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A Model-Based Approach and Analysis for Multi-Period Networks

Author

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  • Seyed Ahmad Hosseini

    (Sabanci University)

Abstract

The aim of this contribution is to address a general class of network problems, very common in process systems engineering, where spoilage on arcs and storage in nodes are inevitable as time changes. Having a set of capacities, so-called horizon capacity which limits the total flow passing arcs over all periods, the min-cost flow problem in the discrete-time model with time-varying network parameters is investigated. While assuming a possibility of storage or and spoilage, we propose some approaches employing polyhedrals to obtain optimal solutions for a pre-specified planning horizon. Our methods describe some reformulations based on polyhedrals that lead to LP problems comprising a set of sparse subproblems with exceptional structures. Considering the sparsity and repeating structure of the polyhedrals, algorithmic approaches based on decomposition techniques of block-angular and block-staircase cases are proposed to handle the global problem aiming to reduce the computational resources required.

Suggested Citation

  • Seyed Ahmad Hosseini, 2013. "A Model-Based Approach and Analysis for Multi-Period Networks," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 486-512, May.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:2:d:10.1007_s10957-012-0183-6
    DOI: 10.1007/s10957-012-0183-6
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    References listed on IDEAS

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    1. D. Klingman & A. Napier & J. Stutz, 1974. "NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems," Management Science, INFORMS, vol. 20(5), pages 814-821, January.
    2. Stefansson, Hlynur & Sigmarsdottir, Sigrun & Jensson, Pall & Shah, Nilay, 2011. "Discrete and continuous time representations and mathematical models for large production scheduling problems: A case study from the pharmaceutical industry," European Journal of Operational Research, Elsevier, vol. 215(2), pages 383-392, December.
    3. L. R. Ford & D. R. Fulkerson, 1958. "Constructing Maximal Dynamic Flows from Static Flows," Operations Research, INFORMS, vol. 6(3), pages 419-433, June.
    4. Roman L. Weil & Paul C. Kettler, 1971. "Rearranging Matrices to Block-Angular form for Decomposition (And Other) Algorithms," Management Science, INFORMS, vol. 18(1), pages 98-108, September.
    5. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    6. Moin, N.H. & Salhi, S. & Aziz, N.A.B., 2011. "An efficient hybrid genetic algorithm for the multi-product multi-period inventory routing problem," International Journal of Production Economics, Elsevier, vol. 133(1), pages 334-343, September.
    7. Xiaoqiang Cai & Dan Sha & C. K. Wong, 2007. "Time-Varying Network Optimization," International Series in Operations Research and Management Science, Springer, number 978-0-387-71215-4, July-Dece.
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