Benders decomposition [1] is a solving strategy based on the separation of the variables of the problem. It is often introduced as a basis for models and techniques using the complementary strengths of constraint programming and optimization techniques. Hybridization schemes have appeared recently and provided interesting computational results [4, 5, 7, 8]. They have been extended [2, 3, 6] to ...

The Magnanti–Wong method – accelerating Benders decomposition – is shown to exhibit difficulties due to its dependence on the subproblem; an independent version is therefore introduced. The method additionally requires a – sometimes intractable – master problem core point; for several applications it is proved and experimentally verified that alternative points may be used. c © 2008 Elsevier B....

We describe models and exact solutions approaches for an integrated aircraft fleeting and routing problem arising at TunisAir. Given a schedule of flights to be flown, the problem consists of determining a minimum cost route assignment for each aircraft so as to cover each flight by exactly one aircraft while satisfying maintenance activity constraints. We investigate two tailored approaches fo...

Abstract We propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). call this algorithm nested Benders (NC-NBD). NC-NBD is based on solving dynamically improved linear outer approximations of the MINLP, obtained by piecewise relaxations functions. Those MILPs are solved global optimality using an enhancement decomposi...

This paper addresses two major issues related to the convergence of generalized Benders decomposition which is an algorithm for the solution of mixed integer linear and nonlinear programming problems. First, it is proved that a mixed integer nonlinear programming formulation with zero nonlinear programming relaxation gap requires only one Benders cut in order to converge, namely the cut corresp...

With stochastic integer programming as the motivating application, we investigate techniques to use integrality constraints to obtain improved cuts within a Benders decomposition algorithm. We compare the effect of using cuts in two ways: (i) cut-and-project, where integrality constraints are used to derive cuts in the extended variable space, and Benders cuts are then used to project the resul...

Benders decomposition uses a strategy of “learning from one’s mistakes.” The aim of this paper is to extend this strategy to a much larger class of problems. The key is to generalize the linear programming dual used in the classical method to an “inference dual.” Solution of the inference dual takes the form of a logical deduction that yields Benders cuts. The dual is therefore very different f...