Elimination of Source A and B Errors in p-Median Location Problems

The p-median problem is a powerful tool in analyzing facility location options when the goal of the location scheme is to minimize the average distance that demand must traverse to reach its nearest facility. It may be used to determine the number of facilities to site, as well as the actual facility locations. Demand data are frequently aggregated in p-median location problems to reduce the computational complexity of the problem. Demand data aggregation, however, results in the loss of locational information. This loss may lead to suboptimal facility location configurations (optimality errors) and inaccurate measures of the resulting travel distances (cost errors). Hillsman and Rhoda (1978) have identified three error components: Source A, B, and C errors, which may result from demand data aggregation. In this article, a method to measure weighted travel distances in p-median problems which eliminates Source A and B errors is proposed. Test problem results indicate that the proposed measurement scheme yields solutions with lower optimality and cost errors than does the traditional distance measurement scheme.     

PREHISTORIC FLINT MINES AND THEIR IDENTIFICATION AS SOURCES OF RAW MATERIAL

This paper is a statistical and geological study of the results of analysis of flint from British and West European flint mines, carried out by emission and atomic absorption spectroscopy. Groups of flint specimens were studied from each geographically separate flint mining area. Flints were analysed for a group of easily measured trace elements shown by previous work to be generally present. The ratios between the trace elements form a consistent pattern for each flint mine and statistically valid differences of pattern can be recognized between different flint mines. A geological investigation shows that the measured trace elements may be derived from clay minerals and explains geographical and statistical variation in the composition of flint in terms of its mode of origin in the chalk. An advanced statistical technique allows individual flint specimens of unknown origin to be attributed by their composition to one or other of the identified flint sources. The archaeological implications of this study are discussed.