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Multi-Objective Stochastic Linear Programming with General form of Distributions

Vincent Charles (vcharles***at***pucp.edu.pe)
S.I. Ansari(saiful.islam.ansari***at***gmail.com)
M.M Khalid(v.chals***at***gmail.com)

Abstract: Probabilistic or Stochastic programming is a framework for modeling optimization problems that involve uncertainty. The basic idea used in solving stochastic optimization problems has so far been to convert a stochastic model into an equivalent deterministic model and is possible when the right hand side resource vector follows some specific distributions such as normal, lognormal and exponential distributions. In this paper, a multi-objective stochastic programming problem has been considered with right hand side resource vector following general form of distributions, which include many distributions such as Power Function distribution, Pareto distribution, Beta distribution of first kind, Weibull distribution, and Burr type XII distribution. In this approach, the multi-objective stochastic programming problem is converted into an equivalent deterministic model, which is then solved by a multi-objective programming genetic algorithm using Matlab. Few numerical examples are presented to illustrate the proposed approach.

Keywords: Multi-objective stochastic programming; Deterministic equivalence; General form of distributions; Joint constraints

Category 1: Stochastic Programming

Citation: Working paper 01011209: CENTRUM Católica, Pontificia Universidad Católica del Perú, Santiago de Surco, Peru.

Download: [PDF]

Entry Submitted: 11/01/2009
Entry Accepted: 11/02/2009
Entry Last Modified: 11/01/2009

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