Optimal Number of Facilities in Flow Covering Location Problems

Abstract

This paper develops an analytical model for determining the number of flow demand facilities that cover trips. The proportions of covered trips within a specified deviation distance are derived for grid and random patterns of facilities. The analytical expressions for the proportions of covered trips demonstrate how the deviation distance, the number of facilities, and the pattern of facilities affect the level of coverage. The number of facilities required to achieve a certain level of coverage is then obtained. The coverage level is represented as the combination of the deviation distance and the proportion of covered trips. The coverage by the second nearest facility is also considered for the random pattern to deal with the case where facilities are subject to failures. The model incorporates any level of coverage and provides a versatile framework for determining the number of flow demand facilities.