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Asymptotic Analysis of a Greedy Heuristic for the Multi-Period Single-Sourcing Problem: The Acyclic Case

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Abstract

The multi-period single-sourcing problem that we address in this paper can be used as a tactical tool for evaluating logistics network designs in a dynamic environment. In particular, our objective is to find an assignment of customers to facilities, as well as the location, timing and size of production and inventory levels, that minimizes total assignment, production, and inventory costs. We propose a greedy heuristic, and prove that this greedy heuristic is asymptotically optimal in a probabilistic sense for the subclass of problems where the assignment of customers to facilities is allowed to vary over time. In addition, we prove a similar result for the subclass of problems where each customer needs to be assigned to the same facility over the planning horizon, and where the demand for each customer exhibits the same seasonality pattern. 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. These results suggest that the greedy heuristic may be asymptotically optimal even for the cases that we were unable to analyze theoretically.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, Florida, 32611-6595

    H. Edwin Romeijn

  2. Saïd Business School, Park End Street, Oxford, OX1 1HP, United Kingdom

    Dolores Romero Morales

Authors
  1. H. Edwin Romeijn
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  2. Dolores Romero Morales
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Romeijn, H.E., Morales, D.R. Asymptotic Analysis of a Greedy Heuristic for the Multi-Period Single-Sourcing Problem: The Acyclic Case. Journal of Heuristics 10, 5–35 (2004). https://doi.org/10.1023/B:HEUR.0000019984.80186.48

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  • DOI: https://doi.org/10.1023/B:HEUR.0000019984.80186.48

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