¹Université Laval, Québec, Canada

Correspondence: N Rizk, FOR@C Research Consortium, Network Organization Technology Research Center (CENTOR), Université Laval, Sainte-Foy, Québec, Canada, G1K 7P4. E-mail: nrizk@videotron.ca

Received May 2005; Accepted July 2006; Published online 1 November 2006.

Abstract

This paper examines the flow synchronization problem between a manufacturing location and multiple destinations. Multiple products can be shipped from the manufacturing location to different locations via multiple transportation modes. These transportation modes may have different transportation lead times. The transportation costs structure of the different transportation modes offer economies of scale and can be represented by general piecewise linear functions. The production system at the manufacturing location is a serial process with a bottleneck stage. At the bottleneck stage, a predetermined production sequence must be maintained as is the case in some process-based industries. We propose a tight mixed integer programming model for integrated planning of production and distribution in the network. We show that by adding simple valid inequalities and special 0-1 variables, major computational improvements can be achieved when solving this problem with commercial solvers such as Cplex. We also propose a sequential solution approach, based on the independent, but synchronized, solutions of the production and distribution sub-problems. Finally, the solution methods proposed are tested experimentally for realistic problems and the advantage of integrated planning over independent but synchronized planning is assessed.