Pickup and delivery routing with hub transshipment across flexible time periods for improving dual objectives on workload and waiting time

•Policy design is used to improve dual objectives on workload and sojourn time.•A square root law of tour length is theorized.•A routing policy based on hub transshipment across flexible time periods is analyzed.•A case study on the courier service of a large hospital is presented.

In contrast to developing routing algorithms, operational policy design of courier services is addressed in this paper with the objective of reducing both courier workload and customer waiting time. A square root law of tour length is verified, extending the literature. A new policy of hub transshipment across flexible time periods is evaluated by mean-value analysis of stochastic routing. Boundary conditions on arrival rate, territory size and transshipment probability in which the new policy outperforms a traditional periodical routing policy are derived. Finally, the effectiveness of the new policy is demonstrated by applying to a large hospital case.