Programming Under Probabilistic Constraint with Discrete Random Variable
The most important static stochastic programming models, that can be formulated in connection with a linear programming problem, where some of the right-hand side values are random variables, are: the simple recourse model, the probabilistic constrained model and the combination of the two. In this paper we present algorithmic solution to the second and third models under the assumption that the random variables have a discrete joint distribution. The solution method uses the concept of a p-level efficient point (pLEP) intoduced by the first author (1990) and works in such a way that first all pLEP’s are enumerated, then a cutting plane method does the rest of the job.
KeywordsProbability Distribution Function Probabilistic Constraint Discrete Random Variable Dual Method Efficient Point
Unable to display preview. Download preview PDF.
- 1.Fiedler, O., A. Prékopa, and Cs. Fábián (1995). “On a Dual Method for a Specially Structured Linear Programming Problem”, RUTCOR Research Report, 25–95.Google Scholar
- 2.Prékopa, A. (1995). “Stochastic Programming”, Kluwer Scientific Publishers, Boston.Google Scholar
- 6.Prékopa A., B. Vizvári, T. Badics (1994) “Programming Under Probabilistic Constraint with Discrete Random Variables”, RUTCOR, Rutgers University, Research Report, RRR 10–96.Google Scholar
- 7.Rockafellar, R. T. (1972). “Convex Analysis”, Princeton University Press, Princeton, N.J.Google Scholar
- 9.Vizvári, B. (1987). “Beitrwge zum Frobenius Problem”, Dr. Sc. Nat. Dissertation, Technische Hochschule “Carl Schorlemmer”, Leuna-Merseburg, Germany.Google Scholar