Applications of pseudo-Boolean methods to economic problems

Abstract

The use of Boolean algebra in logic, switching and automata theory, coding and other technically oriented areas is well known. The role of this paper is to show that Boolean algebra can be instrumental in taking economic decisions.

By a pseudo-Boolean function, a real-valued function with bivalent (0–1) variables will be understood. The symbols 0 and 1 will stay both for their logical meaning and their arithmetical value.

The basic problems which arise frequently in connection with pseudo-Boolean functions are: (1) solution of systems of equations and/or inequalities involving only pseudo-Boolean functions, (2) problems of determining the maximum or the minimum of a free pseudo-Boolean function, or of a pseudo-Boolean function whose variables are subject to constraints; (3) problems of finding the minimax or the maximin of a pseudo-Boolean function.

The basic problems outlined above are exemplified on the case of a company wishing to locate a number of service stations, which - under different assumptions - lead to the above formulated models.