Two Benders-type Branch-and-Cut Algorithms for Capacitated Facility Location with Single-Sourcing

We consider mixed 0-1 integer programs of the form $\min\{cx+hy: Ax+By \geq b, x \in \{0,1\}^n,y \in \{0,1\}^p \times \R^{N-p}_+\}$ in which the subproblem arising when $x$ is fixed has special structure. One such example is the capacitated facility location problem with single-sourcing in which the linear programming relaxation of the subproblem is a transportation … Read more

The continuous knapsack set

We study the convex hull of the continuous knapsack set which consists of a single inequality constraint with n non-negative integer and m non-negative bounded continuous variables. When n = 1, this set is a slight generalization of the single arc flow set studied by Magnanti, Mirchandani, and Vachani (1993). We first show that in … Read more

Covering Linear Programming with Violations

We consider a class of linear programs involving a set of covering constraints of which at most k are allowed to be violated. We show that this covering linear program with violation is strongly NP-hard. In order to improve the performance of mixed-integer programming (MIP) based schemes for these problems, we introduce and analyze a … Read more

Lifting Group Inequalities and an Application to Mixing Inequalities

Given a valid inequality for the mixed integer infinite group relaxation, a lifting based approach is presented that can be used to strengthen this inequality. Bounds on the solution of the corresponding lifting problem and some necessary conditions for the lifted inequality to be minimal for the mixed integer infinite group relaxation are presented. Finally, … Read more

Constrained Infinite Group Relaxations of MIPs

Recently minimal and extreme inequalities for continuous group relaxations of general mixed integer sets have been characterized. In this paper, we consider a stronger relaxation of general mixed integer sets by allowing constraints, such as bounds, on the free integer variables in the continuous group relaxation. We generalize a number of results for the continuous … Read more

Two Row Mixed Integer Cuts Via Lifting

Recently, Andersen et al.(2007), Borozan and Cornuejols (2007) and Cornuejols and Margot(2007) characterized extreme inequalities of a system of two rows with two free integer variables and nonnegative continuous variables. These inequalities are either split cuts or intersection cuts (Balas (1971)) derived using maximal lattice-free convex sets. In order to use these inequalities to obtain … Read more

Single Item Lot-Sizing with Nondecreasing Capacities

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 non-increasing over time, it is known that the minimum cost lot-sizing problem is polynomially … Read more

Lattice based extended formulations for integer linear equality systems

We study different extended formulations for the set $X =\{x\in\mathbb{Z}^n \mid Ax = Ax^0\}$ in order to tackle the feasibility problem for the set $X_+=X \cap \mathbb{Z}^n_+$. Here the goal is not to find an improved polyhedral relaxation of conv$(X_+)$, but rather to reformulate in such a way that the new variables introduced provide good … Read more