Abstract
Machine learning exists in many realistic scheduling situations. This study focuses on permutation flow shop scheduling problems, where the actual processing time of a job is defined by a general non-increasing function of its scheduled position, i.e., general position-dependent learning effects. The objective functions are to minimize the total completion time, the makespan, the total weighted completion time, and the total weighted discounted completion time, respectively. To solve these problems, we present approximation algorithms based on the optimal permutations for the corresponding single machine scheduling problems and analyze their worst-case error bound.
Similar content being viewed by others
References
Biskup, D. (2008). A state-of-the-art review on scheduling with learning effects. European Journal of Operational Research, 188, 315–329.
Fagerholt, K., Hvattum, L. M., Johnsen, T. A. V., & Korsvik, J. E. (2013). Routing and scheduling in project shipping. Annals of Operations Research, 207, 67–81.
Gafarov, E. R., Lazarev, A. A., & Werner, F. (2013). Single machine total tardiness maximization problems: complexity and algorithms. Annals of Operations Research, 207, 121–136.
Gerstl, E., & Mosheiov, G. (2012). Scheduling on parallel identical machines with rejection and position-dependent processing times. Information Processing Letters, 112, 743–747.
Graham, R. L., Lawler, E. L., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1979). Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics, 5, 287–326.
Janiak, A., & Rudek, R. (2009). Experience based approach to scheduling problems with the learning effect. IEEE Transactions on Systems, Man and Cybernetics. Part A. Systems and Humans, 39(2), 344–357.
Janiak, A., Janiak, W., Rudek, R., & Wielgus, A. (2009). Solution algorithms for the makespan minimization problem with the general learning model. Computers & Industrial Engineering, 56, 1301–1308.
Janiak, A., Kovalyov, M. Y., & Lichtenstein, M. (2013). Strong NP-hardness of scheduling problems with learning or aging effect. Annals of Operations Research, 206, 577–583.
Kuo, W.-H., Hsu, C.-J., & Yang, D.-L. (2012). Worst-case and numerical analysis of heuristic algorithms for flowshop scheduling problems with a time-dependent learning effect. Information Sciences, 184, 282–297.
Lee, W.-C. (2011). Scheduling with general position-based learning curves. Information Sciences, 181, 5515–5522.
Lee, W.-C., & Wu, C.-C. (2009). Some single-machine and m-machine flowshop scheduling problems with learning considerations. Information Sciences, 179, 3885–3892.
Lee, K., Leung, J. Y.-T., & Pinedo, M. L. (2013). Makespan minimization in online scheduling with machine eligibility. Annals of Operations Research, 204, 189–222.
Li, G., Wang, X.-Y., Wang, J.-B., & Sun, L.-Y. (2013). Worst case analysis of flow shop scheduling problems with a time-dependent learning effect. International Journal of Production Economics, 142, 98–104.
Mencia, C., Sierra, M. R., & Varela, R. (2013). Depth-first heuristic search for the job shop scheduling problem. Annals of Operations Research, 206, 265–296.
Mor, B., & Mosheiov, G. (2011). Total absolute deviation of job completion times on uniform and unrelated machines. Computers & Operations Research, 38, 660–665.
Mosheiov, G. (2011). Proportionate flowshop with general position-dependent processing times. Information Processing Letters, 111, 174–177.
Mosheiov, G., & Oron, D. (2012). Minimizing the number of tardy jobs on a proportionate flowshop with general position-dependent processing times. Computers & Operations Research, 39, 1601–1604.
Pinedo, M. (2002). Scheduling: theory, algorithms and systems. Englewood Cliffs: Prentice Hall.
Rudek, R. (2011). Computational complexity and solution algorithms for flowshop scheduling problems with the learning effect. Computers & Industrial Engineering, 61, 20–31.
Rudek, R. (2012). Scheduling problems with position dependent job processing times: computational complexity results. Annals of Operations Research, 196, 491–516.
Rudek, A., & Rudek, R. (2013). Makespan minimization flowshop with position dependent job processing times—computational complexity and solution algorithms. Computers & Operations Research, 40, 2071–2082.
