Abstract
We study scheduling problems on a proportionate flowshop. Three objective functions are considered: minimum makespan, minimum total completion time, and minimum total load. We consider a learning process; thus, the processing time of a job processed later in sequence is reduced. The scheduler has the option of job rejection; i.e., only a subset of the jobs are processed and the rejected jobs are penalized. An upper bound on the total permitted rejection cost is assumed. Since the single-machine versions of these problems were shown to be NP-hard, we focus on the introduction of pseudopolynomial dynamic programming algorithms, indicating that the problems are NP-hard in the ordinary sense. We provide an extensive numerical study verifying that the proposed solution algorithms are very efficient and instances containing up to 80 jobs are solved in no more than 5 ms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agnetis, A., & Mosheiov, G. (2017). Scheduling with job-rejection and position-dependent processing times on proportionate flowshops. Optimization Letters, 11, 885–892.
Azzouz, A., Ennigrou, M., & Ben Said, L. (2018). Scheduling problems under learning effects: Classification and cartography. International Journal of Production Research, 56, 1642–1661.
Biskup, D. (1999). Single-machine scheduling with learning considerations. European Journal of Operational Research, 115, 173–178.
Biskup, D. (2008). A state-of-the-art review on scheduling with learning effects. European Journal of Operational Research, 188, 315–329.
Epstein, E., & Zebedat-Haider, H. (2016). Online scheduling of unit jobs on three machines with rejection: A tight result. Information Processing Letters, 116, 252–255.
Fiszman, S., & Mosheiov, G. (2018). Minimizing total load on a proportionate flowshop with position-dependent processing times and job rejection. Information Processing Letters, 132, 39–43.
Gawiejnowicz, S. (1996). A note on scheduling on a single processor with speed dependent on a number of executed jobs. Information Processing Letters, 57, 297–300.
Gawiejnowicz, S. (2008). Time-dependent scheduling. Berlin: Springer.
Gerstl, E., Mor, B., & Mosheiov, G. (2017). Minmax scheduling with acceptable lead-times: Extensions to position-dependent processing times, due-window and job rejection. Computers & Operations Research, 83, 150–156.
Gerstl, E., & Mosheiov, G. (2017). Single machine scheduling problems with generalised due-dates and job-rejection. International Journal of Production Research, 55, 3164–3172.
Hill, C. W. L. (2016). International business: Competing in the global marketplace (6th ed.). New York: McGraw-Hill.
Mor, B., & Mosheiov, G. (2016). Minimizing maximum cost on a single machine with two competing agents and job rejection. Journal of the Operational Research Society, 67, 1524–1531.
Mor, B., & Mosheiov, G. (2018). A note: Minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection. Annals of Operations Research, 271, 1079–1085.
Mor, B., & Shapira, D. (2018). Improved algorithms for scheduling on proportionate flowshop with job-rejection. Journal of the Operational Research Society. https://doi.org/10.1080/01605682.2018.1506540.
Mor, B., Shapira, D. (2019). Scheduling with regular performance measures and optional job rejection on a single machine. Journal of the Operational Research Society. https://doi.org/10.1080/01605682.2019.1621222.
Mosheiov, G. (2001). Scheduling problems with a learning effect. European Journal of Operational Research, 132, 687–693.
Mosheiov, G., & Strusevich, V. (2017). Determining optimal sizes of bounded batches with rejection via quadratic min-cost flow. Naval Research Logistics, 64, 217–224.
Ou, J., Zhong, X., & Li, C. L. (2016). Faster algorithms for single machine scheduling with release dates and rejection. Information Processing Letters, 116, 503–507.
Ou, J., Zhong, X., & Wang, G. (2015). An improved heuristic for parallel machine scheduling with rejection. European Journal of Operational Research, 241, 653–661.
Shabtay, D., Gaspar, N., & Kaspi, M. (2013). A survey on offline scheduling with rejection. Journal of Scheduling, 16, 3–28.
Shabtay, D., Karhi, S., & Oron, D. (2015). Multipurpose scheduling with rejection and job processing times. Journal of Scheduling, 18, 75–88.
Thevenin, S., Zufferey, N., & Widmer, M. (2015). Metaheuristics for a scheduling problem with rejection and tardiness penalties. Journal of Scheduling, 18, 89–105.
Zhang, L., Lu, L., & Yuan, J. (2010). Single-machine scheduling under the job rejection constraint. Theoretical Computer Science, 411, 1877–1882.
Zhong, X., Pan, Z., & Jiang, D. (2017). Scheduling with release times and rejection on two parallel machines. Journal of Combinatorial Optimization, 33, 934–944.
Acknowledgement
The second author was also supported by the Charles I. Rosen Chair of Management, and by The Recanati Fund of The School of Business Administration, The Hebrew University, Jerusalem, Israel.
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
Mor, B., Mosheiov, G. & Shapira, D. Flowshop scheduling with learning effect and job rejection. J Sched 23, 631–641 (2020). https://doi.org/10.1007/s10951-019-00612-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-019-00612-y