Two-Stage Linear Recourse Problems under Non-Probabilistic Uncertainty
In this paper, we apply two-stage recourse programming approach to linear programming problems with uncertain parameters. It is assumed that the set of possible realizations of parameters are known as a polytope. A two-stage recourse problem is formulated in the pessimistic viewpoint. It is shown that this problem is a convex programming problem with respect to the first stage variable vector and a large-scale linear programming problem when all vertices of the polytope representing possible realizations of uncertain parameters are given. A solution algorithm based on a relaxation procedure is proposed. Generally, we need to solve max-min problems or bilinear programming problems during the solution process. Some special cases are discussed in order to solve the max-min problems efficiently.
KeywordsFeasible Solution Programming Problem Linear Programming Problem Uncertain Parameter Convex Programming Problem
Unable to display preview. Download preview PDF.
- 5.Tanaka, H., Guo, P. (1999) Possibilistic Data Analysis for Operations Research. Physica-Verlag, HeidelbergGoogle Scholar
- 7.Inuiguchi, M., Tanino, T. (2000) Portfolio selection under independent possibilistic information. Fuzzy Sets and Systems (to appear)Google Scholar
- 10.Inuiguchi, M. (1992) Stochastic programming problems versus fuzzy mathematical programming problems. Japanese Journal of Fuzzy Theory and Systems 4 (1) 97–109Google Scholar
- 12.Itoh, T., Ishii, H. (1997) Fuzzy two-stage problem by possibility measure. Math-ematica Japonica 46: 279–288Google Scholar
- 13.Dubois D. (1987) Linear programming with fuzzy data, in: Bezdek, J. C. (Ed.), Analysis of Fuzzy Information, Vol. III: Applications in Engineering and Science, CRC Press, Boca Raton, FL, 241–263.Google Scholar
- 16.Stancu-Minasian, I. M. (1984) Stochastic Programming with Multiple Objective Functions, D. Reidel Publishing Company, DordrechtGoogle Scholar
- 17.Birge, J. R., Louveaux, F. (1997) Introduction to Stochastic Programming, Springer-Verlag, New YorkGoogle Scholar
- 19.Horst, R., Tuy, H. (1995) Global Optimization: Deterministic Approaches, Third, Revised and Enlarged Edition, Springer-Verlag, BerlinGoogle Scholar
- 20.Lasdon, L. S. (1970) Optimization Theory for Large Systems, The Macmillan Company, New YorkGoogle Scholar