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Journal of Applied Mathematics
Volume 2014, Article ID 825058, 25 pages
Research Article

A Decomposition-Based Approach for the Multiperiod Multiproduct Distribution Planning Problem

Faculty of Engineering and Natural Sciences, Sabanci University, 34956 Istanbul, Turkey

Received 27 January 2014; Revised 9 July 2014; Accepted 13 July 2014; Published 31 August 2014

Academic Editor: X. Zhang

Copyright © 2014 S. Ahmad Hosseini 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 address the most general case of multiperiod, multiproduct network planning problems, where we allow spoilage on arcs and storage at nodes. In our models, all network parameters change over time and products. The minimum-cost flow problem in the discrete-time model with varying network parameters is investigated when we allow storage and/or spoilage, and some reformulation techniques employing polyhedrals are developed to obtain optimal solutions for a predefined horizon. Our methods rely on appropriate definitions of polyhedrals and matrices that lead to LP problems comprising a set of sparse subproblems with special structures. Knowing that computational expenses of solving such a large-scale planning problem can be decreased by using decomposition techniques, the special structure of polyhedrals is utilized to develop algorithmic approaches based on decomposition techniques to handle the global problem aiming to save computational resources.