Waiting Strategies for Anticipating Service Requests from Known Customer Locations

This paper considers a dynamic and stochastic routing problem in which information about customer locations and probabilistic information about future service requests are used to maximize the expected number of customers served by a single uncapacitated vehicle. The problem is modeled as a Markov decision process, and analytical results on the structure of the optimal policy are derived. For the case of a single dynamic customer, we completely characterize the optimal policy. Using the analytical results, we propose a real-time heuristic and demonstrate its effectiveness compared with a series of other intuitively appealing heuristics. We also use computational tests to determine the heuristic value of knowing both customer locations and probabilistic information about future service requests.