Skip to main content
SpringerLink
Log in

Bi-criterion single-machine scheduling and due-window assignment with common flow allowances and resource-dependent processing times

  • General Paper
  • Published:
Journal of the Operational Research Society

Abstract

This paper addresses single-machine scheduling and due-window assignment with common flow allowances and resource-dependent processing times. Due-window assignment with common flow allowances means that each job has a job-dependent due window, the start time and finish time of which are equal to its actual processing time plus individual job-independent parameters shared by all the jobs, respectively. The processing time of each job can be controlled by extra resource allocation as a linear function of the amount of a common continuously divisible resource allocated to the job. Two criteria are considered, where one criterion is an integrated cost consisting of job earliness, weighted number of tardy jobs, and due-window assignment cost, while the other criterion is the resource consumption cost. Four different models are considered for treating the two criteria. It is shown that the problem under the model where the two criteria are integrated into a single criterion is polynomially solvable, while the problems under the other three models are all NP-hard and an optimal solution procedure is developed for them. Two polynomially solvable cases are also identified and investigated. Finally, numerical studies with randomly generated instances are conducted to assess the performance of the proposed algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anger FD, Lee CY and Martin-Vega LA (1986). Single machine scheduling with tight windows. Research Report No. 86-16. Industrial and Systems Engineering Department, University of Florida, Florida.

  • Cheng TCE and Gupta MC (1989). Survey of scheduling research involving due date determination decisions. European Journal of Operational Research 38(2): 156–166.

    Article  Google Scholar 

  • Cheng TCE, Yang SJ and Yang DL (2012). Common due-window assignment and scheduling of linear time-dependent deteriorating jobs and a deteriorating maintenance activity. International Journal of Production Economics 135(1): 154–161.

    Article  Google Scholar 

  • Gerstl E and Mosheiov G (2015). Scheduling with a due-window for acceptable lead-times. Journal of the Operational Research Society 66(9): 1578–1588.

    Article  Google Scholar 

  • Gordon VS, Proth JM and Chu C (2002a). Due date assignment and scheduling: SLK, TWK and other due date assignment models. Production Planning and Control 13(2): 117–132.

    Article  Google Scholar 

  • Gordon VS, Proth JM and Chu C (2002b). A survey of the state-of-the-art of common due date assignment and scheduling research. European Journal of Operational Research 139(1): 1–25.

    Article  Google Scholar 

  • Gordon VS, Strusevich V and Dolgui A (2012). Scheduling with due date assignment under special conditions on job processing. Journal of Scheduling 15(4): 447–456.

    Article  Google Scholar 

  • Graham RL, Lawler EL, Lenstra JK and Rinnooy Kan AHG (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics 5: 287–326.

    Article  Google Scholar 

  • Huang RH, Yang CL and Huang HT (2009). Parallel machine scheduling with common due windows. Journal of the Operational Research Society 61(4): 640–646.

    Article  Google Scholar 

  • Janiak A (1987). One-machine scheduling with allocation of continuously-divisible resource and with no precedence constraints. Kybernetika 23(4): 289–293.

    Google Scholar 

  • Janiak A, Janiak WA, Kovalyov MY, Kozan E and Pesch E (2013). Parallel machine scheduling and common due window assignment with job independent earliness and tardiness costs. Information Sciences 224: 109–117.

    Article  Google Scholar 

  • Janiak A, Janiak WA, TomaszKrysiak T and Kwiatkowski T (2015). A survey on scheduling problems with due windows. European Journal of Operational Research 242(2): 347–357.

    Article  Google Scholar 

  • Janiak A, Kovalyov MY and Marek M (2007). Soft due window assignment and scheduling on parallel machines. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 37(5): 614–620.

    Article  Google Scholar 

  • Ji M, Ge JJ, Chen K and Cheng TCE (2013). Single-machine due-window assignment and scheduling with resource allocation, aging effect, and a deteriorating rate-modifying activity. Computers and Industrial Engineering 66(4): 952–961.

    Article  Google Scholar 

  • Koulamas C, Gupta S and Kyparisis GJ (2010). A unified analysis for the single-machine scheduling problem with controllable and non-controllable variable job processing times. European Journal of Operational Research 205(2): 479–482.

    Article  Google Scholar 

  • Lauff V and Werner F (2004). Scheduling with common due date, earliness and tardiness penalties for multimachine problems: A survey. Mathematical and Computer Modelling 40(5–6): 637–655.

    Article  Google Scholar 

  • Leyvand Y, Shabtay D and Steiner G (2010). Optimal delivery time quotation to minimize total tardiness penalties with controllable processing times. IIE Transactions 42(3): 221–231.

    Article  Google Scholar 

  • Liman SD, Panwalkar SS and Thongmee S (1997). A single machine scheduling problem with common due window and controllable processing times. Annals of Operations Research 70(0): 145–154.

    Article  Google Scholar 

  • Liu J, Wang Y and Min X (2013). Single-machine scheduling with common due-window assignment for deteriorating jobs. Journal of the Operational Research Society 65(2): 291–301.

