An adaptive dynamic programming algorithm for dynamic fleet management, II: Multiperiod travel times

In a companion paper (Godfrey and Powell 2002) we introduced an adaptive dynamic programming algorithm for stochastic dynamic resource allocation problems, which arise in the context of logistics and distribution, fleet management, and other allocation problems. The method depends on estimating separable nonlinear approximations of value functions, using a dynamic programming framework. That paper considered only the case in which the time to complete an action was always a single time period. Experiments with this technique quickly showed that when the basic algorithm was applied to problems with multiperiod travel times, the results were very poor. In this paper, we illustrate why this behavior arose, and propose a modified algorithm that addresses the issue. Experimental work demonstrates that the modified algorithm works on problems with multiperiod travel times, with results that are almost as good as the original algorithm applied to single period travel times.