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mow - A ROUTING SYSTEM BASED ON SPACEFILLING CURVES John J...

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A ROUTING SYSTEM BASED ON SPACEFILLING CURVES John J. Bartholdi, III * April 11, 1995; revised April 1, 2003 Abstract We describe some fundamental issues in routing and distribution and illustrate them in a case study, which shows how to build a commercial-quality routing sys- tem in one day and with no computer. 1 Routing and distribution Distribution is the getting the product to the customer. The management of distribu- tion has continued to change rapidly after deregulation in the early 1980’s and with the development of new technologies such as on-board computers, radio, and global- positioning systems. It is cheapest to ship long distance by train and so railroads are capturing an in- creasing amount of long-haul freight. Small, urgently-needed goods move by more expensive plane. But currently the bulk of freight, and all local freight, is handled by truck. The basic problem faced by a distribution manager, then, is this: How best to co¨ordinate a fleet of vehicles to deliver goods to their destination 1 . One would like to accomplish many things, some of which work at cross-purposes, such as Allocate the goods among the vehicles so that not too many trucks are required. * Copyright c 1995,6 John J. Bartholdi, III. All rights reserved. The author may be contacted at [email protected] . 1 For a journalist’s view of one trucking company, see Rounds, 1993. 1
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Route each truck to reduce the travel time. In addition, there may be constraints of various types that limit one’s choices: A trailer can hold only a limited volume of freight. The axle weight of a trailer must lie within certain limits specified by law. It may be that delivery to a customer is allowed only within a certain “time- window”, such as between 08:00 and 10:00. A driver may work only for a limited time (say no more than ten hours). Routing is just one aspect of the problem of distribution. There must be sufficient room in the shipping department to accumulate the freight in advance so it can be loaded on the trailer in reverse order of delivery. (Otherwise either the trailer must be unloaded and reloaded at each stop; or else the delivery sequence is arbitrarily deter- mined by the order in which the freight happened to have been loaded.) The simplest abstraction of the problem of routing is the “Travelling Salesman Problem” (TSP) which can be formalized as: Given n locations, find a tour of minimum total length. (A tour is a path that visits all the required locations and then returns to its origin). The TSP is a famous problem because it is simple to understand but hard to solve, at least for instances of realistic size. For a survey of solution techniques see Lawler et al., 1985. Let us look at a commercial routing problem . . . 2 Meals on Wheels Senior Citizen Services, Inc. is a private, nonprofit corporation in Atlanta, Georgia whose purpose is to provide social services for the elderly, especially the elderly poor, in Fulton County. One of their major services is the “Meals on Wheels” program
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