A branch-and-cut-and-price algorithm for one-and two-dimensional two-staged cutting (stock) problems

Article history: Received 20 November 2009 Accepted 3 January 2011 Available online 8 January 2011

Branch-and-Cut is the most commonly used algorithm for solving Integer and Mixed-Integer Linear Programs. In order to reduce the number of nodes that have to be enumerated before optimality of a solution can be proven, branching on general disjunctions (i.e. split disjunctions involving more than one variable, as opposed to branching on simple disjunctions defined on one variable only) was show...

A important strategic phase in the planning process of a railway operator is the development of a line plan, i.e., a set of routes (paths) in a network of tracks, operated at a given hourly frequency. We consider a model formulation of the line-planning problem where total operating costs are to be minimized. This model is solved with a branch-and-cut approach, for which we develop a variety of...

In many mixed integer programs there is some embedded problem structure which can be exploited, often by a decomposition. When the relaxation in each node of a branch-andbound tree is solved by column generation, one speaks of branch-and-price. Optionally, cutting planes can be added in order to strengthen the relaxation, and this is called branchprice-and-cut. We introduce the common concepts ...

In the pickup and delivery problem with time windows (PDPTW), capacitated vehicles must be routed to satisfy a set of transportation requests between given origins and destinations. In addition to capacity and time window constraints, vehicle routes must also satisfy pairing and precedence constraints on pickups and deliveries. This paper introduces two new formulations for the PDPTW and the cl...

A co-biclique of a simple undirected graph G = (V, E) is the edge-set of two disjoint complete subgraphs of G. (A co-biclique is the complement of a biclique.) A subset F ⊆ E is an independent of G if there is a co-biclique B such that F ⊆ B, otherwise F is a dependent of G. This paper describes the minimal dependents of G. (A minimal dependent is a dependent C such that any proper subset of C ...

This paper deals with the cutting-plane approach to the maximum stable set problem. We provide theoretical results regarding the facet-defining property of inequalities obtained by a known project-and-lift-style separation method called edge-projection, and its variants. An implementation of a Branch and Cut algorithm is described, which uses edge-projection and two other separation tools which...