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

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  • 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
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    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.

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