## Abstract

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 language | English |
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Pages (from-to) | 451-473 |

Number of pages | 23 |

Journal | European Journal of Operational Research |

Volume | 79 |

Issue number | 3 |

DOIs | |

State | Published - 22 Dec 1994 |

## Keywords

- Distribution
- Heuristics
- Inventory
- Partitioning problems
- Routing problems