IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v270y2015icp312-333.html
   My bibliography  Save this article

Non-permutation flow shop scheduling with order acceptance and weighted tardiness

Author

Listed:
  • Xiao, Yiyong
  • Yuan, Yingying
  • Zhang, Ren-Qian
  • Konak, Abdullah

Abstract

This paper studies the non-permutation solution for the problem of flow shop scheduling with order acceptance and weighted tardiness (FSS-OAWT). We formulate the problem as a linear mixed integer programming (LMIP) model that can be optimally solved by AMPL/CPLEX for small-sized problems. In addition, a non-linear integer programming (NIP) model is presented to design heuristic algorithms. A two-phase genetic algorithm (TP-GA) is developed to solve the problem of medium and large sizes based on the NIP model. The properties of FSS-OAWT are investigated and several theorems for permutation and non-permutation optimum are provided. The performance of the TP-GA is studied through rigorous computational experiments using a large number of numeric instances. The LMIP model is used to demonstrate the differences between permutation and non-permutation solutions to the FSS-OAWT problem. The results show that a considerably large portion of the instances have only an optimal non-permutation schedule (e.g., 43.3% for small-sized), and the proposed TP-GA algorithms are effective in solving the FSS-OAWT problems of various scales (small, medium, and large) with both permutation and non-permutation solutions.

