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Zbl 0694.90044
Anily, S.; Federgruen, A.
One warehouse multiple retailer systems with vehicle routing costs. (English)
[J] Manage. Sci. 36, No.1, 92-114 (1990). ISSN 0025-1909; ISSN 1526-5501/e

Summary: We consider distribution systems with a depot and many geographically dispersed retailers each of which faces external demands occurring at constant, deterministic but retailer specific rates. All stock enters the system through the depot from where it is distributed to the retailers by a fleet of capacitated vehicles combining deliveries into efficient routes. Inventories are kept at the retailers but not at the depot. \par We wish to determine feasible replenishmnt strategies (i.e., inventory rules and routing patterns) minimising (infinite horizon) long-run average transportation and inventory costs. We restrict ourselves to a class of strategies in which a collection of regions (sets of retailers) is specified which cover all outlets: if an outlet belongs to several regions, a specific fraction of its sales/operations is assigned to each of these regions. Each time one of the retailers in a given region receives a delivery, this delivery is made by a vehicle who visits all other outlets in the region as well (in an efficient route). \par We describe a class of low complexity heuristics and show under mild probabilistic assumptions that the generated solutions are asymptotically optimal (within the above class of strategies). We also show that lower and upper bounds on the system-wide costs may be computed and that these bounds are asymptotically tight under the same assumptions. A numerical study exhibits the performance of these heuristics and bounds for problems of moderate size.

MSC 2000:: *90B05 Inventory management

Keywords: logistics; distribution systems; depot; geographically dispersed retailers; capacitated vehicles; efficient routes; feasible replenishmnt strategies; inventory rules; routing patterns; infinite horizon; transportation and inventory costs; heuristics

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