Abstract
The flowshop sequence dependent group scheduling problem with minimization of makespan as the objective (F m |fmls, S plk, prmu|C max ) is considered in this paper. It is assumed that several groups with different number of jobs are assigned to a flow shop cell that has m machines. The goal is to find the best sequence of processing the jobs in each group and the groups themselves with minimization of makespan as the objective. A mathematical model for the research problem is developed in this paper. As the research problem is shown to be NP-hard, a hybrid ant colony optimization (HACO) algorithm is developed to solve the problem. A lower bounding technique based on relaxing a few constraints of the mathematical model developed for the original problem is proposed to evaluate the quality of the HACO algorithm. Three different problem structures, with two, three, and six machines, are used in the generation of the test problems to test the performance of the algorithm and the lower bounding technique developed. The results obtained from the HACO algorithm and those that have appeared in the published literature are also compared. The comparative results show that the HACO algorithm has a superior performance compared to the best available algorithm based on memetic algorithm with an average percentage deviation of around 1.0% from the lower bound.
Similar content being viewed by others
References
Allahverdi A, Gupta JND, Aldowaisian T (1999) A review of scheduling research involving setup considerations. Int J Manag Sci Omega 27:219–239
Panwalker SS, Dudek RA, Smith ML (1973) Sequencing research and the industrial scheduling problem. Symposium on the theory of scheduling and its applications. Springer, New York, pp 29–38
Wortman DB (1992) Managing capacity: getting the most from your Firm’s assets. Ind Eng 24:47–49
Schaller JE, Gupta JND, Vakharia AJ (2000) Scheduling a flowline manufacturing cell with sequence dependent family setup times. Eur J Oper Res 125:324–339
Cheng TCE, Gupta JND, Wang G (2000) A review of flowshop scheduling research with setup times. Prod Oper Manag 9(3):262–282
Zhu X, Wilhelm WE (2006) Scheduling and lot sizing with sequence-dependent setups: a literature review. IIE Trans 38:987–1007
Allahverdi A, Ng CT, Cheng TCE, Kovalyov MY (2008) A survey of scheduling problems with setup times or costs. Eur J Oper Res 187:985–1032
Hejazi SR, Saghafian S (2005) Flowshop-scheduling problems with makespan criterion: a review. Int J Prod Res 43(14):2895–2929
Jordan C (1996) Batching and scheduling: models and methods for several problem classes. Springer, Berlin
Franca PM, Gupta JND, Mendes AS, Moscato P, Veltink KJ (2005) Evolutionary algorithms for scheduling a flowshop manufacturing cell with sequence dependent family setups. Comput Ind Eng 48(3):491–506
Logendran R, Salmasi N, Sriskandarajah C (2006) Two-machine group scheduling problems in discrete parts manufacturing with sequence-dependent setups. J Comput Oper Res 33:158–180
Hendizadeh H, Faramarzi H, Mansouri SA, Gupta JND, Elmekkawy TY (2008) Meta-heuristics for scheduling a flowshop manufacturing cell with sequence dependent family setup times. Int J Prod Econ 111:593–605
Salmasi N, Logendran R (2008) A heuristic approach for multi-stage sequence-dependent group scheduling problems. J Ind Eng Int 4(7):48–58
Pinedo M (2008) Scheduling theory algorithms and systems, Third Edition, Prentice Hall
Gajpal Y, Rajendran C (2006) An ant-colony optimization algorithm for minimizing the completion-time variance of jobs in flowshops. Int J Prod Econ 101:259–272
Gajpal Y, Rajendran C, Ziegler H (2006) An ant colony algorithm for scheduling in flowshops, with sequence-dependent setup times of jobs. Int J Adv Manuf Technol 30:416–424
Nawaz M, Enscore E, Ham I (1983) A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem, omega. Int J Manag Sci 11(1):91–95
Dorigo M (1992) Optimization, learning, and natural algorithms, PhD thesis, Politecnico di Milano
Dorigo M, Gambardella LM (1997) Ant colonies for the traveling salesman problem. BioSystems 43(2):73–81
ILOG, CPLEX (2003) Release 9.0, Paris, France
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Salmasi, N., Logendran, R. & Skandari, M.R. Makespan minimization of a flowshop sequence-dependent group scheduling problem. Int J Adv Manuf Technol 56, 699–710 (2011). https://doi.org/10.1007/s00170-011-3206-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-011-3206-9