A Dynamic and Stochastic Cumulative Capacitated Vehicle Routing Problem

The cumulative capacitated vehicle routing problem (CCVRP) is a variant of the classical capacitated vehicle routing problem in which the objective is the minimization of customers’ total waiting time prior to service. Inspired by the first-mile pick-up service within 3rd-Party Logistics operations, we study a dynamic and stochastic variant of the CCVRP. In this variant, a capacitated vehicle undertakes a single tour to collect customers’ parcels, taking into account stochastic service requests, stochastic service cancellations, and stochastic demand (i.e., changes in parcel size) simultaneously. Conditional on maximizing the usage of the vehicle’s capacity, we minimize the total waiting time of both customers who are served and those who request services but are not served due to cancellation or capacity violation. We formulate this problem as a Markov decision process and solve it using a hybrid approach that combines approximate dynamic programming and rollout algorithm. Our main contributions include (i) the construction of the stage cost that leverages a property of the Poisson process, and (ii) consideration of service fairness-based acceptance/rejection rule in response to excessive stochastic service requests. In the numerical study, our approach is examined to outperform an 2-Opt-based re-optimization policy in terms of both customers’ waiting time and service-request satisfying rate. More importantly, computational results heuristically show that there is no cost to adopting the service fairness-based rule, which is obviously a valuable managerial insight.