IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v131y2011i1p383-391.html
   My bibliography  Save this article

Using a mathematical programming model to examine the marginal price of capacitated resources

Author

Listed:
  • Kefeli, Ali
  • Uzsoy, Reha
  • Fathi, Yahya
  • Kay, Michael

Abstract

Accurate information on dual prices of capacitated resources is of interest in a number of applications, such as cost allocation and pricing. To gain insight we focus on the dual prices of capacity and demand in a single-stage single-product production-inventory system, and discuss their interpretation. In particular, we examine the behavior of two different production planning models: a conventional linear programming model and a nonlinear model that captures queuing behavior at resources in an aggregate manner using nonlinear clearing functions. The classical linear programming formulation consistently underestimates the dual price of capacity due to its failure to capture the effects of queuing. The clearing function formulation, in contrast, produces positive dual prices even when utilization is below one and exhibits more realistic behavior, such as holding finished inventory at utilization levels below one.

Suggested Citation

  • Kefeli, Ali & Uzsoy, Reha & Fathi, Yahya & Kay, Michael, 2011. "Using a mathematical programming model to examine the marginal price of capacitated resources," International Journal of Production Economics, Elsevier, vol. 131(1), pages 383-391, May.
    • Handle: RePEc:eee:proeco:v:131:y:2011:i:1:p:383-391
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925-5273(10)00114-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Morton, T.E. & Singh, M., 1988. "Implicit Costs And Prices For Resources With Busy Periods," GSIA Working Papers 88-89-02, Carnegie Mellon University, Tepper School of Business.
    2. Morton, T.E. & Lawrence, S.R. & Rajagopolan, S. & Kekre, S., 1988. "Sched-Star A Price-Based Shop Scheduling Module," GSIA Working Papers 88-89-03, Carnegie Mellon University, Tepper School of Business.
    3. Srinivasan, A. & Carey, M. & Morton, T.E., 1988. "Resource Pricing And Aggregate Scheduling In Manufacturing Systems," GSIA Working Papers 88-89-58, Carnegie Mellon University, Tepper School of Business.
    4. Carson E. Agnew, 1976. "Dynamic Modeling and Control of Congestion-Prone Systems," Operations Research, INFORMS, vol. 24(3), pages 400-419, June.
    5. Mark L. Spearman, 1991. "An Analytic Congestion Model for Closed Production Systems with IFR Processing Times," Management Science, INFORMS, vol. 37(8), pages 1015-1029, August.
    6. Stephen C. Graves, 1986. "A Tactical Planning Model for a Job Shop," Operations Research, INFORMS, vol. 34(4), pages 522-533, August.
    7. Steven T. Hackman & Robert C. Leachman, 1989. "A General Framework for Modeling Production," Management Science, INFORMS, vol. 35(4), pages 478-495, 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. de Sampaio, Raimundo J.B. & Wollmann, Rafael R.G. & Vieira, Paula F.G., 2017. "A flexible production planning for rolling-horizons," International Journal of Production Economics, Elsevier, vol. 190(C), pages 31-36.
    2. Gopalswamy, Karthick & Uzsoy, Reha, 2021. "Conic programming models for production planning with clearing functions: Formulations and duality," European Journal of Operational Research, Elsevier, vol. 292(3), pages 953-966.
    3. Ghadimi, Foad & Aouam, Tarik & Haeussler, Stefan & Uzsoy, Reha, 2022. "Integrated and hierarchical systems for coordinating order acceptance and release planning," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1277-1289.
    4. Aouam, Tarik & Brahimi, Nadjib, 2013. "Integrated production planning and order acceptance under uncertainty: A robust optimization approach," European Journal of Operational Research, Elsevier, vol. 228(3), pages 504-515.

