期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2009
卷号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：Here we study the discrete lot-sizing problem with an initial stock variable and an
associated variable upper bound constraint. This problem is of interest in its own
right, and is also a natural relaxation of the constant capacity lot-sizing problem
with upper bounds and fixed charges on the stock variables. We show that the
convex hull of solutions of the discrete lot-sizing problem is obtained as the
intersection of two simpler sets, one involving just 0-1 variables and the second a
mixing set with a variable upper bound constraint. For these two sets we derive
both inequality descriptions and polynomial-size extended formulations of their
respective convex hulls. Finally we carry out some limited computational tests on
single-item constant capacity lot-sizing problems with upper bounds and fixed
charges on the stock variables in which we use the extended formulations derived
above to strengthen the initial mixed integer programming formulations
