Dynamic multi-period vehicle routing : approximate value iteration based on dynamic lookup tables

We consider a dynamic mult-period vehicle routing problem with stochastic service requests. Requests occur within the days, i.e., periods and can be either accepted for same-day service or postponed to the following period. The objective is to maximize the number of same-day services over all periods with respect to limited time per period. For the single-period version of the problem, the existing anticipatory time budgeting approach (ATB) allows intra-period anticipation of future requests. ATB estimates the expected number of future same-day services regarding the point of time and the free time budget left in the period by means of approximate value iteration. We extend ATB to mATB considering free time budget of the current and following period to allow inter-period anticipation. Since the consideration of multiple periods leads to an exponential increase in the state space size, we combine approximate value iteration with a dynamic lookup table (DLT) for dynamic adaptions of the state space partitioning. Computational studies show that the DLT is mandatory to achieve inter-period anticipation. keywords: multi-period dynamic vehicle routing, stochastic requests, time budget, approximate dynamic programming, approximate value iteration, dynamic lookup table