National Center for Geographic Information and Analysis A Comparison of Strategies for Data Storage Reduction in Location-Allocation Problems

Many solution techniques for discrete location-allocation problems make use of a sorted distance strings data structure in order to speed processing time. Such data structures are commonly used, for example, within interchange heuristics and lagrangian relaxation codes. The primary drawback to distance strings is that in a standard computer architecture they require approximately 50% additional memory storage in comparison to a standard distance matrix. This is due to the fact that distance strings must store not only distances, but also the order of the nodes sorted by increasing distance. To reduce the additional memory requirements of distance strings, researchers such as Hillsman [1980] and Densham and Rushton [1992a] have proposed a strategy for cutting the distance strings to include only sets of relatively close neighbor nodes. This has become an important implementation issue for solving relatively large locationallocation problems. In fact, the new Location-Allocation module of the ARC/Info GIS system uses a distance string structure and a string cutoff option to save storage and processing time. The danger in employing only partial distance strings is that if too few distance entries are stored in the distance strings, heuristic or algorithmic performance may be compromised in that the quality of the solutions generated may be less than desirable. This paper tests the effects on solution quality of imposing different distance string definitions and sizes. The goal is to establish guidelines concerning the degree to which the distance strings data structure may be reduced for memory savings without adversely affecting solution quality. The paper proposes and compares two alternative methods to that of Hillsman and of Densham and Rushton for the selection of nodes to be included within the distance strings data structure. We show that the two new alternative methods for defining distance strings appear to outperform the earlier approach. The results of this paper can be used to aid users in determining the extent that distance string cutoffs should be employed in application as well as aid in the development of location modeling software.