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Journal of Intelligent Manufacturing

, Volume 26, Issue 6, pp 1099–1112 | Cite as

Unrelated parallel-machine scheduling to minimize total weighted completion time

  • Jeng-Fung ChenEmail author
Article

Abstract

This research deals with the unrelated parallel-machine scheduling to minimize total weighted completion time. There are \(N\) jobs, each having a weight and requiring a single stage of processing on one of the \(M\) machines. Because of the attribute and mechanical structure of the machines, the processing time depends on both the job and the machine. A sequence-dependent setup time is required if the type of job scheduled is different from the previous one on the same machine. The required setup time depends on the previous job type, the current job type, and the machine on which the job is processed. Furthermore, the jobs (i.e., orders) from primary customers have rigid due date constraints. In this research, a revised SWPT and improvement procedures are applied to generate a feasible schedule. Three effective heuristics, two based on record-to-record travel (RRT1 and RRT2) and one based on random descent search, are developed to improve the feasible schedule. Computational performance of the proposed heuristics is evaluated through an extensive experiment. Computational results show that RRT1 performs better than the other two heuristics and is able to improve the initial solutions effectively. Computational experiences also indicate that RRT1 is capable of obtaining the optimal solutions for the small-size tested problems very efficiently.

Keywords

Record-to-record travel Setup time  Total weighted completion time Unrelated parallel machine 

