Abstract
In this paper, we study a planning and scheduling problem for unrelated parallel machines. There are n jobs that have to be assigned and sequenced on m unrelated parallel machines. Each job has a weight that represents the priority of the corresponding customer order, a given due date, and a release date. An Automated Guided Vehicle is used to transport at maximum Load max jobs into a storage space in front of the machines in a given period of time. We consider t max consecutive periods. We are interested in minimizing the total weighted tardiness of the jobs across the periods. This measure is important when we are interested in a good on-time delivery performance. We present an appropriate mixed integer program. To solve this NP-hard problem, we develop a heuristic methodology based on decomposition and variable neighborhood search (VNS). The proposed approaches are assessed using randomly generated problem instances. We compare them with a simple heuristic based on decomposition and list scheduling using the Apparent Tardiness Cost dispatching rule. The results demonstrate that the heuristic approach based on VNS performs comparably to the mixed integer program while having reasonable solution times and outperforms the simple heuristic and a genetic algorithm (GA) from previous research.
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References
Akturk M. S., Ozdemir D.: A new dominance rule to minimize total weighted tardiness with unequal release dates. European Journal of Operational Research 135, 394–412 (2001)
Almeder, C., & Mönch, L. (2009). Variable Neighborhood Search for Parallel Batch Machine Scheduling. In Proceedings of the 8th Metaheuristic International Conference (MIC 2009).
Anghinolfi D., Paolucci M.: Parallel machine total tardiness scheduling with a new hybrid metaheuristic approach. Computers and Operations Research 34, 3471–3490 (2007)
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, accepted for publication.
Blazewicz J., Ecker K. H., Pesch E., Schmidt G., Weglarz J.: Scheduling computer and manufacturing processes (2nd ed.). Springer, Berlin (2001)
Graham R. L., Lawler E. L., Lenstra J. K., &Rinnooy Kan A. H. G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 5, 287–326 (1997)
Habla, C., Mönch, L., Pfund, M., & Fowler, J. W. (2007). A decomposition Heuristic for planning and scheduling of jobs on unrelated parallel machines. In Proceedings of the 3rd Multidisciplinary International Scheduling Conference: Theory and Applications, 112–119.
Hansen P., Mladenovic N.: Variable neighborhood search: Principles and applications. European Journal of Operational Research 130, 449–467 (2001)
Klemmt, A., Weigert, G., Almeder, C., & Mönch, L. (2009). A comparison of MIP-based decomposition techniques and VNS approaches for batch scheduling problems. In Proceedings of the Modeling and Analysis of Semiconductor Manufacturing Conference (MASM) 2009, 1686–1694.
Kreipl S., Pinedo M.: Planning and scheduling in supply chains: An overview of issues in practice. Production and Operations Management 13(1), 77–92 (2004)
Lawler E. L.: A “Pseudopolynomial” time algorithm for sequencing jobs to minimize totalWeighted tardiness. Annals of Discrete Mathematics 1, 331–342 (1977)
Liao C.-J., Cheng C.-C.: A variable neighborhood search for minimizing single machine weighted earliness and tardiness with common due date. Computers and Industrial Engineering 52, 404–413 (2007)
Liaw C.-F., Lin Y.-K., Cheng C.-F., Chen M.: Scheduling unrelated parallel machines to minimize total weighted tardiness. Computers and Operations Research 30, 1777–1789 (2003)
Mehta S. V., Uzsoy R.: Minimizing total tardiness on a batch processing machine with incompatible job families. IIE Transactions 30, 165–178 (1998)
Mladenovic N., Hansen P.: Variable neighborhood search. Computers and Operations Research 24, 1097–1100 (1997)
Mönch L., Balasubramanian H., Fowler J. W., Pfund M. E.: Heuristic scheduling of jobs on parallel batch machines with incompatible job families and unequal ready times. Computers and Operations Research 32, 2731–2750 (2005)
Mönch L., Zimmermann J., Otto P.: Machine learning techniques for scheduling jobs with incompatible families and unequal ready times on parallel batch machines. Journal of Engineering Applications of Artificial Intelligence 19(3), 235–245 (2006)
Ovacik I. M., Uzsoy R.: Decomposition methods for complex factory scheduling problems. Kluwer Academic Publishers, Boston (1997)
Pfund, M. E. (2002). Evaluation of uncertainty on scheduling algorithms in printed wiring board manufacturing, PhD Dissertation, Arizona State University, Department of Industrial Engineering.
Pfund M. E., Fowler J. W., Gupta J. N. D.: A survey of algorithms for single and multi-objective unrelated parallel-machine deterministic scheduling problems. Journal of the Chinese Institute of Industrial Engineers 21(3), 230–241 (2004)
Pinedo M.: Scheduling: Theory, algorithms, and systems (3rd ed.). Prentice Hall, Englewood Cliffs, NJ (2008)
Rabadi G., Moraga R. J., Al-Salem A.: Heuristics for the unrelated parallel machine scheduling problem with setup times. Journal of Intelligent Manufacturing 17(1), 85–97 (2006)
Rocha M. L., Ravetti M. G., Mateus G. R., Pardalos P. M. : Solving parallel machines scheduling problems with Sequence-dependent setup times using variable neighbourhood search. IMA Journal of Management Mathematics 18, 101–115 (2007)
Sevkli, M., & Aydin, M. E. (2006). A variable neighbourhood search algorithm for job shop scheduling problems. In Proceedings EvoCOP 2006, LNCS 3906 (pp. 261–271).
Vepsalainen A., Morton T. E.: Priority rules and lead time estimates for job shop Scheduling with weighted tardiness costs. Management Science 33, 1036–1047 (1987)
Wang X., Tang L.: A population-based variable neighborhood search for the single machine total weighted tardiness problem. Computers and Operations Research 36(6), 2105–2110 (2009)
Yu L., Shih H. M., Pfund M. E., Carlyle W. M., Fowler J. W.: Scheduling of unrelated parallel machines: An application to PWB manufacturing. IIE Transactions 32, 921–931 (2002)
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Bilyk, A., Mönch, L. A variable neighborhood search approach for planning and scheduling of jobs on unrelated parallel machines. J Intell Manuf 23, 1621–1635 (2012). https://doi.org/10.1007/s10845-010-0464-6
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DOI: https://doi.org/10.1007/s10845-010-0464-6