A Parallelizable And Approximate Dynamic Programming-Based Dynamic Fleet Management Model With Random Travel Times And Multiple Vehicle Types

This chapter presents an approximate dynamic programming-based dynamic fleet management model that can handle random load arrivals, random travel times and multiple vehicle types. Our model decomposes the fleet management problem into a sequence of time-indexed subproblems by formulating it as a dynamic program and uses approximations of the value function. To handle random travel times, the state variable of our dynamic program includes all individual decisions over a relevant portion of the history. We propose a sampling-based strategy to approximate the value function under this high-dimensional state variable in a tractable manner. Under our value function approximation strategy, the fleet management problem decomposes into a sequence of time-indexed min-cost network flow subproblems that naturally yield integer solutions. Moreover, the subproblem for each time period further decomposes by the locations, making our model suitable for parallel computing. Computational experiments show that our model yields high-quality solutions within reasonable runtimes