Optimal Dispatching of an Infinite-Capacity Shuttle: Control at a Single Terminal

We study the optimal control of a shuttle system consisting of a single infinite-capacity carrier transporting passengers between two terminals. Passengers arrive according to independent Poisson processes, and at only one of the terminals can the dispatcher hold the carrier for more passengers. Our objective: to determine dispatching rules that minimize the long-run average of a linear passenger-waiting-time cost and a charge per trip made by the carrier. When complete information about the system state is available, and travel times are not random, we prove that it is best to dispatch the carrier if, and only if, the total number of passengers waiting at both terminals is greater than a cutoff value. To compute this cutoff value, we propose an iterative method and find that we can approximate it quite well by a simple function of system costs and parameters similar to the economic-lot-size formula. We propose a dispatching rule (which may not be optimal) for the case when only the number of passengers waiting at one terminal is known, and we compare its efficiency to that of the optimal rule that uses complete information. We outline extensions to other optimality criteria and to the case of stochastic travel times.