Abstract
In this paper, we consider the problem of scheduling jobs on unrelated parallel machines with eligibility constraints, where job-processing times are controllable through the allocation of a nonrenewable common resource, and can be modeled by a linear resource consumption function. The objective is to assign the jobs to the machines and to allocate the resource so that the makespan is minimized. We provide an exact formulation of the addressed problem as an integer programming model. As the problem has been proven to be NP-hard even for the fixed job-processing times, two ant colony optimization (ACO) algorithms based on distinct procedures, respectively, are also presented and analyzed. Numerical results show that both the proposed algorithms are capable of solving large-sized problems within reasonable computational time and accuracy.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Blum C, Dorigo M (2004) The hyper-cube framework for ant colony optimization. IEEE Trans Syst Man Cybern 34(2):1161–1172
Dorigo M, Gambardella LM (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1(1):53–66
Jansen K, Mastrolilli M (2004) Approximation schemes for parallel machine scheduling problems with controllable processing times. Comput Oper Res 31:1565–1581
Jozefowska J, Mika M, Rozycki R (2002) A heuristic approach to allocating the continuous resource in discrete continuous scheduling problems to minimize the makespan. J Sched 5:487–499
Lenstra JK, Shmoys DB, Tardos E (1990) Approximation algorithms for scheduling unrelated parallel machines. Math Program 46:259–271
Mokhtari H, Abadi INK, Cheraghalikhani A (2010) A multi-objective flow shop scheduling with resource-dependent processing times: trade-off between makespan and cost of resources. Int J Prod Res 49(19):5851–5875
Shabtay D, Kaspi (2006) Parallel machine scheduling with a convex resource consumption function. Eur J Oper Res 173:92–107
Shabtay D, Steiner G (2007) A survey of scheduling with controllable processing times. Discrete Appl Math 155:1643–1666
Su LH, Lien CY (2009) Scheduling parallel machines with resource-dependent processing times. Int J Prod Econ 117(2):256–266
Acknowledgments
This work is partially supported by the National Science Council under Grant NSC-101-2221-E-224-070. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Singapore
About this paper
Cite this paper
Low, C., Li, RK., Wu, GH. (2013). Ant Colony Optimization Algorithms for Unrelated Parallel Machine Scheduling with Controllable Processing Times and Eligibility Constraints. In: Lin, YK., Tsao, YC., Lin, SW. (eds) Proceedings of the Institute of Industrial Engineers Asian Conference 2013. Springer, Singapore. https://doi.org/10.1007/978-981-4451-98-7_10
Download citation
DOI: https://doi.org/10.1007/978-981-4451-98-7_10
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-4451-97-0
Online ISBN: 978-981-4451-98-7
eBook Packages: EngineeringEngineering (R0)