Tools for reformulating logical forms into zero-one mixed integer programs

A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Programming (ILP) formulation or a Mixed Integer Programming (MIP) formulation is presented. A reformulation procedure which uses the extended reverse Polish notation to represent a compound logical form is then described. The syntax of an LP modelling language is extended to incorporate statements in propositional logic forms with linear algebraic forms whereby 0–1 MIP models can be automatically formulated. A prototype user interface by which logical forms can be reformulated and the corresponding MIP constructed and analysed within an existing Mathematical Programming modelling system is illustrated. Finally, the steps to formulate a discrete optimisation model in this way are illustrated by means of an example.