Abstract
In this paper we focus on an unrelated parallel workgroup scheduling problem where each workgroup is composed of a number of personnel with similar work skills which has eligibility and human resource constraints. The most difference from the general unrelated parallel machine scheduling with resource constraints is that one workgroup can process multiple jobs at a time as long as the resources are available, which means that a feasible scheduling scheme is impossible to get if we consider the processing sequence of jobs only in time dimension. We construct this problem as an integer programming model with the objective of minimizing makespan. As it is incapable to get the optimal solution in the acceptable time for the presented model by exact algorithm, meta-heuristic is considered to design. A pure genetic algorithm based on special coding design is proposed firstly. Then a hybrid genetic algorithm based on bin packing strategy is further developed by the consideration of transforming the single workgroup scheduling to a strip-packing problem. Finally, the proposed algorithms, together with exact approach, are tested at different size of instances. Results demonstrate that the proposed hybrid genetic algorithm shows the effective performance.
Similar content being viewed by others
References
Afzalirad, M., & Shafipour, M. (2018). Design of an efficient genetic algorithm for resource-constrained unrelated parallel machine scheduling problem with machine eligibility restrictions. Journal of Intelligent Manufacturing, 29(2), 423–437. https://doi.org/10.1007/s10845-015-1117-6.
Akyol Ozer, E., & Sarac, T. (2019). MIP models and a matheuristic algorithm for an identical parallel machine scheduling problem under multiple copies of shared resources constraints. TOP, 27(1), 94–124. https://doi.org/10.1007/s11750-018-00494-x.
Blazewicz, J. (1981). Solving the resource constrained deadline scheduling problem via reduction to the network flow problem. European Journal of Operational Research, 6(1), 75–79. https://doi.org/10.1016/0377-2217(81)90331-3.
Burke, E., Hellier, R., Kendall, G., & Whitwell, G. (2006). A new bottom-left-fill heuristic algorithm for the two—dimensional irregular packing problem. Operations Research, 54(3), 587–601. https://doi.org/10.1287/opre.1060.0293.
Chen, L., Ye, D., & Zhang, G. (2018). Parallel machine scheduling with speed-up resources. European Journal of Operational Research, 268(1), 101–112. https://doi.org/10.1016/j.ejor.2018.01.037.
Cox, D. R., & Quenouille, M. H. (1953). The design and analysis of experiment. Biometrika, 40(3/4), 471–472.
Edis, E. B., Oguz, C., & Ozkarahan, I. (2012). Solution approaches for simultaneous scheduling of jobs and operators on parallel machines. Journal of the Faculty of Engineering and Architecture of Gazi University, 27(3), 527–535.
Edis, E. B., Oguz, C., & Ozkarahan, I. (2013). Parallel machine scheduling with additional resources: Notation, classification, models and solution methods. European Journal of Operational Research, 230(3), 449–463. https://doi.org/10.1016/j.ejor.2013.02.042.
Fanjul-Peyro, L., Perea, F., & Ruiz, R. (2017). Models and matheuristics for the unrelated parallel machine scheduling problem with additional resources. European Journal of Operational Research, 260(2), 482–493. https://doi.org/10.1016/j.ejor.2017.01.002.
Fu, Y., Jiang, G., Tian, G., & Wang, Z. (2019). Job scheduling and resource allocation in parallel-machine system via a hybrid nested partition method. IEEJ Transactions on Electrical and Electronic Engineering, 14(4), 597–604. https://doi.org/10.1002/tee.22842.
Gyorgyi, P. (2017). A PTAS for a resource scheduling problem with arbitrary number of parallel machines. Operations Research Letters, 45(6), 604–609. https://doi.org/10.1016/j.orl.2017.09.007.
Holland, & John, H. (1973). Genetic algorithms and the optimal allocation of trials. SIAM Journal on Computing, 2(2), 88–105. https://doi.org/10.1137/0202009.
