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The Probability Distribution Function of the Optimum of a 0-1 Linear Program with Randomly Distributed Coefficients of the Objective Function and the Right-Hand Side

Author

Listed:
  • H.-J. Zimmermann

    (Technische Hochschule Aachen, Aachen, West Germany)

  • M. A. Pollatschek

    (Technion—Israel Institute of Technology, Haifa, Israel)

Abstract

This paper proposes and discusses exact and approximate methods for solving the distribution problem of a linear 0-1 program with stochastic b and c . It shows that, in decision-making situations, severe errors can arise when mathematical expectations are substituted for the stochastic coefficients and the problem is treated as a deterministic one. Thus, a knowledge of the distribution function of the optimal value of the objective function as a function of the distributions of the coefficients—or close bounds on it—is a genuine help for the decision maker in situations of risk or uncertainty.

Suggested Citation

  • H.-J. Zimmermann & M. A. Pollatschek, 1975. "The Probability Distribution Function of the Optimum of a 0-1 Linear Program with Randomly Distributed Coefficients of the Objective Function and the Right-Hand Side," Operations Research, INFORMS, vol. 23(1), pages 137-149, February.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:1:p:137-149
    DOI: 10.1287/opre.23.1.137
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    Cited by:

    1. Huang, G. H. & Baetz, B. W. & Patry, G. G., 1995. "Grey fuzzy integer programming: An application to regional waste management planning under uncertainty," Socio-Economic Planning Sciences, Elsevier, vol. 29(1), pages 17-38, March.
    2. Huang, Guo H. & Baetz, Brian W. & Patry, Gilles G., 1995. "Grey integer programming: An application to waste management planning under uncertainty," European Journal of Operational Research, Elsevier, vol. 83(3), pages 594-620, June.

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