PROGRAMMING UNDER UNCERTAINTY: THE COMPLETE PROBLEM

Abstract

We define the complete problem of a two-stage linear programming under uncertainty, to be: Minimize z(x) = E sub xi ( c x + q(+)y(+) + q(-)y(-)) subject to A x = b; T x + I y(+) + I y(-) = xi x > or = O y(+) > or = y(-) > or = O where x is the first-stage decision variable, the pair (y(+), y(-)) represents the second-stage decision variables. In order to solve this class of problem, we derive a convex programming problem, whose set of optimal solutions is identical to the set of optimal solutions of our original problem. This problem is called the equivalent convex programming. If the random variable xi has a continuous distribution, we give an algorithm to solve the equivalent convex program. Moreover, we derive explicitly the equivalent convex program for a few common distributions.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1964
Accession Number
AD0608990

Entities

People

  • Roger J-B Wets

Organizations

  • Boeing

Tags

Communities of Interest

  • Air Platforms
  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • California
  • Computations
  • Convex Programming
  • Discontinuities
  • Discrete Distribution
  • Distribution Functions
  • Evolutionary Algorithms
  • Heuristic Methods
  • Linear Programming
  • Notation
  • Probability
  • Probability Distributions
  • Random Variables
  • Simplex Method
  • Standards
  • Universities

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Operations Research