Multi-facility network location problem

Ranganath S Nuggehalli, Purdue University

Abstract

We examine the problem of locating multi-facilities on a general transportation network. The location of facilities on networks has widespread practical applications. In network location problems, transportation arteries such as roads, rivers, shipping lines, airways, aisles on factory floors, or telephone lines in a communication network, are represented as arcs of the network. Their intersections, such as bus stations, airports, river ports, work stations, flexible manufacturing systems, information processing units, and telephone switching stations are represented as nodes. The facilities are restricted to be placed on arcs or at nodes. Travel is restricted to occur only along arcs. A further assumption of network location problems is that the demand for service is generated by a finite set of points, which are usually nodes. Even when this assumption is not valid, the demand locations are often idealized as points. Multi-facility location problems involve locating a number of distinct new facilities to serve customers (or existing facilities, work stations). The new facilities may also provide service to each other, in which case the location decisions are interdependent. It is this interaction between new facilities that makes the problem difficult to solve. This research focuses on developing and evaluating solution procedures for minimizing the total weighted transportation cost, when a number of new facilities have to be located on the network. Most of the existing literature rely on the assumption that the transportation network is a tree (i.e. the network that has no cycles). This problem on general transportation networks (i.e. networks with cycles) is NP-hard. We have been able to obtain a new compact integer programming formulation for this problem. The LP relaxation of this new formulation provides a lower bound which is at least as good as the known existing methods. We have developed a heuristic based on the LP relaxation of this new formulation for locating these facilities. Limited computational results are very encouraging. We also have developed polynomial algorithms for solving multi-facility network location problems when the interactions between the new facilities exhibit certain special structures. This algorithm can also consider the costs which are not distance-related costs, but related to certain predetermined locations, thus widening its scope of application. This methodology may be used to locate warehouses, production and distribution facilities, flexible manufacturing cells, distributed information processing systems, communication switching stations, work centers in production plants, etc.

Degree

Ph.D.

Advisors

Ward, Purdue University.

Subject Area

Transportation|Management

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