Suggested Citation

  • Xiao, Yiyong & Yuan, Yingying & Zhang, Ren-Qian & Konak, Abdullah, 2015. "Non-permutation flow shop scheduling with order acceptance and weighted tardiness," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 312-333.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:312-333
    DOI: 10.1016/j.amc.2015.08.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315010668
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.08.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jianzhong Du & Joseph Y.-T. Leung, 1990. "Minimizing Total Tardiness on One Machine is NP-Hard," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 483-495, August.
    2. M. L. Smith & S. S. Panwalkar & R. A. Dudek, 1975. "Flowshop Sequencing Problem with Ordered Processing Time Matrices," Management Science, INFORMS, vol. 21(5), pages 544-549, January.
    3. Li, Gang & Wang, Xiao-Yuan & Wang, Ji-Bo & Sun, Lin-Yan, 2013. "Worst case analysis of flow shop scheduling problems with a time-dependent learning effect," International Journal of Production Economics, Elsevier, vol. 142(1), pages 98-104.
    4. Pourbabai, Behnam, 1989. "A short term production planning and scheduling model," Engineering Costs and Production Economics, Elsevier, vol. 18(2), pages 159-167, December.
    5. Cheng, T. C. E. & Ding, Q. & Lin, B. M. T., 2004. "A concise survey of scheduling with time-dependent processing times," European Journal of Operational Research, Elsevier, vol. 152(1), pages 1-13, January.
    6. Raaymakers, W. H. M. & Hoogeveen, J. A., 2000. "Scheduling multipurpose batch process industries with no-wait restrictions by simulated annealing," European Journal of Operational Research, Elsevier, vol. 126(1), pages 131-151, October.
    7. De, Prabuddha & Ghosh, Jay B. & Wells, Charles E., 1993. "Job selection and sequencing on a single machine in a random environment," European Journal of Operational Research, Elsevier, vol. 70(3), pages 425-431, November.
    8. Zhang, Yi & Li, Xiaoping & Wang, Qian, 2009. "Hybrid genetic algorithm for permutation flowshop scheduling problems with total flowtime minimization," European Journal of Operational Research, Elsevier, vol. 196(3), pages 869-876, August.
    9. Mehravaran, Yasaman & Logendran, Rasaratnam, 2012. "Non-permutation flowshop scheduling in a supply chain with sequence-dependent setup times," International Journal of Production Economics, Elsevier, vol. 135(2), pages 953-963.
    10. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    11. Sushil K. Gupta & Jerzy Kyparisis & Chi-Ming Ip, 1992. "Note---Project Selection and Sequencing to Maximize Net Present Value of the Total Return," Management Science, INFORMS, vol. 38(5), pages 751-752, May.
    12. Wang, Xiuli & Xie, Xingzi & Cheng, T.C.E., 2013. "Order acceptance and scheduling in a two-machine flowshop," International Journal of Production Economics, Elsevier, vol. 141(1), pages 366-376.
    13. B. J. Lageweg & J. K. Lenstra & A. H. G. Rinnooy Kan, 1978. "A General Bounding Scheme for the Permutation Flow-Shop Problem," Operations Research, INFORMS, vol. 26(1), pages 53-67, February.
    14. Og[breve]uz, Ceyda & Sibel Salman, F. & Bilgintürk YalçIn, Zehra, 2010. "Order acceptance and scheduling decisions in make-to-order systems," International Journal of Production Economics, Elsevier, vol. 125(1), pages 200-211, May.
    15. Koulamas, Christos, 1998. "A new constructive heuristic for the flowshop scheduling problem," European Journal of Operational Research, Elsevier, vol. 105(1), pages 66-71, February.
    16. Sun, Lin-Hui & Sun, Lin-Yan & Wang, Ming-Zheng & Wang, Ji-Bo, 2012. "Flow shop makespan minimization scheduling with deteriorating jobs under dominating machines," International Journal of Production Economics, Elsevier, vol. 138(1), pages 195-200.
    17. Cheng, Yushao & Sun, Shijie, 2009. "Scheduling linear deteriorating jobs with rejection on a single machine," European Journal of Operational Research, Elsevier, vol. 194(1), pages 18-27, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rossit, Daniel Alejandro & Tohmé, Fernando & Frutos, Mariano, 2018. "The Non-Permutation Flow-Shop scheduling problem: A literature review," Omega, Elsevier, vol. 77(C), pages 143-153.
    2. Mohamadreza Dabiri & Mehdi Yazdani & Bahman Naderi & Hassan Haleh, 2022. "Modeling and solution methods for hybrid flow shop scheduling problem with job rejection," Operational Research, Springer, vol. 22(3), pages 2721-2765, July.
    3. Xiao, Yiyong & Zhang, Siyue & Yang, Pei & You, Meng & Huang, Jiaoying, 2019. "A two-stage flow-shop scheme for the multi-satellite observation and data-downlink scheduling problem considering weather uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 263-275.
    4. Chen, Wenchong & Gong, Xuejian & Rahman, Humyun Fuad & Liu, Hongwei & Qi, Ershi, 2021. "Real-time order acceptance and scheduling for data-enabled permutation flow shops: Bilevel interactive optimization with nonlinear integer programming," Omega, Elsevier, vol. 105(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    2. Li, Xin & Ventura, Jose A., 2020. "Exact algorithms for a joint order acceptance and scheduling problem," International Journal of Production Economics, Elsevier, vol. 223(C).
    3. Stanisław Gawiejnowicz, 2020. "A review of four decades of time-dependent scheduling: main results, new topics, and open problems," Journal of Scheduling, Springer, vol. 23(1), pages 3-47, February.
    4. Wang, Xiuli & Cheng, T.C.E., 2015. "A heuristic for scheduling jobs on two identical parallel machines with a machine availability constraint," International Journal of Production Economics, Elsevier, vol. 161(C), pages 74-82.
    5. Wang, Xiuli & Zhu, Qianqian & Cheng, T.C.E., 2015. "Subcontracting price schemes for order acceptance and scheduling," Omega, Elsevier, vol. 54(C), pages 1-10.
    6. Zhong, Xueling & Ou, Jinwen & Wang, Guoqing, 2014. "Order acceptance and scheduling with machine availability constraints," European Journal of Operational Research, Elsevier, vol. 232(3), pages 435-441.
    7. Shi-Sheng Li & Ren-Xia Chen & Qi Feng & Cheng-Wen Jiao, 2019. "Parallel-machine scheduling with job-dependent cumulative deterioration effect and rejection," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 957-971, October.
    8. Ou, Jinwen & Zhong, Xueling & Wang, Guoqing, 2015. "An improved heuristic for parallel machine scheduling with rejection," European Journal of Operational Research, Elsevier, vol. 241(3), pages 653-661.
    9. Jinwen Ou & Xueling Zhong, 2017. "Order acceptance and scheduling with consideration of service level," Annals of Operations Research, Springer, vol. 248(1), pages 429-447, January.
    10. Lei, Deming & Guo, Xiuping, 2015. "A parallel neighborhood search for order acceptance and scheduling in flow shop environment," International Journal of Production Economics, Elsevier, vol. 165(C), pages 12-18.
    11. Esmaeilbeigi, Rasul & Charkhgard, Parisa & Charkhgard, Hadi, 2016. "Order acceptance and scheduling problems in two-machine flow shops: New mixed integer programming formulations," European Journal of Operational Research, Elsevier, vol. 251(2), pages 419-431.
    12. Shih-Hsin Chen & Yeong-Cheng Liou & Yi-Hui Chen & Kun-Ching Wang, 2019. "Order Acceptance and Scheduling Problem with Carbon Emission Reduction and Electricity Tariffs on a Single Machine," Sustainability, MDPI, vol. 11(19), pages 1-16, September.
    13. Koulamas, Christos & Kyparisis, George J., 2023. "A classification of dynamic programming formulations for offline deterministic single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 305(3), pages 999-1017.
    14. Liu, Zhixin & Lu, Liang & Qi, Xiangtong, 2020. "Price quotation for orders with different due dates," International Journal of Production Economics, Elsevier, vol. 220(C).
    15. Wen-Hung Wu & Yunqiang Yin & T C E Cheng & Win-Chin Lin & Juei-Chao Chen & Shin-Yi Luo & Chin-Chia Wu, 2017. "A combined approach for two-agent scheduling with sum-of-processing-times-based learning effect," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(2), pages 111-120, February.
    16. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    17. Li, Shisheng & Ng, C.T. & Cheng, T.C.E. & Yuan, Jinjiang, 2011. "Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 210(3), pages 482-488, May.
    18. Lodree Jr., Emmett J. & Geiger, Christopher D., 2010. "A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration," European Journal of Operational Research, Elsevier, vol. 201(2), pages 644-648, March.
    19. Wang, Xiuli & Xie, Xingzi & Cheng, T.C.E., 2013. "Order acceptance and scheduling in a two-machine flowshop," International Journal of Production Economics, Elsevier, vol. 141(1), pages 366-376.
    20. Xin Chen & Sergey Kovalev & Małgorzata Sterna & Jacek Błażewicz, 2021. "Mirror scheduling problems with early work and late work criteria," Journal of Scheduling, Springer, vol. 24(5), pages 483-487, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:312-333. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.