A branch and bound algorithm for extreme point mathematical programming problems

Abstract This paper deals with a class of nonconvex mathematical programs called Extreme Point Mathematical Programs. This class is a generalization of zero-one integer programs and is a special case of the Generalized Lattice Point Problem, and finds applications in various areas such as production scheduling, load balancing, and concave programming. The current work existing on this class of problems is limited to certain dual types of extreme point ranking methods (which do not find a feasible solution until optimality) and some non-convergent cutting plane algorithms. No computational experience exists. This paper develops a finitely convergent branch and bound algorithm for solving the problem. The principles involved in the design of this algorithm are quite general and apply to a wider class of mathematical programs including the Generalized Lattice Point Problem. A random problem generator is described which is capable of generating problems of varying levels of difficulty. Computational experience on such problems is provided.