ADP- and rollout-based dynamic vehicle routing for pick-up service via budgeting capacity

We address a dynamic parcel pick-up problem for a capacitated vehicle, which involves collecting customers’ parcels and handling service cancellations and requests. In the existing studies, service cancellation and/or the reuse of the released capacity from cancellation have not been considered by state-based decisions (i.e., decision policy) with incorporating stochastic information into decision-making. Aimed at minimizing the expected total travel distance while maximizing vehicle capacity usage, we formulate the problem as a Markov decision process and develop an approximate dynamic programming method. First, we aggregate the post-decision state, consisting of multiple numerical and set components, into a two-dimensional numerical vector by budgeting the vehicle’s capacity for future requests. This results in a decrease in the size of the state searching space from exponential to quadratic. Second, we use the aggregation vector to approximate the post-decision state and obtain an offline policy in a lookup-table representation through Approximate Value Iteration. Third, we apply the post-decision rollout algorithm online with the offline policy as its base policy, resulting in an online rollout policy. To evaluate our approaches, we conduct two sets of computational experiments with two stepsize rules (i.e., constant stepsize rule and 1/n stepsize rule) together with a \(\varepsilon\) $\epsilon$ -heuristic exploration measure adopted in developing offline base policy. The first set benchmarks a dynamic programming-solvable optimal policy on a simplified model to evaluate the optimality degree of our solving method. The second set compares our rollout policy with both the counterpart base policy and a 2-Opt-based heuristic, verifies its performance advantage, provides practical application insights, and analyzes its sensitivity to problem-setting parameters.