NDLI: Nonconvex quadratic inventory control problems by conic optimization

Content Provider	IEEE Xplore Digital Library
Author	Cheng Cong Tang Lixin
Copyright Year	2014
Description	Author affiliation: Logistics Inst., Northeastern Univ., Shenyang, China (Cheng Cong; Tang Lixin)
Abstract	Inventory control is to find a optimal strategy to minimum the cost or maximum the profit. There have been numerous research on inventory control with the linear or other convex objective functions. However, the nonconvex cases are the more frequently occurring in practice, which are more difficult to handle than the convex one. In this paper, a class of inventory control with nonconvex quadratic objective is considered. The Lagrange decomposition method is used for generating convex relaxations for the nonconvex quadratic inventory control problem. We show that the best decomposition can be identified by solving an semidefinite problem(SDP) through a network flow problem on a directed acyclic graph and the totally unimodular(TUM) structure. For practical large-scale inventory control, a second order cone problem(SOCP) is constructed to overcome the computational difficulty of SDP, which sacrifices a little tightness. Besides, the nonconvex linear-quadratic(LQ)control is discussed as an extension. The optimal solution of the nonconvex LQ can be computed by a conic relaxation problem.
Starting Page	9094
Ending Page	9099
File Size	154240
Page Count	6
File Format	PDF
ISBN	9789881563873
ISSN	19341768
DOI	10.1109/ChiCC.2014.6896532
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-07-28
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	TCCT, CAA
Subject Keyword	Semidefinite Symmetric matrices Transmission line matrix methods Lagrange Decomposition Optimal control Production Inventory control Linear programming Conic Optimization Nonconvex Optimization
Content Type	Text
Resource Type	Article

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