Given a graph with nonnegative edge weights and node pairs Q, we study the problem of constructing a minimum weight set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L edges between each pair in Q. Using the layered representation introduced by Gouveia (1998), we present a formulation for the problem valid for any K, L ! 1. We use a Benders dec...

Many real problems can bemodelled as robust shortest path problems on digraphs with interval costs, where intervals represent uncertainty about real costs and a robust path is not too far from the shortest path for each possible configuration of the arc costs. In this paper we discuss the application of a Benders decomposition approach to this problem. Computational results confirm the efficien...

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 n...

Motivated by an industrial application, we study a specific employee timetabling problem. Several investigations are being conducted: a lower bound by Lagrangian relaxation, a heuristic based on a cut generation process and an exact method by Benders decomposition. Experimental results on real and generated instances are reported.

The author regrets that some terms are missing or misspecified in the Karush–Kuhn–Tucker conditions in Sections 3.7–3.10 on page 346. Corrections are given below. add multiplier p m c m (discount rate in tree node m multiplied by the probability of its occurrence) to d d (number of days in demand season d).

Network Design 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 origin-destination pair demands. Benders decomposition methods, based on the idea of partition and delayed constraint generation, have been successfully applied to many of these problems. This article presents a review of these applicati...

In this thesis, a Benders decomposition algorithm is designed and implemented to solve both deterministic and stochastic pooling problems to global optimality. Convergence of the algorithm to a global optimum is proved and then it is implemented both in GAMS and C++ to get the best performance. A series of example problems are solved, both with the proposed Benders decomposition algorithm and c...

Abstract A general enhancement of the Benders’ decomposition (BD) algorithm can be achieved through improved use large neighbourhood search heuristics within mixed-integer programming solvers. While solvers are endowed with an array heuristics, few, if any, have been designed for BD. Further, typically is limited to finding solutions BD master problem. Given lack frameworks BD, only ad hoc appr...