Abstract
This paper studies single machine scheduling with batch deliveries, where a common due window for all jobs has to be determined, not given in advance. The objective is to minimize the overall cost for the process and delivery. Concretely, it includes the penalty of a job being early or tardy, the cost for holding and delivering a job, and the cost incurred by a late starting or a long duration of the common due window. Observing the NP-hardness, we provide an optimal algorithm of the problem and convert it to a fully polynomial time approximation scheme for a special case.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Assarzadegan P, Rasti-Barzoki M (2016) Minimizing sum of the due date assignment costs, maximum tardiness and distribution costs in a supply chain scheduling problem. Appl Soft Comput 47:343–356
Chen ZL (1996) Scheduling and common due date assignment with earliness-tardiness penalties and batch delivery costs. Eur J Oper Res 93:49–60
Cheng TCE (1988) Optimal common due-date with limited completion time deviation. Comput Oper Res 15:91–96
Cheng TCE, Yang SJ, Yang DL (2012) Common due window assignment and scheduling of linear time-dependent deteriorating jobs and a deteriorating maintenance activity. Int J Prod Econ 135:154–161
Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 4:287–326
Hermann JW, Lee CY (1993) On scheduling to minimize earliness-tardiness and batch delivery costs with a common due date. Eur J Oper Res 70:272–288
Liman SD, Rawaswamy S (1994) Earliness-tardiness scheduling problems with a common delivery window. Oper Res Lett 15:195–203
Liman SD, Rawaswamy S, Thongmee S (1996) Determination of common due window location in a single machine scheduling problem. Eur J Oper Res 93:68–74
Liman SD, Rawaswamy S, Thongmee S (1998) Common due window size and location determination in a single machine scheduling problem. J Oper Res Soc 49:1007–1010
Mor B, Mosheiov G (2017) A two-agent single machine scheduling problem with due-window assignment and a common flow-allowance. J Combin Optim 33:1454–1468
Mosheiov G, Sarig A (2008) A due window assignment problem with position-dependent processing times. J Oper Res Soc 59:997–1003
Mosheiov G, Sarig A (2009) Scheduling a maintenance activity and due window assignment on a single machine. Comput Oper Res 36:2541–2545
Selvarajah E, Steiner G (2009) Approximation algorithms for the suppliers supply chain scheduling problem to minimize delivery and inventory holding costs. Oper Res 57:426–438
Selvarajah E, Zhang R (2014) Supply chain scheduling to minimize holding costs with outsourcing. Ann Oper Res 217:479–490
Yang SJ, Yang DL, Cheng TCE (2010) Single-machine due window assignment and scheduling with job-dependent aging effects and deteriorating maintenance. Comput Oper Res 37:1510–1514
Yeung WK, Oguz C, Cheng TCE (2001) Minimizing weighed number of early and tardy jobs with a common due window involving location penalty. Ann Oper Res 108:33–54
Yeung WK, Oguz C, Cheng TCE (2004) Two-stage flow shop earliness and tardiness machine scheduling involving a common due window. Int J Prod Econ 90:421–434
Yeung WK, Oguz C, Cheng TCE (2009) Two-machine flow shop scheduling with due window to minimize weighted number of early and tardy jobs. Nav Res Logist 56:593–599
Yeung WK, Choi TM, Cheng TCE (2010) Optimal scheduling of a single-supplier single-manufacturer supply chain with common due windows. IEEE Trans Autom Control 55:2767–2777
Yin Y, Cheng T, Xu D, Wu C (2012) Common due date assignment and scheduling with a rate-modifying activity to minimize the due date, earliness, tardiness, holding, and batch delivery cost. Comput Ind Eng 63:223–234
Yin Y, Cheng T, Hsu C, Wu C (2013a) Single-machine batch delivery scheduling with an assignable common due window. Omega 41:216–225
Yin Y, Cheng T, Wang J, Wu C (2013b) Single-machine common due window assignment and scheduling to minimize the total cost. Discrete Optim 10:42–53
Yin Y, Wang D, Cheng T, Wu C (2016a) Bi-criterion single-machine scheduling and due-window assignment with common flow allowances and resource-dependent processing times. J Oper Res Soc 67:1169–1183
Yin Y, Wang D, Cheng T, Wang D, Wu C (2016b) Two-agent single-machine scheduling to minimize the batch delivery cost. Comput Ind Eng 92:16–30
Zhang L (2017) Two-stage supply chain scheduling with a limited holding time. Oper Res Trans 21:126–134 (in Chinese)
Zhang L, Zhang Y, Bai Q (2019) Two-stage medical supply chain scheduling with an assignable common due window and shelf life. J Combin Optim 37:319–329
Acknowledgements
Dedicated to Professor Minyi Yue on the Occasion of His \(100^{th}\) Birthday. This work was supported by the National Science Foundation of China under Grants 11771251 and 71771138, Special Foundation for Taishan Scholars of Shandong Province, China under Grant tsqn201812061, and Science and Technology Research Program for Higher Education of Shandong Province, China under Grant 2019KJI006.
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
Zhang, L., Zhang, Y. & Bai, Q. An approximation algorithm for a supply-chain scheduling problem with an assignable common due window and holding time. J Comb Optim 44, 2167–2179 (2022). https://doi.org/10.1007/s10878-020-00594-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-020-00594-0