Dynamic parcel pick-up routing problem with prioritized customers and constrained capacity via lower-bound-based rollout approach

Abstract

In this study, we address a parcel pick-up routing problem that involves prioritized customers and constrained capacity, in the context of dynamic vehicle routing. The number and locations of potential customers are known in advance, but the sizes of their parcels are stochastic and unknown until their requests reveal. To tackle this problem, we formulate it as a Markov decision process (MDP), where dynamic requests are handled periodically. Specifically, in each stage, if the total size of the dynamic customers’ parcels that have accumulated fits within the vehicle’s remaining capacity, all of the requests are accepted. Otherwise, requests are accepted according to customers’ priorities. Our objective is to minimize the total expected waiting time of customers. However, the multi-dimensional MDP state causes the curse of dimensionality, making the problem challenging to solve. Therefore, we propose a rollout approach to solve the problem. First, unlike traditional rollout-related methods, we derive a lower bound of the post-decision state’s value function and use it to develop a base policy. Second, we apply a post-decision rollout algorithm to determine an online rollout policy that theoretically satisfies the rolloutimproving property. In our numerical study, we compare our rollout policy with a general value function approximation-based rollout policy and a model-independent greedy method. Our results show that our rollout policy outperforms both of them with a significant advantage, while the latter two methods have ups and downs on both sides.