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How to Analyze the Results of Linear Programs—Part 2: Price Interpretation

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  • Harvey J. Greenberg

    (Mathematics Department, University of Colorado at Denver, PO Box 173364, Denver, Colorado 80217-3364)

Abstract

In the second part of a four-part series, I consider an exercise in analysis that arises in many applications: Why is the price of 〈 some commodity 〉 equal to 〈 whatever its solution value 〉? The ability to interpret dual prices in a linear programming solution is part of economic analysis, and the mathematical basis is as old as linear programming, itself. New approaches, however, go beyond the usual duality arguments in answering this question in more practical terms. One of these new approaches is path tracing, which seeks a portion of the linear program that accounts for the row's price by activity costs from sources to the row. In some cases this is a simple path in a network problem. More generally, in ordinary network terms, it can be a tree or involve embedded cycles, but it is regarded as a path in hypergraph terms.

Suggested Citation

  • Harvey J. Greenberg, 1993. "How to Analyze the Results of Linear Programs—Part 2: Price Interpretation," Interfaces, INFORMS, vol. 23(5), pages 97-114, October.
    • Handle: RePEc:inm:orinte:v:23:y:1993:i:5:p:97-114
    DOI: 10.1287/inte.23.5.97
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    Cited by:

    1. Murphy, Frederic H. & Mudrageda, Murthy & Soyster, Allen L. & Saric, Andrija T. & Stankovic, Aleksandar M., 2010. "The effect of contingency analysis on the nodal prices in the day-ahead market," Energy Policy, Elsevier, vol. 38(1), pages 141-150, January.
    2. Yilmaz, Hasan Ümitcan & Kimbrough, Steven O. & van Dinther, Clemens & Keles, Dogan, 2022. "Power-to-gas: Decarbonization of the European electricity system with synthetic methane," Applied Energy, Elsevier, vol. 323(C).
    3. Murthy Mudrageda & Frederic H. Murphy, 2008. "OR PRACTICE---An Economic Equilibrium Model of the Market for Marine Transportation Services in Petroleum Products," Operations Research, INFORMS, vol. 56(2), pages 278-285, April.
    4. Richard E. Wendell, 2004. "Tolerance Sensitivity and Optimality Bounds in Linear Programming," Management Science, INFORMS, vol. 50(6), pages 797-803, June.
    5. Zornig, Peter & Gal, Tomas, 1996. "On the connectedness of optimum-degeneracy graphs," European Journal of Operational Research, Elsevier, vol. 95(1), pages 155-166, November.

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    Keywords

    programming: linear;

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