IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v33y2016i05ns021759591650038x.html
   My bibliography  Save this article

Linear Programming Formulation of Idle Times for Single-Server Discrete-Event Simulation Models

Author

Listed:
  • Wai Kin Victor Chan

    (Department of Industrial and Systems Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA)

Abstract

Mathematical programming representations (MPRs) are discrete-event simulation models represented using math programming. In this paper, we first introduce an MPR formulation for single-server queueing systems based on idle times. We use this formulation to conduct a perturbation analysis to study the effect of imposing a constraint on idle times. We apply the formulation to obtain a linear programming-based gradient estimator for idle times. We demonstrate the integration of optimization into MRP and identify properties of the optimal solution to facilitate finding the optimal solution.

Suggested Citation

  • Wai Kin Victor Chan, 2016. "Linear Programming Formulation of Idle Times for Single-Server Discrete-Event Simulation Models," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-17, October.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:05:n:s021759591650038x
    DOI: 10.1142/S021759591650038X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S021759591650038X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S021759591650038X?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. Jie Xu & Si Zhang & Edward Huang & Chun-Hung Chen & Loo Hay Lee & Nurcin Celik, 2016. "MO2TOS: Multi-Fidelity Optimization with Ordinal Transformation and Optimal Sampling," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-26, June.
    2. Stefan Helber & Katja Schimmelpfeng & Raik Stolletz & Svenja Lagershausen, 2011. "Using linear programming to analyze and optimize stochastic flow lines," Annals of Operations Research, Springer, vol. 182(1), pages 193-211, January.
    3. S. Thomas McCormick & Michael L. Pinedo & Scott Shenker & Barry Wolf, 1989. "Sequencing in an Assembly Line with Blocking to Minimize Cycle Time," Operations Research, INFORMS, vol. 37(6), pages 925-935, December.
    4. Rajan Suri & Michael A. Zazanis, 1988. "Perturbation Analysis Gives Strongly Consistent Sensitivity Estimates for the M/G/1 Queue," Management Science, INFORMS, vol. 34(1), pages 39-64, January.
    5. Alfieri, Arianna & Matta, Andrea, 2012. "Mathematical programming formulations for approximate simulation of multistage production systems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 773-783.
    6. Jie Xu & Edward Huang & Chun-Hung Chen & Loo Hay Lee, 2015. "Simulation Optimization: A Review and Exploration in the New Era of Cloud Computing and Big Data," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-34.
    Full references (including those not matched with items on IDEAS)

    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. Jianpei Wen & Hanyu Jiang & Jie Song, 2019. "A Stochastic Queueing Model for Capacity Allocation in the Hierarchical Healthcare Delivery System," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-24, February.
    2. Lingxuan Liu & Leyuan Shi, 2019. "Simulation Optimization on Complex Job Shop Scheduling with Non-Identical Job Sizes," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(05), pages 1-26, October.
    3. Giulia Pedrielli & K. Selcuk Candan & Xilun Chen & Logan Mathesen & Alireza Inanalouganji & Jie Xu & Chun-Hung Chen & Loo Hay Lee, 2019. "Generalized Ordinal Learning Framework (GOLF) for Decision Making with Future Simulated Data," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(06), pages 1-35, December.
    4. Pai Liu & Xi Zhang & Zhongshun Shi & Zewen Huang, 2017. "Simulation Optimization for MRO Systems Operations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(02), pages 1-23, April.
    5. Yu Zhao & Xi Zhang & Zhongshun Shi & Lei He, 2017. "Grain Price Forecasting Using a Hybrid Stochastic Method," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(05), pages 1-24, October.
    6. Khayyati, Siamak & Tan, Barış, 2020. "Data-driven control of a production system by using marking-dependent threshold policy," International Journal of Production Economics, Elsevier, vol. 226(C).
    7. Li, Na & Zhang, Yue & Teng, De & Kong, Nan, 2021. "Pareto optimization for control agreement in patient referral coordination," Omega, Elsevier, vol. 101(C).
    8. Kolb, Oliver & Göttlich, Simone, 2015. "A continuous buffer allocation model using stochastic processes," European Journal of Operational Research, Elsevier, vol. 242(3), pages 865-874.
    9. Robert Cuckler & Kuo-Hao Chang & Liam Y. Hsieh, 2017. "Optimal Parallel Machine Allocation Problem in IC Packaging Using IC-PSO: An Empirical Study," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(06), pages 1-20, December.
    10. Smith, Kate & Palaniswami, M. & Krishnamoorthy, M., 1996. "Traditional heuristic versus Hopfield neural network approaches to a car sequencing problem," European Journal of Operational Research, Elsevier, vol. 93(2), pages 300-316, September.
    11. Shuang Xiao & Guo Li & Yunjing Jia, 2017. "Estimating the Constant Elasticity of Variance Model with Data-Driven Markov Chain Monte Carlo Methods," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(01), pages 1-23, February.
    12. Pempera, Jaroslaw & Smutnicki, Czeslaw, 2018. "Open shop cyclic scheduling," European Journal of Operational Research, Elsevier, vol. 269(2), pages 773-781.
    13. S. Göttlich & S. Kühn & J. A. Schwarz & R. Stolletz, 2016. "Approximations of time-dependent unreliable flow lines with finite buffers," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(3), pages 295-323, June.
    14. M. Hossein Safizadeh, 1990. "Optimization in simulation: Current issues and the future outlook," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(6), pages 807-825, December.
    15. James T. Lin & Chun-Chih Chiu & Edward Huang & Hung-Ming Chen, 2018. "A Multi-Fidelity Model Approach for Simultaneous Scheduling of Machines and Vehicles in Flexible Manufacturing Systems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(01), pages 1-20, February.
    16. Herbon, Avi, 2020. "An approximated solution to the constrained integrated manufacturer-buyer supply problem," Operations Research Perspectives, Elsevier, vol. 7(C).
    17. Kats, Vladimir & Lei, Lei & Levner, Eugene, 2008. "Minimizing the cycle time of multiple-product processing networks with a fixed operation sequence, setups, and time-window constraints," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1196-1211, June.
    18. Ronconi, Débora P. & Henriques, Luís R.S., 2009. "Some heuristic algorithms for total tardiness minimization in a flowshop with blocking," Omega, Elsevier, vol. 37(2), pages 272-281, April.
    19. Smutnicki, Czeslaw & Pempera, Jaroslaw & Bocewicz, Grzegorz & Banaszak, Zbigniew, 2022. "Cyclic flow-shop scheduling with no-wait constraints and missing operations," European Journal of Operational Research, Elsevier, vol. 302(1), pages 39-49.
    20. Jia, Shuai & Li, Chung-Lun & Xu, Zhou, 2020. "A simulation optimization method for deep-sea vessel berth planning and feeder arrival scheduling at a container port," Transportation Research Part B: Methodological, Elsevier, vol. 142(C), pages 174-196.

    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:wsi:apjorx:v:33:y:2016:i:05:n:s021759591650038x. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.