A new formulation of the optimization problem implementing European market rules for non- convex day-ahead electricity markets is presented, that avoids the use of complementarity constraints to express market equilibrium conditions, and also avoids the introduction of auxiliary binary variables...

In this note, we present a simple geometric argument to determine a lower bound on the split rank of intersection cuts. As a first step of this argument, a polyhedral subset of the lattice-free convex set that is used to generate the intersection cut is constructed. We call this subset the...

A separation heuristic for mixed integer programs is presented that theoretically allows one to derive several families of "strong" valid inequalities for specific models and computationally gives results as good as or better than those obtained from several existing separation routines...

Much progress has been made in recent years in solving certain classes of production planning problems using mixed integer programming. One of the major challenges is how to make this expertise available and easy to use to the non-specialist and to the practitioners. Here we describe a modeling...

We study two different lot-sizing problems with time windows that have been proposed recently. For the case of production time windows, in which each client specific order must be produced within a given time interval, we derive tight extended formulations for both the constant capacity and...

This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for i) general integer programs, ii) problems with local structure such as knapsack constraints, and iii) problems with 0-1 coefficient matrices, such as set packing,...

Providing a good formulation is an important part of solving a mixed integer program. We suggest to measure the quality of a formulation by whether it is possible to strengthen the coefficients of the formulation. Sequentially strengthening coefficients can then be used as a tool for improving...

We study a special case of a structured mixed integer programming model that arises in a number of applications. For the most general case of the model, called PI, we have earlier analyzed the polyhedral structure (Miller et al. [2000a]), including identifying facet-defining valid inequalities....

We consider the single item lot-sizing problem with capacities that are non-decreasing over time. When the cost function is i) non-speculative or Wagner-Whitin (for instance, constant unit production costs and non-negative unit holding costs), and ii) the production set-up costs are...

We examine a variant of the uncapacitated lot-sizing model of Wagner-Whitin involving sales instead of fixed demands, and lower bounds on stocks. Two extended formulations are presented, as well as a dynamic programming algorithm and a complete description of the convex hull of solutions. When...