Different types of formulations are proposed in the literature to model vehicle routing problems. Currently, the most used ones can be fitted into two classes, namely vehicle flow formulations and set partitioning formulations. These types of formulations differ from each other not only due to their variables and constraints but also due to their main features. Vehicle flow formulations have th...

When integer programming (IP) models are used in operational situations there is a need to consider the tradeoff between the conflicting goals of solution quality and solution time, since for many problems solving realistic-size instances to a tight tolerance is still beyond the capability of state-of-the-art solvers. However, by appropriately defining small instances, good primal solutions fre...

We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch and bound tree We present classes of models for which this approach decomposes the problem provides tighter LP relaxations and eliminates symmetry We then d...

The generalized assignment problem examines the maximum pro t assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents A new algorithm for the generalized assignment problem is presented that employs both column generation and branch and bound to obtain optimal integer solutions to a set partitioning formulation of the pro...

In this paper we consider the problem of designing a container liner shipping feeder network. The designer has to choose which port to serve during many rotations that start and end at a central hub. Many operational characteristics are considered, such as variable leg-by-leg speeds and cargo transit times. Realistic instances are generated from the LinerLib benchmark suite. The problem is solv...

In this work we study a suppliers selection and routing problem where a fleet of homogeneous vehicles with a predefined capacity is available for procuring different products from different suppliers with the aim to minimize both the traveling and the purchasing costs. Decisions are further complicated by the presence of pairwise incompatibility constraints among products, implying the impossib...

http://dx.doi.org/10.1016/j.ejor.2014.03.006 0377-2217/ 2014 Elsevier B.V. All rights reserved. ⇑ Corresponding author. Tel.: +56 2 29784380; fax: +56 2 26894206. E-mail addresses: [email protected] (C.E. Cortés), [email protected] (M. Gendreau), [email protected] (L.M. Rousseau), sebastian. [email protected] (S. Souyris), [email protected] (A. Weintraub). Cris...

The G12 project is developing a software environment for stating and solving combinatorial problems by mapping a high-level model of the problem to an efficient combination of solving methods. Model annotations are used to control this process. In this paper we explain the mapping to branch-and-price solving. G12 supports the selection of specialised sub-problem solvers, the aggregation of iden...

This is a report on how mixed integer programming works. It starts by showing the form of a mixed integer program with n variables and m constraints. They explain the branch and bound method which is the most widely used method for solving integer programs. It goes into some detail about how the variables have only two possible restrictions, one and zero. There’s also some mention of the branch...