We compare two branch-and-price approaches for the cutting stock problem. Each algorithm is based on a different integer programming formulation of the column generation master problem. One formulation results in a master problem with 0–1 integer variables while the other has general integer variables. Both algorithms employ column generation for solving LP relaxations at each node of a branch-...

The railway crew scheduling problem is to determine an optimal crew assignment to minimize the number of crews required to cover all of railway assignment satisfying several crew working constraints. The problem can be formulated as a huge set covering problem. Column generation method is commonly used to solve the railway crew scheduling problem. Conventional column generation method has a sho...

Research addressing two-dimensional irregular shape packing has largely focused on the strip packing variant of the problem. However, it can be argued that this is a simplification. Materials from which pieces are required to be cut will ultimately have a fixed length either due to the physical dimensions of the material or through constraints on the cutting machinery. Hence, in order to cut al...

Seaport container terminals are source of many interesting large-scale optimization problems, which arise in the management of operations at several decision levels. In this paper we firstly illustrate a recently proposed framework, called two-stage column generation (Salani and Vacca, 2008), which is suitable for a particular class of large-scale problems, where the structure of the original f...

In this paper, we consider a network design problem of stacking multiple bi-directional self-healing-rings (BSHRs) on a given physical conduit ring in order to meet given demand requirements. The objective is then to find a cost-minimizing solution which not only specifies how many and what kinds of BSHR rings to install, but also indicates how to split the demand requirements among the install...

A of April 2007, the European Union has new regulations concerning driver working hours. These rules force the placement of breaks and rests into vehicle routes when consecutive driving or working time exceeds certain limits. This paper proposes a large neighborhood search method for the vehicle routing problem with time windows and driver regulations. In this method, neighborhoods are explored...

We investigate two cutting problems and their variants in which orthogonal rotations are allowed. We present a dynamic programming based algorithm for the Two-dimensional Guillotine Cutting Problem with Value (GCV) that uses the recurrence formula proposed by Beasley and the discretization points defined by Herz. We show that if the items are not so small compared to the dimension of the bin, t...

Abstract: Avella et al. (2006) [Avella, P., D’Auria, B., Salerno, S. (2006). A LP-based heuristic for a time-constrained routing problem. European Journal of Operational Research 173:120-124] investigate a timeconstrained routing (TCR) problem. The core of the proposed solution approach is a large-scale linear program (LP) that grows both rowand column-wise when new variables are introduced. Th...

Kidney exchange is a barter market where patients trade willing but medically incompatible donors. These trades occur via cycles, where each patient-donor pair both gives and receives a kidney, and via chains, which begin with an altruistic donor who does not require a kidney in return. For logistical reasons, the maximum length of a cycle is typically limited to a small constant, while chains ...

Dantzig-Wolfe decomposition (or reformulation) is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs) in practice. However, the method is not implemented in any state-of-the-art MIP solver as it is considered to require structural problem knowledge and tailoring to this structure. We provide a computational proof-of-concept that the process can be aut...