Some finite horizon dispatching problems

Abstract

An arrival process (N(t), 0 = or t = or T) is to be dispatched one or more times in the time interval (0,T). The problem is to determine the optimal number of dispatches K given there are n available and to determine sequentially the epochs of dispatch tau sub 1, ..., tau sub K. There are two trade off costs c sub w and c sub d, which are respectively the cost per unit time of a waiting customer and the cost of dispatching a single unit. A general result is found which gives one optimal tau sub 1, ..., tau sub K for fixed K (i.e. the K-optimal policy) under certain regularity conditions. This is used to obtain suboptimal policies for multiple dispatching of a Poisson process and single dispatching of a birth-death process. Applications to problems in transportation, repair facilities and insect-control are indicated. (Author)