    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. Jakob Asmundsson & Ronald L. Rardin & Can Hulusi Turkseven & Reha Uzsoy, 2009. "Production planning with resources subject to congestion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 142-157, March.
    2. Julia Pahl & Stefan Voß & David Woodruff, 2007. "Production planning with load dependent lead times: an update of research," Annals of Operations Research, Springer, vol. 153(1), pages 297-345, September.
    3. Missbauer, Hubert, 2011. "Order release planning with clearing functions: A queueing-theoretical analysis of the clearing function concept," International Journal of Production Economics, Elsevier, vol. 131(1), pages 399-406, May.
    4. Ghadimi, Foad & Aouam, Tarik & Haeussler, Stefan & Uzsoy, Reha, 2022. "Integrated and hierarchical systems for coordinating order acceptance and release planning," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1277-1289.
    5. Manda, A.B. & Uzsoy, Reha, 2021. "Managing product transitions with learning and congestion effects," International Journal of Production Economics, Elsevier, vol. 239(C).
    6. de Sampaio, Raimundo J.B. & Wollmann, Rafael R.G. & Vieira, Paula F.G., 2017. "A flexible production planning for rolling-horizons," International Journal of Production Economics, Elsevier, vol. 190(C), pages 31-36.
    7. Gopalswamy, Karthick & Uzsoy, Reha, 2021. "Conic programming models for production planning with clearing functions: Formulations and duality," European Journal of Operational Research, Elsevier, vol. 292(3), pages 953-966.
    8. Abhijit Upasani & Reha Uzsoy, 2008. "Incorporating manufacturing lead times in joint production-marketing models: A review and some future directions," Annals of Operations Research, Springer, vol. 161(1), pages 171-188, July.
    9. Aouam, Tarik & Brahimi, Nadjib, 2013. "Integrated production planning and order acceptance under uncertainty: A robust optimization approach," European Journal of Operational Research, Elsevier, vol. 228(3), pages 504-515.
    10. Missbauer, Hubert, 2009. "Models of the transient behaviour of production units to optimize the aggregate material flow," International Journal of Production Economics, Elsevier, vol. 118(2), pages 387-397, April.
    11. Rong Yuan & Stephen C. Graves, 2016. "Setting optimal production lot sizes and planned lead times in a job shop," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6105-6120, October.
    12. A. Mustafin & A. Kantarbayeva, 2022. "Clearing function in the context of the invariant manifold method," Papers 2206.11205, arXiv.org.
    13. Subba Rao, S. & Gunasekaran, A. & Goyal, S. K. & Martikainen, T., 1998. "Waiting line model applications in manufacturing," International Journal of Production Economics, Elsevier, vol. 54(1), pages 1-28, January.
    14. Tardif, Valerie & Maaseidvaag, Lars, 2001. "An adaptive approach to controlling kanban systems," European Journal of Operational Research, Elsevier, vol. 132(2), pages 411-424, July.
    15. Gahm, Christian & Uzunoglu, Aykut & Wahl, Stefan & Ganschinietz, Chantal & Tuma, Axel, 2022. "Applying machine learning for the anticipation of complex nesting solutions in hierarchical production planning," European Journal of Operational Research, Elsevier, vol. 296(3), pages 819-836.
    16. Peter J. H. Hulshof & Martijn R. K. Mes & Richard J. Boucherie & Erwin W. Hans, 2016. "Patient admission planning using Approximate Dynamic Programming," Flexible Services and Manufacturing Journal, Springer, vol. 28(1), pages 30-61, June.
    17. Craig A. Tovey, 2002. "Tutorial on Computational Complexity," Interfaces, INFORMS, vol. 32(3), pages 30-61, June.
    18. Cherchye, Laurens & De Rock, Bram & Kerstens, Pieter Jan, 2018. "Production with storable and durable inputs: Nonparametric analysis of intertemporal efficiency," European Journal of Operational Research, Elsevier, vol. 270(2), pages 498-513.
    19. S. David Wu & Eui-Seok Byeon & Robert H. Storer, 1999. "A Graph-Theoretic Decomposition of the Job Shop Scheduling Problem to Achieve Scheduling Robustness," Operations Research, INFORMS, vol. 47(1), pages 113-124, February.
    20. Delasay, Mohammad & Ingolfsson, Armann & Kolfal, Bora & Schultz, Kenneth, 2019. "Load effect on service times," European Journal of Operational Research, Elsevier, vol. 279(3), pages 673-686.

    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:proeco:v:131:y:2011:i:1:p:383-391. 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: http://www.elsevier.com/locate/ijpe .

    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.