On the Optimum Location of Checking Stations

Abstract

Items move uniformly from the initial to the terminal point of a route. Checking stations that detect and repair imperfect items can be located along the route. If the condition of an item changes from “perfect” to “imperfect,” an operating cost is incurred which increases with the distance traveled in the imperfect condition to the nearest checking station. Given an arbitrary increasing operating cost function, data on the likelihood of failure of an item at any point enroute, the volume of traffic per unit time and the cost per unit time of maintaining a checking station, the dynamic programming technique is used to find the number and placement of checking stations which minimize the sum of operating and checking costs. The model is applicable to the problem of locating “hot-box” detectors along a railroad right-of-way. The analysis of the convex cost functional involved may be of independent interest.