This paper is about modeling and solving mixed integer programming (MIP) problems. In the last decade, the use of mixed integer programming models has increased dramatically. Fifteen years ago, mainframe computers were required to solve problems with a hundred integer variables. Now it is possible to solve problems with thousands of integer variables on a personal computer and obtain provably g...

Contents 1. Introduction 1 1.1. Formulations and exact methods for OPP 1 1.2. Relaxations and bounds 2 1.3. Our contributions 2 2. The interval-graph model and a simplification 3 Discussion 4 3. An overview of the algorithm of Fekete and Schepers 4 3.

We address the service network design problem with asset management considerations for consolidation-based freight carriers. Given a set of demands to be transported from origins to destinations and a set of transshipment facilities, the objective is to select services and their schedules, build routes for the assets (vehicles) operating these scheduled services, and move the demands (commoditi...

We consider the problem of designing hierarchical two layer ring networks. The top layer consists of a federal-ring which establishes connection between a number of node disjoint metro-rings in a bottom layer. The objective is to minimize the costs of links in the network, taking both the fixed link establishment costs and the link capacity costs into account. Hierarchical ring network design p...

The shift-scheduling problem was originally introduced by Edie in 1954 in the context of scheduling highway toll booth operators. It was solved a short time later, by Georges Dantzig, using a set covering formulation. However, the Multi-Activity Shift Scheduling (MASSP) version of that problem, where one not only needs to schedule when employees are working or resting, but more precisely, what ...

We consider the multi-vehicle one-to-one pickup and delivery problem with split loads, a NP-hard problem linked with a variety of applications for bulk product transportation, bike-sharing systems and inventory re-balancing. This problem is notoriously difficult due to the interaction of two challenging vehicle routing attributes, “pickups and deliveries” and “split deliveries”. This possibly l...

Kidney exchange is a type of barter market where patients exchange willing but incompatible donors. These exchanges are conducted via cycles—where each incompatible patient-donor pair in the cycle both gives and receives a kidney—and chains, which are started by an altruist donor who does not need a kidney in return. Finding the best combination of cycles and chains is hard. The leading algorit...

Branch-and-price algorithms combine a branch-and-bound search with an exponentiallysized LP formulation that must be solved via column generation. Unfortunately, the standard branching rules used in branch-and-bound for integer programming interfere with the structure of the column generation routine; therefore, most such algorithms employ alternate branching rules to circumvent this difficulty...

The resource-constrained elementary shortest path problem arises as a pricing subproblem in branch-and-price algorithms for vehicle routing problems with additional constraints. We address the optimization of the resource-constrained elementary shortest path problem and we present and compare three methods. The first method is a well-known exact dynamic programming algorithm improved by new ide...

Branch-and-price algorithms combine a branch-and-bound search with an exponentiallysized LP formulation that must be solved via column generation. Unfortunately, the standard branching rules used in branch-and-bound for integer programming interfere with the structure of the column generation routine; therefore, most such algorithms employ alternate branching rules to circumvent this difficulty...