Lot-Sizing Problems :

A Library of Models and Matrices

 

Production planning problems involving lot-sizing come in many different forms. One approach to the solution of such problems is using mixed integer programming. However for such approaches to work, it is often insufficient to just run an initial model with a commercial mixed integer programming system. Rather work has to be done to obtain first an appropriate formulation, and then an effective algorithm, involving perhaps cutting planes and heuristics that take into account the lot-sizing structure of the problem.
The aim here is to provide a problem test set including an initial presentation of the problem instance, its formulation in one (and later hopefully more) standard LP modelling language, an MPS file, and possibly comments on effective ways to solve it, references, origin, etc.
The hope is that this will stimulate and facilitate more research and improved solution methods, and that others will submit new and interesting instances to be added to the library. Comments and submissions to mailto:wolsey@core.ucl.ac.be

PROBLEM CLASSIFICATION
At present the notation used, and the problem classification used is taken from
Lot-Sizing Problems: "Modelling Issues and a Specialized Branch-and-Cut System bc-prod", G. Belvaux and L.A. Wolsey, CORE Discussion Paper 9849, Center for Operations Research and Econometrics, Universite Catholique de Louvain, (1998). psfile

Mathematical formulations of the models can be found in

LOTSIZELIB: A Library of Models and Matrices for Lot-Sizing Problems, G. Belvaux and L.A. Wolsey, Internal Report,  Center for Operations Research and Econometrics, Universite Catholique de Louvain (1999). psfile

The first level classification is into

  • Single Level Big Bucket Models
  • Single Level Small Bucket Models with only One Item produced per Period
  • Single Level Small Bucket Models with up to Two Items produced per Period
  • Multi-level Big Bucket Models


    Other sources: The MPS files of a certain number of lot-sizing models can be found in the MIPLIB3.0 library
    Data on the  lot-sizing instances used in three articles can be found at http://www.eng.auburn.edu/~gaoyubo/

          Home    ShortCV  LOTSIZELIB