    Article  Google Scholar 

  • Mosheiov G (2001). A common due-date assignment problem on parallel identical machines. Computers and Operations Research 28(8): 719–732.

    Article  Google Scholar 

  • Mor B and Mosheiov G (2012). Scheduling a maintenance activity and due-window assignment based on common flow allowance. International Journal of Production Economics 135(1): 222–230.

    Article  Google Scholar 

  • Mosheiov G and Oron D (2010). Job dependent due-window assignment based on a common flow allowance. Foundations of Computing and Decision Sciences 35(3): 185–195.

    Google Scholar 

  • Ng CTD, Cheng TCE, Janiak A and Kovalyov MY (2005). Group scheduling with controllable setup and processing times: Minimizing total weighted completion time. Annals of Operations Research 133(1): 163–174.

    Article  Google Scholar 

  • Oron D (2013). Scheduling controllable processing time jobs in a deteriorating environment. Journal of the Operational Research Society 65(11): 49–56.

    Google Scholar 

  • Rudek A and Rudek R (2011). A note on optimization in deteriorating systems using scheduling problems with the aging effect and resource allocation models. Computers and Mathematics with Applications 62(4): 1870–1878.

    Article  Google Scholar 

  • Shabtay D, Bensoussan Y and Kaspi M (2012). A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system. International Journal of Production Economics 136(1): 67–74.

    Article  Google Scholar 

  • Shabtay D and Steiner G (2007). A survey of scheduling with controllable processing times. Discrete Applied Mathematics 155(13): 1643–1666.

    Article  Google Scholar 

  • Shabtay D and Steiner G (2011). A bicriteria approach to minimize the total weighted number of tardy jobs with convex controllable processing times and assignable due dates. Journal of Scheduling 14(5): 455–469.

    Article  Google Scholar 

  • T’kindt V and Billaut JC (2006). Multicriteria Scheduling: Theory, Models and Algorithms. 2nd edn, Springer: Berlin.

    Google Scholar 

  • Wang JB (2006). Single machine common flow allowance scheduling with controllable processing times. Applied Mathematics and Computing 21(1–2): 249–257.

    Google Scholar 

  • Wang JB and Wang JJ (2014). Single machine group scheduling with time dependent processing times and ready times. Information Sciences 275: 226–231.

    Article  Google Scholar 

  • Yang DL, Lai CJ and Yang SJ (2014). Scheduling problems with multiple due windows assignment and controllable processing times on a single machine. International Journal of Production Economics 150: 96–103.

    Article  Google Scholar 

  • Yeung WK, Oguz C and Cheng TCE (2004). Two-stage flowshop earliness and tardiness machine scheduling involving a common due window. International Journal of Production Economics 90(3): 421–434.

    Article  Google Scholar 

  • Yeung WK, Oguz C and Cheng TCE (2009). Two-machine flow shop scheduling with due window to minimize weighted number of early and tardy jobs. Naval Research Logistics 56(7): 593–599.

    Article  Google Scholar 

  • Yin YQ, Cheng TCE, Cheng SR and Wu CC (2013a). Single-machine batch delivery scheduling with an assignable common due date and controllable processing times. Computers and Industrial Engineering 65(2): 652–662.

    Article  Google Scholar 

  • Yin YQ, Cheng TCE, Hsu CJ and Wu CC (2013b). Single-machine batch delivery scheduling with an assignable common due window. Omega 41(2): 216–225.

    Article  Google Scholar 

  • Yin YQ, Cheng TCE, Wu CC and Cheng SR (2013c). Single-machine common due-date scheduling with batch delivery costs and resource-dependent processing times. International Journal of Production Research 51(17): 5083–5099.

    Article  Google Scholar 

  • Yin YQ, Cheng TCE, Wu CC and Cheng SR (2014). Single-machine due window assignment and scheduling with a common flow allowance and controllable job processing times. Journal of the Operational Research Society 65(1): 1–13.

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the Editors-in-Chief, an Associate Editor, and anonymous referees for their helpful comments on earlier versions of this paper. This paper was supported in part by the National Natural Science Foundation of China (Nos. 11561036, 71501024, 71301022); in part by the MOST of Taiwan under grant numbers NSC 102-2221-E-035-070-MY3 and MOST 103-2410-H-035-022-MY2; and Cheng was supported in part by The Hong Kong Polytechnic University under the Fung You King-Wing Hang Bank Endowed Professorship in Business Administration.

Author information

Authors and Affiliations

  1. Kunming University of Science and Technology, Kunming, China

    Yunqiang Yin

  2. Dalian University of Technology, Dalian, China

    Du-Juan Wang

  3. The Hong Kong Polytechnic University, Kowloon, Hong Kong

    T C E Cheng

  4. Feng Chia University, Taichung, Taiwan

    Chin-Chia Wu

Authors
  1. Yunqiang Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Du-Juan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T C E Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chin-Chia Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yin, Y., Wang, DJ., Cheng, T. et al. 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 (2016). https://doi.org/10.1057/jors.2016.14

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/jors.2016.14

Keywords

Search

Navigation