Initialization of the Benders master problem using valid inequalities applied to fixed-charge network problems

Network problems concern the selection of arcs in a graph in order to satisfy, at minimum cost, some flow requirements, usually expressed in the form of node–node pair demands. Benders decomposition methods, based on the idea of partitioning of the initial problem to two sub-problems and on the generation of cuts, have been successfully applied to many of these problems. This paper presents a novel way to reinitialize the Benders master problem for this group of problems using a series of valid inequalities. A generic presentation of the developed valid inequalities is presented as well as a case study of a refinery system is used in order to illustrate the advantage of the proposed procedure. The valid inequalities significantly restrict the solution space of the Benders master problem from the first iteration of the algorithm leading to improved convergence. 2009 Elsevier Ltd. All rights reserved.