The recursive definition of stochastic linear programming problems within an algebraic modeling language

Many optimization problems can be expressed naturally in a recursive manner. Problems with a dynamic structure are commonly expressed in this way especially when they are to be solved by dynamic programming. Many stochastic linear programming problems have an underlying Markov structure, and for these a recursive definition is natural. Real-world examples of such problems are often so large that it is not practical to solve them without a modeling language. No existing algebraic modeling language provides a natural way of specifying a model using a dynamic programming recurrence. This paper describes the advantages of recursive model definition for stochastic linear programming problems, and presents the language constructs necessary to implement this within an algebraic modeling language.