Abstract
In our current fast-paced era, customers are often willing to pay extra premium for shorter lead times, which motivates further research on the scheduling problem with due-date assignment and customer-specified lead times. As part of this effort, we extend the classic minsum ‘DIF’ scheduling model to allow optional job-rejection, thus adding an important component of real-life applications, namely, the possibility that the scheduler decides to process only a subset of the jobs and outsource the disjoint set. The scheduler is penalised for rejecting certain jobs by setting job-dependent rejection costs, and he is limited by a given upper bound on the total rejection cost. The most general version of the minsum DIF problem includes job-dependent cost parameters and lead-times, and it is strongly NP-hard. Therefore, we study six variants of the problem, where either only the cost parameters or the lead-times are job dependent. All alternatives are extended by optional job-rejection that possibly bounds the constraints or the underlying cost functions. We establish that all studied problems are NP-hard in the ordinary sense and present pseudo-polynomial dynamic programming algorithms and extensive numerical studies for most solutions.
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References
Cao, Z.G., Wang, Z., Zhang, Y.Z., Liu, S.P.: On several scheduling problems with rejection or discretely compressible processing times. Lect. Notes Comput. Sci. 3959, 90–98 (2006)
Du, J., Leung, J.Y.T.: Minimizing total tardiness on one machine is NP-hard. Math. Oper. Res. 15, 483–495 (1990)
Gerstl, E., Mor, B., Mosheiov, G.: Minmax scheduling with acceptable lead-times: extensions to position-dependent processing times, due-window and job rejection. Comput. Oper. Res. 83, 150–156 (2017)
Gerstl, E., Mosheiov, G.: Single machine scheduling problems with generalised due-dates and job-rejection. Int. J. Prod. Res. 55, 3164–3172 (2017)
Gerstl, E., Mosheiov, G.: Minmax due-date assignment with a time window for acceptable lead-times. Ann. Oper. Res. 211(1), 167–177 (2013)
Gerstl, E., Mosheiov, G.: Scheduling with a due-window for acceptable lead-times. J. Oper. Res. Soc. 66(9), 1578–1588 (2015)
Kacem, I.: Fully polynomial time approximation scheme for the total weighted tardiness minimization with a common due date. Discret. Appl. Math. 158, 1035–1040 (2010)
Kellerer, H., Strusevich, V.A.: A fully polynomial approximation scheme for the single machine weighted total tardiness problem with a common due date. Theoret. Comput. Sci. 369, 230–238 (2006)
Kianfar, K., Moslehi, G.: A note on “Fully polynomial time approximation scheme for the total weighted tardiness minimization with a common due date.” Discrete Appl. Math. 161, 2205–2206 (2013)
Lawler, E.L.: A “pseudopolynomial” algorithm for sequencing jobs to minimize total tardiness. Ann. Discrete Math. 1, 331–342 (1977)
Leyvand, Y., Shabtay, D., Steiner, G.: A unified approach for scheduling with convex resource consumption functions using positional penalties. Eur. J. Oper. Res. 206, 301–312 (2010)
Mor, B., Mosheiov, G., Shabtay, D.: A note: minmax due-date assignment problem with lead-time cost. Comput. Oper. Res. 40, 2161–2164 (2013)
Mor, B., Shapira, D.: Scheduling with regular performance measures and optional job rejection on a single machine. J. Oper. Res. Soc. 71(8), 1315–1325 (2020)
Mosheiov, G., Pruwer, S.: On the minmax common-due-date problem: extensions to position-dependent processing times, job rejection, learning effect, uniform machines and flowshops. Eng. Optim. 53(3), 408–424 (2021)
Seidmann, A., Panwalkar, S.S., Smith, M.L.: Optimal assignment of due-dates for a single processor scheduling problem. Int. J. Prod. Res. 19, 393–399 (1981)
Shabtay, D.: Scheduling and due date assignment to minimize earliness, tardiness, holding, due date assignment and batch delivery costs. Int. J. Prod. Econ. 123, 235–242 (2010)
Shabtay, D., Gaspar, N., Kaspi, M.: A survey on offline scheduling with rejection. J. Sched. 16, 3–28 (2013)
Shabtay, D., Steiner, G.: Two due-date assignment problems in scheduling a single machine. Oper. Res. Lett. 34, 683–691 (2006)
Shabtay, D., Steiner, G.: The single-machine earliness-tardiness scheduling problem with due-date assignment and resource-dependent processing times. Ann. Oper. Res. 159, 25–40 (2008)
Shabtay, D., Steiner, G.: Optimal due date assignment in multi-machine scheduling environments. J. Sched. 11, 217–228 (2008)
Steiner, G., Zhang, R.: Revised delivery-time quotation in scheduling with tardiness penalties. Oper. Res. 59, 1504–1511 (2011)
Yuan, J.: The NP-hardness of the single machine common due date weighted tardiness problem. Tabriz Univ. Ser. 5, 328–333 (1992)
Zhang, L., Lu, L., Yuan, J.: Single-machine scheduling under the job rejection constraint. Theoret. Comput. Sci. 411, 1877–1882 (2010)
Zhao, C., Yin, Y., Cheng, T.C.E., Wu, C.C.: Single-machine scheduling and due date assignment with rejection and position-dependent processing times. J. Indus. Manag. Optim. 10(3), 691–700 (2014)
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Mor, B., Shapira, D. Minsum scheduling with acceptable lead-times and optional job rejection. Optim Lett 16, 1073–1091 (2022). https://doi.org/10.1007/s11590-021-01763-8
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DOI: https://doi.org/10.1007/s11590-021-01763-8