We study different extended formulations for the set X = {x [belong] Z exp.n | Ax = Ax exp.0} in order to tackle the feasibility problem for the set X+ = X [intersection] Z+ exp.n . Here the goal is not to find an improved polyhedral relaxation of conv(X+), but rather to reformulate in such a...

BC-PROD is a prototype modelling and optimization system designed and able to tackle a wide variety of the discrete-time lot-sizing problems arising both in practice and in the literature. To use BC-PROD, the user needs to formulate his/her problem as a mixed integer program using XPRESS-MP's...

Recently, Andersen et al. [1], Borozan and Cornuéjols [6] and Cornuéjols and Margot [9] 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 derived using...

For the problem of lot-sizing on a tree with constant capacities, or stochastic log-sizing with a scenario tree, we present various reformulations based on mixing sets. We also show how earlier results for uncapacitated problems involving (Q, SQ) inequalities can be simplified and extended....

We examine the single-item lot-sizing problem with Wagner-Whitin costs over an n period horizon, i.e. Pt + ht ≥ Pt+l for t = 1, ... , n - 1, where Pt, ht are the unit production and storage costs in period t respectively, so it always pays to produce as late as possible. We describe integral...

Constraints arising in practice often contain many 0-1 variables and one or a small number of continuous variables. Existing knapsack separation routines cannot be used on such constraints. Here we study such constraint sets, and derive valid inequalities that can be used as cuts for such sets,...

In spite of the remarkable improvements in the quality of general purpose mixed integer programming software, the effective solution of a variety of lot-sizing problems depends crucially on the development of tight formulations for the special problem features occurring in practice. After...

We consider a multi-item lot-sizing problem in which there are demands, and unit production and storage costs. In addition production of any mix of items is measured in batches of fixed size, and there is a fixed set-up cost per batch in each period. Suppose that the unit production costs are...

In problems involving the simultaneous optimization of production and transportation, the requirement that an order can only be shipped once its production has been completed is a natural one. One example is a problem of optimizing shipping costs subject to a production capacity constraint...