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On the Integrated Production and Distribution Problem with Bidirectional Flows

Department of Supply Chain Management and Marketing Sciences, Rutgers University, Newark and New Brunswick, New Jersey 07102
Economics & Business Division, State University of New York College at Oneonta, Oneonta, New York 13820
Department of Industrial and Systems Engineering, Rutgers University, Piscataway, New Jersey 08854
llei{at}business.rutgers.edu
zhongh{at}oneonta.edu
wchaoval{at}rci.rutgers.edu

The integrated production and distribution problem with bidirectional flows is a complicated optimization problem, usually with large problem sizes when encountered in practice. In this study, we propose a partial linear programming relaxation-based heuristic approach to solve a variation of this problem. The approach is called a partial relaxation in the sense that it relaxes the integer requirements only on selected variables. We also report on the gaps between the optimal solution and the heuristic solution provided by this partial relaxation, including analytical gaps for a special case and empirical gaps for randomly generated test cases. Our study of this problem was motivated by the operational planning problem of a medical equipment leasing network that involves a forward flow for new and refurbished devices and a reverse flow for used devices to be returned to suppliers over a multiple time-period planning horizon.

Key words: partial linear programming relaxation; heuristic; integrated production and distribution; bidirectional flows
History: received December 2004; revised July 2008; accepted September 2008.