Transformation of propositional calculus statements into integer and mixed integer programs: An approach towards automatic reformulation

Abstract : 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) respectively is presented. An ILP stated as a system of linear constraints involving integer variables and an objective function, provides a powerful representation of decision problems through a tightly interrelated closed system of choices. It supports direct representation of logical (Boolean or propositional calculus) expressions. Binary variables (hereafter called logical variables) are first introduced and methods of logically connecting these to other variables are then presented. Simple constraints can be combined to construct logical relationships; the methods of formulating these are also discussed. These reformulation procedures are illustrated by two examples. A scheme of implementation within an LP modelling system is outlined.

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