) Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times. Computers and Operations Research 35(4): 1250–1264
Shchepin E., Vakhania N. (2006) An absolute approximation algorithm for scheduling unrelated machines. Naval Research Logistics 53(6): 502–507
Shchepin E. V., Vakhania N. (2005) An optimal rounding gives a better approximation for scheduling unrelated machines. Operations Research Letters 33(2): 127–133
Weng M., Lu J., Ren H. (2001) Unrelated parallel machine scheduling with setup consideration and a total weighted completion time objective. International Journal of Production Economics 70: 215–226
Author information
Authors and Affiliations
Corresponding author
Additional information
This research has been supported by the Cyprus Research Promotion Foundation (Project TEXNO/0603/08—NETEXNOPRO).
Rights and permissions
About this article
Cite this article
Fleszar, K., Charalambous, C. & Hindi, K.S. A variable neighborhood descent heuristic for the problem of makespan minimisation on unrelated parallel machines with setup times. J Intell Manuf 23, 1949–1958 (2012). https://doi.org/10.1007/s10845-011-0522-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10845-011-0522-8