Extending algebraic modelling languages for Stochastic Programming

Abstract

The algebraic modelling languages (AML) 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, as well as chance constrained problems. This design is presented as a stochastic extension of the AMPL language which we call SAMPL.