We describe an approach that computes an optimal primal basic solution given an optimal vector of dual multipliers. It consists in restricting the dual prob...

This article presents a formulation for the job shop problem based on the Dantzig- Wolfe decomposition with a subproblem for each machine. Each subproblem i...

In most vehicle routing and crew scheduling applications solved by column generation, the subproblem corresponds to a shortest path problem with resource con...

We give a didactic introduction to the use of the column generation technique in linear and in particular in integer programming. We touch on both, the relev...

This paper proposes a generalization of the proximal point algorithm using both penalty and trust region concepts. Finite convergence is established while as...

This article reviews some of the best metaheuristics proposed in recent years for the Vehicle Routing Problem. These are based on local search, on populatio...

The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most...

The problem of determining a shortest loop incident to each cell of a block layout is considered. A compact formulation is developed for this problem and a ...

Conjectures in graph theory have multiple forms and involve graph invariants, graph classes, subgraphs, minors and other concepts in premisses and/or conclu...

Computer-assisted and automated conjecture-making in graph theory is reviewed, focusing on the three operational systems GRAPH, Graffiti and AutoGraphiX (AGX...

We consider the multiple depot vehicle scheduling problem (MDVSP) and propose a branch-and-bound algorithm for solving it that combines column generation, va...

Two ways for bounding <i>n</i>-variables functions over a box, based on interval evalu- ations of first order derivatives, are compared. The optimal Baumann...

The shortest path problem with resource constraints consists of finding the minimum cost path between two specified points while respecting constraints on r...

In this study we develop optimization, decomposition, and heuristic procedures to design a unidirectional loop flow pattern along with the pickup and delive...

This paper presents some new heuristics based on variable neighborhood search to solve the vertex weighted <i>k</i>-cardinality tree problem. An efficient l...

We consider the bilevel uncapacitated facility location problem with user preferences. It is known that this model may be reformulated as a one-level locati...

The multiprocessor scheduling problem with communication delays that we consider in this paper consists of finding a static schedule of an arbitrary task gra...

In some schools and universities, students must sometimes be divided into several teams in such a way that each team provides a good representation of the cl...

Dantzig-Wolfe decomposition and column generation, devised for linear programs, is a success story in large scale integer programming. We outline and relate ...

We propose a differential game to study retailer’s allocation strategy of shelf-space shares between the manufacturers of two competing brands. Each manufact...