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Extending Algebraic Modelling Languages for Stochastic Programming

Christian Valente(Christian.Valente***at***brunel.ac.uk)
Gautam Mitra(Gautam.Mitra***at***brunel.ac.uk)
Mustapha Sadki(Mustapha.Sadki***at***brunel.ac.uk)
Robert Fourer(4er***at***iems.northwestern.edu)

Abstract: Algebraic modelling languages have gained wide acceptance and use in Mathematical Programming by researchers and practitioners. At a basic level, stochastic programming models can be defined using these languages by constructing their deterministic equivalent. Unfortunately, this leads to very large model data instances. We propose 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 not only to a natural definition of the SP model, the resulting generated instance is also a compact representation of the otherwise large problem data. The proposed constructs enable the formulation of two stage and multistage scenario based recourse problems. The design is presented as a stochastic extension of the AMPL language which we call SAMPL; this in turn is embedded in an environment called SPInE (Stochastic Programming Integrated Environment) which facilitates modelling and investigation of SP problems.

Keywords: stochastic programming, modeling languages; AMPL

Category 1: Stochastic Programming

Category 2: Optimization Software and Modeling Systems (Modeling Languages and Systems )

Category 3: Optimization Software and Modeling Systems (Optimization Software Design Principles )

Citation: Technical report, CARISMA, Brunel University and OptiRisk Systems, Uxbridge, Middlesex, UK; December 2006.

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Entry Submitted: 12/27/2006
Entry Accepted: 01/01/2007
Entry Last Modified: 12/27/2006

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