The usefulness of group theoretic methods in solving integer programming (IP) problems is extended by procedures for controlling the size of the groups. The main procedure given shows how an optimal linear programming basis can be altered to reduce the magnitude of its determinant thereby...

Multi-item capacitated lot-sizing problems are reformulated using a class of valid inequalities, which are facets for the single-item uncapacitated problem. Computational results using this reformulation are reported, and problems with up to 20 items and 13 periods have been solved to optimality...

Based on research on the polyhedral structure of lot-sizing models over the last 20 years, we claim that there is a nontrivial fraction of practical lot-sizing problems that can now be solved by nonspecialists just by taking an appropriate a priori reformulation of the problem, and then feeding...

We consider two classes of multi-item lot-sizing problems. The first is a class of single stage problems involving joint machine capacity constraints and/or start up costs, and the second is a class of multistage problems with general product structure. The problems are solved as mixed integer...

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...

By relaxing the nonnegativity constraints on a set of basic variables, an integer programming problem can be reduced to a shortest route problem over a finite Abelian group. Here it is shown how given a similar relaxation on any set of variables, a structurally simpler problem is obtained, which...

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...