Shchepin, E. V., & Vakhania, N. (2008). On the geometry, preemptions and complexity of multiprocessor and shop scheduling. Annals of Operations Research, 159, 183–213.
Shen, L., & Wu, Y.-B. (2013). Single machine past-sequence-dependent delivery times scheduling with general position-dependent and time-dependent learning effects. Applied Mathematical Modelling, 37, 5444–5451.
Shen, L., Mönch, L., & Buscher, U. (2013). An iterative approach for the serial batching problem with parallel machines and job families. Annals of Operations Research, 206, 425–448.
Smutnicki, C. (1998). Some results of worst-case analysis for flow shop scheduling. European Journal of Operational Research, 109, 66–87.
Sun, L.-H., Cui, K., Chen, J.-H., Wang, J., & He, X.-C. (2013). Some results of the worst-case analysis for flow shop scheduling with a learning effect. Annals of Operations Research. doi:10.1007/s10479-013-1368-6.
Tanrisever, F., & Kutanoglu, E. (2008). Forming and scheduling jobs with capacitated containers in semiconductor manufacturing: single machine problem. Annals of Operations Research, 159, 5–24.
Wang, J.-B., & Wang, M.-Z. (2011). Worst-case behavior of simple sequencing rules in flow shop scheduling with general position-dependent learning effects. Annals of Operations Research, 191, 155–169.
Wang, J.-B., & Wang, M.-Z. (2012). Worst-case analysis for flow shop scheduling problems with an exponential learning effect. Journal of the Operational Research Society, 63, 130–137.
Wang, J.-B., & Wang, J.-J. (2013). Scheduling jobs with a general learning effect model. Applied Mathematical Modelling, 37, 2364–2373.
Wu, C.-C., & Lee, W.-C. (2009). A note on the total completion time problem in a permutation flowshop with a learning effect. European Journal of Operational Research, 192, 343–347.
Wu, C.-C., Yin, Y., & Cheng, S.-R. (2011). Some single-machine scheduling problems with a truncation learning effect. Computers & Industrial Engineering, 60, 790–795.
Wu, C.-C., Yin, Y., & Cheng, S.-R. (2012a). Single-machine and two-machine flowshop scheduling problems with truncated position-based learning functions. Journal of the Operational Research Society, 64, 147–156.
Wu, C.-C., Yin, Y., Wu, W.-H., & Cheng, S.-R. (2012b). Some polynomial solvable single-machine scheduling problems with a truncation sum-of-processing-times based learning effect. European Journal of Industrial Engineering, 6, 441–453.
Xu, Z., Sun, L., & Gong, J. (2008). Worst-case analysis for flow shop scheduling with a learning effect. International Journal of Production Economics, 113, 748–753.
Xu, K., Feng, Z., & Ke, L. (2011). Single machine scheduling with total tardiness criterion and convex controllable processing times. Annals of Operations Research, 186, 383–391.
Yau, H., & Shi, L. (2009). Nested partitions for the large-scale extended job shop scheduling problem. Annals of Operations Research, 168, 23–39.
Yin, Y., Liu, M., Hao, J., & Zhou, M. (2012). Single-machine scheduling with job-position-dependent learning and time-dependent deterioration. IEEE Transactions on Systems, Man and Cybernetics. Part A. Systems and Humans, 42, 192–200.
Zhang, X., Yan, G., Huang, W., & Tang, G. (2011). Single-machine scheduling problems with time and position dependent processing times. Annals of Operations Research, 186, 345–356.
Acknowledgements
We are grateful to two anonymous referees for their helpful comments on an earlier version of this paper. This research was supported by the open project of The State Key Laboratory for Manufacturing Systems Engineering (Grant no. sklms2012009), the Program for Shanxi Natural science foundation research (Grant no. 2012JQ9006) and the National Natural Science Foundation of China (Grant No. 71272117).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sun, LH., Cui, K., Chen, JH. et al. Research on permutation flow shop scheduling problems with general position-dependent learning effects. Ann Oper Res 211, 473–480 (2013). https://doi.org/10.1007/s10479-013-1481-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-013-1481-6