We present a branch-and-cut algorithm to solve capacitated network design problems. Given a capacitated network and point-to-point traac demands, the objective is to install more capacity on the edges of the network and route traac simultaneously, so that the overall cost is minimized. We study a mixed-integer programming formulation of the problem and identify some new facet deening inequaliti...

Many combinatorial optimization problems have relaxations that are semidefinite programming problems. In principle, the combinatorial optimization problem can then be solved by using a branch-and-cut procedure, where the problems to be solved at the nodes of the tree are semidefinite programs. It is desirable that the solution to one node of the tree should be exploited at the child node in ord...

We study a scheduling problem, motivated by air-traffic control, in which a set of aircrafts are about to land on a single runway. When coming close to the landing area of the airport, a set of time windows in which the landing is possible, is automatically assigned to each aircraft. The objective is to maximize the minimum time elapsed between any two consecutive landings. We study the complex...

We study mixed integer programming formulations of variants of the discrete lot–sizing problem. Our approach is to identify simple mixed integer sets within these models and to apply tight formulations for these sets. This allows us to define integral linear programming formulations for the discrete lot–sizing problem in which backlogging and/or safety stocks are present, and to give extended f...

Decomposition has proved to be one of the more effective tools for the solution of large-scale problems, especially those arising in stochastic programming. A decomposition method with wide applicability is Benders’ decomposition, and has been applied to both stochastic programming, as well as integer programming problems. However, this method of decomposition relies on convexity of the value f...

We study the polyhedral structure of simple mixed integer sets that generalize the two variable set {(s, z) ∈ IR1+×Z 1 : s ≥ b−z}. These sets form basic building blocks that can be used to derive tight formulations for more complicated mixed integer programs. For four such sets we give a complete description by valid inequalities and/or an integral extended formulation, and we also indicate wha...

The purpose of this paper is to introduce, model and solve a rich multi-period inventory-routing problem with simultaneous pickups and deliveries. Commodities can be brought from and to the depot, as well as being exchanged among customers to efficiently manage their inventory shortages and surpluses. A single customer can both provide and receive commodities at different periods, since its dem...

The qualifying phase of the Chilean soccer championship follows the structure of a compact single round robin tournament. Good schedules are of major importance for the success of the tournament, making them more balanced, profitable, and attractive. The schedules were prepared by ad hoc procedures until 2004, when a rough integer programming strategy was proposed. In this work, we improve the ...

The truss design problem is to nd the optimal placement and size of structural bars that can support a given load The problem is nonlinear and in the version addressed here the bars must take certain discrete sizes It is shown that a logic based method that dispenses with integer variables and branches directly on logical disjunctions can solve sub stantially larger problems than mixed integer ...

in this paper, for the first time, blood inventory-routing problem (irp) is defined and a mixed integer linear programming formulation is presented. to do so, the concepts of assigned inventory, transfusion to crossmatch ratio, crossmatch release period, older-first policy and order-up-to level inventory policy along with perishability considerations are incorporated into the latest inventory-r...