Jin, J., & Ji, P. (2017). Scheduling jobs with resource-dependent ready times and processing times depending on their starting times and positions. The Computer Journal, 61(9), 1323–1328. https://doi.org/10.1093/comjnl/bxx120.
Lann, A., & Mosheiov, G. (2003). A note on the maximum number of on-time jobs on parallel identical machines. Computers and Operations Research, 30(11), 1745–1749. https://doi.org/10.1016/S0305-0548(02)00084-9.
Lee, W. C., Chuang, M. C., & Yeh, W. C. (2012). Uniform parallel-machine scheduling to minimize makespan with position-based learning curves. Computers and Industrial Engineering, 63(4), 813–818. https://doi.org/10.1016/j.cie.2012.05.003.
Lenstra, J. K., Rinnooy Kan, A. H. G., & Brucker, P. (1977). Complexity of machine scheduling problems. Annals of Discrete Mathematics, 1(4), 343–362. https://doi.org/10.1016/S0167-5060(08)70743-X.
Liang, X., Zhou, S., Chen, H., & Xu, R. (2019). Pseudo transformation mechanism between resource allocation and bin-packing in batching environments. Future Generation Computer Systems., 95, 79–88. https://doi.org/10.1016/j.future.2019.01.006.
McNaughton, R. (1959). Scheduling with deadlines and loss functions. Management Science, 6(1), 210.
Mokotoff, E., & Chrétienne, P. (2002). A cutting plane algorithm for the unrelated parallel machine scheduling problem. European Journal of Operational Research, 141(3), 515–525. https://doi.org/10.1016/S0377-2217(01)00270-3.
Peng, B. T., & Zhou, Y. W. (2012). Recursive heuristic algorithm for the 2D rectangular strip packing problem. Journal of Software, 23(10), 2600–2611. https://doi.org/10.3724/SP.J.1001.2012.04187. (In Chinese).
Pinedo, M. L. (2016). Scheduling: Theory, algorithms and systems (5th ed.). New York, USA: Springer. https://doi.org/10.1007/978-3-319-26580-3.
Ruiz, R., & Maroto, C. (2006). A genetic algorithm for hybrid flow shops with sequence dependent setup times and machine eligibility. European Journal of Operational Research, 169(3), 781–800. https://doi.org/10.1016/j.ejor.2004.06.038.
Slowinski, R. (1980). Two approaches to problems of resource allocation among project activities—a comparative study. Journal of the Operational Research Society, 31(8), 711–723. https://doi.org/10.1057/jors.1980.134.
Ta, Q. C., Billaut, J.-C., & Bouquard, J.-L. (2015). Matheuristic algorithms for minimizing total tardiness in the m-machine flow-shop scheduling problem. Journal of Intelligent Manufacturing, 29(3), 617–628. https://doi.org/10.1007/s10845-015-1046-4.
Ventura, J. A., & Kim, D. (2000). Parallel machine scheduling about an unrestricted due date and additional resource constraints. IIE Transactions, 32(2), 147–153. https://doi.org/10.1023/a:1007662314880.
Wang, Z., Xiao, C., Lin, X., & Lu, Y. (2017). Single machine total absolute differences penalties minimization scheduling with a deteriorating and resource-dependent maintenance activity. The Computer Journal, 61(1), 105–110. https://doi.org/10.1093/comjnl/bxx044.
Acknowledgements
This work was supported by National Natural Science Foundation of China under Grant 71671090 and 71871117, Joint research project of National Natural Science Foundation of China and Royal Society of UK under Grant of 71811530338, the Fundamental Research Funds for the Central Universities under Grant NP2018466 and Qinglan Project for excellent youth or middle-aged academic leaders in Jiangsu Province (China).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Su, B., Xie, N. & Yang, Y. Hybrid genetic algorithm based on bin packing strategy for the unrelated parallel workgroup scheduling problem. J Intell Manuf 32, 957–969 (2021). https://doi.org/10.1007/s10845-020-01597-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10845-020-01597-8