The problem of efficient districting
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The problem of efficient districting improving distributed operations depends on efficient partitioning of a service area into districts -
Dirk Cattrysse, Dirk Van Oudheusden and Tsippy Lotan in which arcs need to be serviced (such as: mail delivery, waste collection, SflOW removal, salt spreading etc). A lot of literature exists on both types of routeings and their variants. For node-
Districting involves a partition of a large area into subareas (districts) in order to maintain distributed opera-
tions within each sub-area. In general, each district
contains at least one local centre (depot) and is independently responsible for the operations performed within its
routeing see, for example, reviews by Laporte (1992) and Fisher (1995), for arc-routeing Eiselt (1995a & 1995b), and Assad and Golden (1995) provide recent
borders. The operations within each district typically involve roilteing. There is a lot of work in the literature
reviews.
on location of depots and ou routeing from given depots to
a given network. However, very little work exists on the del c'rminatioii of district borders in a way that would ensure efficient operations. In this article the ant hors highlight the importance of performing good districting
Not surprisingly, the state of the art on combined location-routeing problems (LRP) is much less developed than that associated with either pure location or pure routeing problems. In his survey on LRP, Laporte (1988) claims that this deficiency is
as a bridging step between location and routeing, and emphasise its potential to obtain improved operation
mainly due to lack of recognition that in many cases
schemes.
the two problems should be dealt with simultaneously, and due to the increased complexity of LRP (LRP are, in general, NP-hard). Furthermore, there is often an inherent difference between location and routeing problems. Whereas location decisions are of a more static and strategic nature, routeings are more operational and dynamic, hence the distinction between the two is in many cases natural.
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Motivation and background Problems of location on the one hand, and routeing on the other hand have been receiving continuous and extensive attention both in theory and in practical applications. Location analysis deals with the problem of locating one or several facilities such that a certain economical criterion is optimised. Facilities
We define districting as a partition of a large area into sub-areas (districts) such that each district is responsible for the operations performed within its
can be plants, warehouses, schools, hospitals,
borders. Typically each district contains at least one local centre (depot) which is independently responsible for the performance of a series of operations.
administrative buildings, waste material dumps, ambulance and fire engine depots etc, Labbe et al. (1995) provided a recent survey of location on
Many of the operations within each district frequently involve routeing where routes start and end at the depot.
networks.
As for r
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