ON STOCHASTIC LINEAR PROGRAMMING

Abstract

The general linear programming problem is considered in which the coefficients of the objective function to be maximized are assumed to be random variables with a known multinormal distribution. Three deterministic reformulations involve maximizing the expected value, the alpha-fractile (alpha fixed, 0 < alpha < 1/2), and the probability of exceeding a predetermined level of payoff, respectively. In this paper the author's previous work on 'bi- criterion programs' is applied to derive an algorithm for routinely and efficiently solving the second and third reformulations. A by-product of the calculations in each case is the tradeoff-curve between the criterion being maximized and expected payoff. The intimate relationships between all three reformulations are illuminated.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1966
Accession Number
AD0638852

Entities

People

  • Arthur M. Geoffrion

Organizations

  • University of California, Los Angeles

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Classification
  • Computer Programming
  • Contractors
  • Distribution Functions
  • Evolutionary Algorithms
  • Governments
  • Heuristic Methods
  • Inequalities
  • Linear Programming
  • Mathematical Programming
  • Normal Distribution
  • Parametric Programming
  • Probability
  • Quadratic Programming
  • Theorems
  • United States Government

Readers

  • Statistical inference.
  • Systems Analysis and Design