A branch and bound algorithm for solving separable convex integer programming problems

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Abstract

This paper proposes a branch and bound method that solves a class of nonlinear integer programming problems. A separable convex objective function is minimized over a feasible region defined by the constraints which are separable and convex. The “traditional branch and bound approach” has been to relax integrality restrictions on the decision variables and solve hard nonlinear continuous subproblems. In contrast, the algorithm presented in this paper linearizes all nonlinear functions to form a linear programming problem at each node, which can be solved efficiently by the simplex method. Appropriate branching, bounding, fathoming, partitioning, and reoptimizing schemes are developed. In the computational study, our “linear subproblem approach” is compared with the “traditional nonlinear subproblem approach”. For the test problems randomly generated, our algorithm is shown to be better than the nonlinear subproblem approach.

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    Won J. Lee is an assistant professor of Management at Marquette University. He obtained a B.B.A. from Sungkyunkwan University, an M.B.A. from University of Michigan, and a Ph.D. from Indiana University. His current research interests are in applied management science, production/marketing interface, and inventory and lot sizing.

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    A. Victor Cabot is a Professor in the Decision and Information Systems in the School of Business at Indiana University. He holds a BSIE from the University of Miami and an MSIE and Ph.D. from Northwestern University. Professor Cabot has held visiting positions at the University of Grenoble and the Naval Postgraduate School.

    M. A. Venkataramanan is an Associate Professor of Decision and Information Systems in the School of Business at Indiana University. His current teaching and research interests are in applied operations research, network programming and high speed computing.

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