Extending algebraic modelling languages for stochastic programming

Christian Valente*, Gautam Mitra, Mustapha Sadki, Robert Fourer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

Abstract

Algebraic modelling languages have gained wide acceptance and use by researchers and practitioners in mathematical programming. At a basic level, these languages can define stochastic programming (SP) models by constructing their deterministic equivalents. Unfortunately, this leads to very large model data instances. We propose instead a direct approach in which the random values of the model coefficients and the stage structure of the decision variables and constraints are "overlaid" on the underlying deterministic (core) model of the SP problems. This leads to a natural definition of the SP model, while the resulting generated instance is also a compact representation of the otherwise large problem data. As an example of the workability of our approach, we describe the design of a stochastic extension for the AMPL language that enables the formulation of twostage and multistage scenario-based recourse problems. This extended language, which we call SAMPL, is in turn embedded in a stochastic programming integrated environment that facilitates modelling and investigation of SP problems.

Original languageEnglish (US)
Pages (from-to)107-122
Number of pages16
JournalINFORMS Journal on Computing
Volume21
Issue number1
DOIs
StatePublished - Jan 2009

Keywords

  • Algebraic modelling language
  • Decomposition methods
  • Multistage recourse problem
  • SMPS
  • Scenario tree
  • Stochastic programming
  • Two-stage recourse problem

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Computer Science Applications
  • Management Science and Operations Research

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