期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2007
卷号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：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 formulations. We believe this method could
be useful for analyzing and producing tight formulations of problems that arise in
practice. We illustrate the use of the approach on a problem in production scheduling.
We also prove that coefficient strengthening leads to formulations with a desirable
property: if no coefficient can be strengthened, then no constraint can be replaced by
an inequality that dominates it. The effect of coefficient strengthening is tested on a
number of problems in a computational experiment. The strengthened formulations
are compared to reformulations obtained by the preprocessor of a commercial
software package. For several test problems, the formulations obtained by coefficient
strengthening are substantially stronger than the formulations obtained by the
preprocessor. In particular, we use coefficient strengthening to solve two difficult
problems to optimality that have only recently been solved.
