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Mathematical Problems in Engineering
Volume 2017, Article ID 7209303, 18 pages
Research Article

Fix-and-Optimize and Variable Neighborhood Search Approaches for Stochastic Multi-Item Capacitated Lot-Sizing Problems

1Department of Automation, Tsinghua University, Beijing 100084, China
2Department of Basic Science, Military Transportation University, Tianjin 300161, China

Correspondence should be addressed to Shiji Song; nc.ude.auhgnist.liam@sijihs

Received 19 October 2016; Revised 18 January 2017; Accepted 1 March 2017; Published 12 April 2017

Academic Editor: Honglei Xu

Copyright © 2017 Liuxi Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We discuss stochastic multi-item capacitated lot-sizing problems with and without setup carryovers (also known as link lot size), S-MICLSP and S-MICLSP-L. The two models are motivated from a real-world steel enterprise. To overcome the nonlinearity of the models, a piecewise linear approximation method is proposed. We develop a new fix-and-optimize (FO) approach to solve the approximated models. Compared with the existing FO approach(es), our FO is based on the concept of “-degree-connection” for decomposing the problems. Furthermore, we also propose an integrative approach combining our FO and variable neighborhood search (FO-VNS), which can improve the solution quality of our FO approach by diversifying the search space. Numerical experiments are performed on the instances following the nature of realistic steel products. Our approximation method is shown to be efficient. The results also show that the proposed FO and FO-VNS approaches significantly outperform the recent FO approaches, and the FO-VNS approaches can be more outstanding on the solution quality with moderate computational effort.