Logical representation of integer programming models

Abstract

From the formulation point of view, the Integer Programming (IP) formulation is no more than indicating some decision variables in a Linear Programming model to integer variables. Nevertheless, the interpretation as well as formulation of the IP model is not an easy task at all, because the model has implicit logical meanings in some of the variables and constraints. To explicitly represent the formulation of an integer programming model, eleven logical operators are identified. So the model formulated at this level is called the Logical Integer Programming model. To formalize the transformation process of the model to the solvable conventional integer programming model (called Base Level Integer Programming model), a series of theorems are derived. This approach is implemented on the system UNIK-IP. UNIK-IP opens a single threaded interface of optimization models with the rule based systems which imply the AND/OR relationships.