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Generalized average shadow prices and bottlenecks

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  • Alejandro Crema

    (Universidad Central de Venezuela)

Abstract

Usually some of the constraints of a 0-1-Mixed Integer Linear Programming problem correspond to resources and in this paper we suppose that they may be redefined. For the availability of the resources the average shadow price is the maximum price that the decision maker is willing to pay for an additional unit of the package (i.e. a combination) of resources defined by some direction. In this paper we present a generalization of the average shadow price and its relation with bottlenecks including the analysis relative to the coefficients matrix of resource constraints. The generalization presented does not have some limitations of the usual average shadow price. A mathematical programming approach to find the strategy for investment in resources is presented.

Suggested Citation

  • Alejandro Crema, 2018. "Generalized average shadow prices and bottlenecks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(1), pages 99-124, August.
    • Handle: RePEc:spr:mathme:v:88:y:2018:i:1:d:10.1007_s00186-018-0630-8
    DOI: 10.1007/s00186-018-0630-8
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    References listed on IDEAS

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    1. Crema, Alejandro, 1995. "Average shadow price in a mixed integer linear programming problem," European Journal of Operational Research, Elsevier, vol. 85(3), pages 625-635, September.
    2. Zuidwijk, R.A., 2005. "Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs," ERIM Report Series Research in Management ERS-2005-055-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Kim, Sehun & Cho, Seong-cheol, 1988. "A shadow price in integer programming for management decision," European Journal of Operational Research, Elsevier, vol. 37(3), pages 328-335, December.
    4. Jansen, B. & de Jong, J. J. & Roos, C. & Terlaky, T., 1997. "Sensitivity analysis in linear programming: just be careful!," European Journal of Operational Research, Elsevier, vol. 101(1), pages 15-28, August.
    5. Yamada, Takeo & Takeoka, Takahiro, 2009. "An exact algorithm for the fixed-charge multiple knapsack problem," European Journal of Operational Research, Elsevier, vol. 192(2), pages 700-705, January.
    6. Jakob Puchinger & Günther R. Raidl & Ulrich Pferschy, 2010. "The Multidimensional Knapsack Problem: Structure and Algorithms," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 250-265, May.
    7. Chatterjee A K & Mukherjee, Saral, 2006. "Unified Concept of Bottleneck," IIMA Working Papers WP2006-05-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
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