LOT-SIZING WITH STOCK UPPER BOUNDS AND FIXED CHARGES

作     者：Di Summa, Marco Wolsey, Laurence A. 

作者机构：Univ Turin Dipartimento Informat I-10149 Turin Italy Catholic Univ Louvain CORE B-1348 Louvain Belgium 

出 版 物：《SIAM JOURNAL ON DISCRETE MATHEMATICS》 (工业与应用数学会离散数学杂志)

年 卷 期：2010年第24卷第3期

页      面：853-875页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：mixed-integer programming discrete lot-sizing stock fixed costs mixing sets 

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 a pure integer set and the other 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.