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An asymptotically optimal greedy heuristic for the multiperiod single‐sourcing problem: The cyclic case

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  • H. Edwin Romeijn
  • Dolores Romero Morales

Abstract

The dynamics of the environment in which supply chains evolve requires that companies frequently redesign their logistics distribution networks. In this paper we address a multiperiod single‐sourcing problem that can be used as a strategic tool for evaluating the costs of logistics network designs in a dynamic environment. The distribution networks that we consider consist of a set of production and storage facilities, and a set of customers who do not hold inventories. The facilities face production capacities, and each customer's demand needs to be delivered by a single facility in each period. We deal with the assignment of customers to facilities, as well as the location, timing, and size of inventories. In addition, to mitigate start and end‐of‐study effects, we view the planning period as a typical future one, which will repeat itself. This leads to a cyclic model, in which starting and ending inventories are equal. Based on an assignment formulation of the problem, we propose a greedy heuristic, and prove that this greedy heuristic is asymptotically feasible and optimal in a probabilistic sense. We illustrate the behavior of the greedy heuristic, as well as some improvements where the greedy heuristic is used as the starting point of a local interchange procedure, on a set of randomly generated test problems. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 412–437, 2003

Suggested Citation

  • H. Edwin Romeijn & Dolores Romero Morales, 2003. "An asymptotically optimal greedy heuristic for the multiperiod single‐sourcing problem: The cyclic case," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(5), pages 412-437, August.
    • Handle: RePEc:wly:navres:v:50:y:2003:i:5:p:412-437
    DOI: 10.1002/nav.10068
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    References listed on IDEAS

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    1. H. Edwin Romeijn & Dolores Romero Morales, 2001. "Generating Experimental Data for the Generalized Assignment Problem," Operations Research, INFORMS, vol. 49(6), pages 866-878, December.
    2. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    3. H. Edwin Romeijn & Nanda Piersma, 2000. "A Probabilistic Feasibility and Value Analysis of the Generalized Assignment Problem," Journal of Combinatorial Optimization, Springer, vol. 4(3), pages 325-355, September.
    4. Fleischmann, Bernhard, 1993. "Designing distribution systems with transport economies of scale," European Journal of Operational Research, Elsevier, vol. 70(1), pages 31-42, October.
    5. Duran, F., 1987. "A large mixed integer production and distribution program," European Journal of Operational Research, Elsevier, vol. 28(2), pages 207-217, February.
    6. Michael A. Trick, 1992. "A linear relaxation heuristic for the generalized assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(2), pages 137-151, March.
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    Cited by:

    1. Balachandran Vaidyanathan & Ravindra K. Ahuja, 2010. "Fast Algorithms for Specially Structured Minimum Cost Flow Problems with Applications," Operations Research, INFORMS, vol. 58(6), pages 1681-1696, December.
    2. Wei Huang & H. Edwin Romeijn & Joseph Geunes, 2005. "The continuous‐time single‐sourcing problem with capacity expansion opportunities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 193-211, April.
    3. David A. Goldberg & Martin I. Reiman & Qiong Wang, 2021. "A Survey of Recent Progress in the Asymptotic Analysis of Inventory Systems," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1718-1750, June.
    4. Richard Freling & H. Edwin Romeijn & Dolores Romero Morales & Albert P. M. Wagelmans, 2003. "A Branch-and-Price Algorithm for the Multiperiod Single-Sourcing Problem," Operations Research, INFORMS, vol. 51(6), pages 922-939, December.
    5. Ravindra K. Ahuja & Wei Huang & H. Edwin Romeijn & Dolores Romero Morales, 2007. "A Heuristic Approach to the Multi-Period Single-Sourcing Problem with Production and Inventory Capacities and Perishability Constraints," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 14-26, February.

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