Automatic teller machines and gasoline service stations are two examples of a growing number of "discretionary service facilities." In consuming service from these facilities, a significant fraction of customers do so on an otherwise preplanned trip (e.g., on the daily commute to and from work). A system planner, in determining the best locations of such facilities, is more concerned with placing the facilities along paths of customer flow rather than, say, near the center of a cluster of residences or work places. We formally model this problem and present a method for determining the optimal locations of m discretionary service facilities so as to intercept the maximum possible potential customer flow. We also show how to determine the minimal number of facilities required to intercept a prespecified fraction of total customer flow. Computational results are included.-2-