The general multi-retailer EOQ problem with vehicle routing costs

Shoshana Anily*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


We study the distribution problem of a single commodity from one warehouse to n geographically dispersed retailers by a fleet of capacitated vehicles. Each of the retailers faces a continuous constant and deterministic demand rate over the infinite horizon. In addition, each of the retailers is characterized by its own inventory holding cost rate. The objective a routing and replenishment strategy which minimizes the long-run average transportation and holding cost. We restrict ourselves to a class of strategies which partitions the overall region into subregions. A retailer can be assinged to several subregions: each subregions is responsible for a certain fraction of the sales of each of its retailers. We first show that the optimal solution can be bounded from below by a special partitioning problem whose solution can be given in a closed form. We then present a simple heuristic which is shown to converge to the lower-bound almost surely under mild probabilistic conditions, when the number of retailers is increased to infinity.

Original languageEnglish
Pages (from-to)451-473
Number of pages23
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - 22 Dec 1994


FundersFunder number
Natural Science Engineering Research Council Canada


    • Distribution
    • Heuristics
    • Inventory
    • Partitioning problems
    • Routing problems


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