Browse > Article

Parallel Machines Scheduling with Rate-Modifying Activities to Minimize Makespan  

Cho, Hang-Min (Department of Industrial Engineering, Hanyang University)
Yim, Seung-Bin (Department of Industrial Engineering, Hanyang University)
Jeong, In-Jae (Department of Industrial Engineering, Hanyang University)
Publication Information
Journal of Korean Society of Industrial and Systems Engineering / v.30, no.2, 2007 , pp. 44-50 More about this Journal
Abstract
This paper deals with the problem of scheduling jobs and rate-modifying activities on parallel machines. A rate-modifying activity is an activity that changes the production rate of equipment such as maintenance and readjustment. If a job is scheduled after the rate-modifying activity, then the processing time varies depending on the modifying rate of the activity. In this study, we extend the single machine problem to parallel machines problem and propose algorithms is to schedule the rate-modifying activities and jobs to minimize the makespan on parallel machines which is NP-hard. We propose a branch and bound algorithm with three lower bounds to solve medium size problems optimally. Also we develop three heuristics, Modified Longest Processing Time, Modified MULTIFIT and Modified COMBINE algorithms to solve large size problems. The test results show that branch and bound algorithm finds the optimal solution in a reasonable time for medium size problems (up to 15 jobs and 5 machines). For large size problem, Modified COMBINE and Modified MULTIFIT algorithms outperform Modified LPT algorithm in terms of solution quality.
Keywords
Makespan; Parallel Machine; Rate-modifying Activity;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Ho, J. C. and Wong J. S.; 'Makespan Minimization for m Parallel Identical Processors,' Naval Research Logistics, 42 : 935-948, 1995   DOI   ScienceOn
2 Lee, C.-Y. and Chen, Z. L.; 'Scheduling of Jobs and Maintenance Activities on Parallel Machines,' Naval Research Logistics, 47 : 145-165, 2000   DOI   ScienceOn
3 Lee, C.-Y. and Massey, J. D.; 'Multiprocessor scheduling: Combining LPT and MULTIFIT,' Discrete Applied mathematics, 20 : 233-242, 1988   DOI   ScienceOn
4 Lee, C. Y. and Lin, C. S.; 'Single-Machine Scheduling with maintenance and repair rate-modifying activities,' European Journal of Operation Research, 135 : 493-513, 2001   DOI   ScienceOn
5 Coffman Jr., E. G. and, Garey, M. R. and Johnson, D. S.; 'An Application of Bin-Packing to Multiprocessor Scheduling,' SIAM Journal on Computing, 7(1) : 1-17, 1978   DOI
6 Graham, R. L.; 'Bounds on Multiprocessing Timing Anomalies,' SIAM Journal on Applied mathematics, 17(2) : 416-429, 1969   DOI   ScienceOn
7 Lee, C.- Y. and Leon, V. J.; 'Machine Scheduling with a Rate-Modifying Activity,' European Journal of Operation Research, 128 : 119-128, 2001   DOI   ScienceOn
8 Ethel Mokotoff; 'An Exact Algorithm for the Identical Parallel Machine Scheduling Problem,' European Journal of Operation Research, 152 : 758-769, 2004   DOI   ScienceOn
9 Graves, G. H. and Lee, C.-Y.; 'Scheduling Maintenance and Semi-resumable Jobs on a Single Machine,' Naval Research Logistics, 46 : 845-863, 1999   DOI   ScienceOn
10 Baker, K. R.; Introduction to Sequencing and Scheduling, 1943-, John Wiley & Sons Inc, 1974
11 Liao, C. J. and Shyur, D. L., and Lin, C. H.; 'Makespan Minimization for Two Parallel Machines with an Availability Constraint,' European Journal of Operation Research, 160 : 445-456, 2005   DOI   ScienceOn
12 Pinedo, M.; Scheduling: Theory, Algorithms, and Systems, 2nd Edition, Prentice-Hall, Englewood Cliffs, NJ, 2002