References

  1. Allahverdi, A., Ng, C., Cheng, T., & Kovalyov, M. (2008). A survey of scheduling problems with setup times or costs. European Journal of Operational Research, 187, 985–1032.zbMATHMathSciNetCrossRefGoogle Scholar
  2. 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, 693–701.CrossRefGoogle Scholar
  3. Azizoglu, M., & Kirca, O. (1999). On the minimization of total weighted flow time with identical and uniform parallel machines. European Journal of Operational Research, 113, 91–100.zbMATHCrossRefGoogle Scholar
  4. Azizoglu, M., & Webster, S. (2003). Scheduling parallel machines to minimize weighted flowtime with family set-up times. International Journal of Production Research, 41, 1199–1215.zbMATHCrossRefGoogle Scholar
  5. Barnes, J. W., & Laguna, M. (1993). Solving the multiple-machine weighted flow time problem using tabu search. IIE Transactions, 25, 121–128.CrossRefGoogle Scholar
  6. Brueggemann, T., & Hurink, J. (2011). Matching based very large-scale neighborhoods for parallel machine scheduling. Journal of Heuristics, 17, 637–658.zbMATHCrossRefGoogle Scholar
  7. Brueggemann, T., Hurink, J., & Kern, W. (2006). Quality of move-optimal schedules for minimizing total weighted completion time. Operations Research Letters, 34, 583–590.zbMATHMathSciNetCrossRefGoogle Scholar
  8. Bruno, J., Coffman, E. G, Jr, & Sethi, R. (1974). Scheduling independent tasks to reduce mean finishing time. Communications of the ACM, 17, 382–387.zbMATHMathSciNetCrossRefGoogle Scholar
  9. Chen, J.-F. (2009). Scheduling on unrelated parallel machines with sequence- and machine-dependent setup times and due-date constraints. International Journal of Advanced Manufacturing Technology, 44, 1204–1212.CrossRefGoogle Scholar
  10. Chen, Z.-L., & Powell, W. B. (2003). Exact algorithms for scheduling multiple families of jobs on parallel machines. Naval Research Logistics, 50, 823–840.zbMATHMathSciNetCrossRefGoogle Scholar
  11. Chudak, F. A. (1999). A min-sum 3/2-approximation algorithm for scheduling unrelated parallel machines. Journal of Scheduling, 2, 73–77.zbMATHMathSciNetCrossRefGoogle Scholar
  12. Dueck, G. T. (1993). New optimization heuristics: The great deluge algorithm and the record-to-record travel. Journal Computing Physics, 104, 86–92.zbMATHCrossRefADSGoogle Scholar
  13. Dunstall, S., & Wirth, A. (2005a). A comparison of branch-and-bound algorithms for a family scheduling problem with identical parallel machines. European Journal of Operational Research, 167, 283–296.zbMATHMathSciNetCrossRefGoogle Scholar
  14. Dunstall, S., & Wirth, A. (2005b). Heuristic methods for the identical parallel machine flowtime problem with set-up times. Computers & Operations Research, 32, 2479–2491.zbMATHCrossRefGoogle Scholar
  15. Fleszar, K., Charalambous, C., & Hindi, K. S. (2012). A variable neighborhood descent heuristic for the problem of makespan minimisation on unrelated parallel machines with setup times. Journal of Intelligent Manufacturing, 23, 1849–1958.CrossRefGoogle Scholar
  16. Ho, J. C., Lopez, F. J., Ruiz-Torres, A. J., & Tseng, T.-L. (2011). Minizing total weighted flowtime subject to minimum makespan on two identical parallel machines. Journal of Intelligent Manufacturing, 22, 179–190.CrossRefGoogle Scholar
  17. Horowitz, E., & Sahni, S. (1976). Exact and approximate algorithms for scheduling nonidentical processors. Journal of the Association for Computing Machinery, 23, 317–327.zbMATHMathSciNetCrossRefGoogle Scholar
  18. Kasahara, H., Kai, M., Narita, S., & Wada, H. (1988). Application of DF/IHS to minimum total weighted flow time multiprocessor scheduling problems. Systems and Computers in Japan, 19, 25–34.Google Scholar
  19. Kawaguchi, T., & Kyan, S. (1986). Worst case bound of an LRF for the mean weighted flow time problem. SIAM Journal of Computing, 15, 1119–1129.zbMATHMathSciNetCrossRefGoogle Scholar
  20. Kumar, V., Marathe, M., Parthasarathy, S., & Srinivasan, A. (2009). A unified approach to scheduling on unrelated parallel machines. Journal of the ACM, 56, 1–31.MathSciNetCrossRefGoogle Scholar
  21. Li, K., & Yang, S-l. (2009). Non-identical parallel-machine scheduling research with minimizing total weighted completion times: Models, relaxations and algorithms. Applied Mathematical Modelling, 33, 2145–2158.zbMATHMathSciNetCrossRefGoogle Scholar
  22. Liao, X.-J., Chao, C.-W., & Chen, L.-C. (2012). An improved heuristic for parallel machine weighted flowtime scheduling with family set-up times. Computers and Mathematics with Applications, 63, 110–117.zbMATHMathSciNetCrossRefGoogle Scholar
  23. Lin, Y. K., Pfund, M. E., & Fowler, J. W. (2011). Heuristics for minimizing regular performance measures in unrelated parallel machine scheduling problems. Computers and Operations Research, 38, 901–916.zbMATHMathSciNetCrossRefGoogle Scholar
  24. Pang, K. C. (1995). Algorithmic analysis of the unrelated parallel machines scheduling problem to minimize mean weighted flowtime. International journal of information and management sciences, 6, 47–72.zbMATHGoogle Scholar
  25. Rabadi, G., Moraga, R., & Al-Salem, A. (2006). Heuristics for the unrelated parallel machine scheduling problem with setup times. Journal of Intelligent Manufacturing, 17, 85–97.CrossRefGoogle Scholar
  26. Sahni, S. (1976). Algorithms for scheduling independent tasks. Journal of ACM, 28, 116–127.MathSciNetCrossRefGoogle Scholar
  27. Sarin, S., Ahn, S., & Bishop, A. (1988). An improved scheme for the branch and bound procedure of scheduling n jobs on m parallel machines to minimize total weighted flowtime. International Journal of Production Research, 26, 1183–1191.zbMATHCrossRefGoogle Scholar
  28. Schulz, A. S. (1996). Scheduling to minimize total weighted completion time: Performance guarantees of LP-based heuristics and lower bound. Lecture Notes in Computer Science, 1084, 301.CrossRefGoogle Scholar
  29. Schulz, A. S., & Skutella, M. (2002). Scheduling unrelated machines by randomized rounding. SIAM Journal of Discrete Mathematics, 15, 450–469.zbMATHMathSciNetCrossRefGoogle Scholar
  30. Unlu, Y., & Masson, S. J. (2010). Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems. Computers & Industrial Engineering, 58, 758–800.CrossRefGoogle Scholar
  31. Webster, S. (1993). Bounds and asymptotic results for the uniform parallel processor weighted flow time problem. Operations Research Letters, 14, 85–90.zbMATHMathSciNetCrossRefGoogle Scholar
  32. Webster, S. (1995). Weighted flow time bounds for scheduling identical processors. European Journal of Operational Research, 80, 103–111.zbMATHCrossRefGoogle Scholar
  33. 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.Google Scholar
  34. Woeginger, G. J. (1999) When does a dynamic programming formulation guarantee the existence of an FPTAS. In Proceedings of the SODA (pp. 820–829).Google Scholar
  35. Ying, K.-C., Lee, Z.-J., & Lin, S.-W. (2012). Makespan minimization for scheduling unrelated parallel machines with setup times. Journal of Intelligent Manufacturing, 23, 1795–1803. Google Scholar
  36. Ying, K.-C., & Wang, D.-M. (2003). Soft computing for scheduling with batch setup times and earliness-tardiness penalties on parallel machines. Journal of Intelligent Manufacturing, 14, 311–322.Google Scholar
  37. Zhou, H.-R., Zheng, P.-E., & Wang, H.-L. (2008). Hierarchical genetic algorithm-based parallel machine scheduling for minimization of total weighted completion time. Journal of System Simulation, 20, 3510–3513.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Systems ManagementFeng Chia UniversityTaichungTaiwan, ROC

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