The pickup and delivery problem with transshipments: Critical review of two existing models and a new formulation

• This paper addresses the pickup and delivery problem with transshipments (PDP-T) and the pickup and delivery problem with time windows and transshipments (PDPTW-T). • We make revisions and modifications to two state-of-the-art models. • We present a new model and generate several benchmarks for future comparison. • The solvable scale is increased significantly by using the new model. • Computational time is reduced by 96% and 40% for PDP-T and PDPTW-T, respectively. The pickup and delivery problem with transshipments (PDP-T) is generalized from the classical pickup and delivery problem (PDP) by allowing the transfer of requests between vehicles. After considering the time window constraints, the PDP-T is further generalized to the pickup and delivery problem with time windows and transshipments (PDPTW-T). In this paper, we review two state-of-the-art models for the PDP-T and PDPTW-T. We point out the possible issues existing in the models and provide our revisions. In addition, we develop a new mixed-integer linear programming formulation to solve the PDP-T and PDPTW-T. The performance of the proposed model is evaluated by solving 340 generated PDP-T instances and 360 open-access PDPTW-T instances. Computational results show that the proposed model outperforms the existing models in terms of solution quality and computing time. PTP-T instances with up to 25 requests and 2 transfer stations are solved to optimality by using the proposed model. As a comparison, the best-known benchmarks in the literature are instances with 5 requests and 1 transfer station. In addition, the computing time is significantly reduced. In our experiments, the average computational time for solving PDP-T is reduced by 96%. For PDPTW-T instances, the solvable scale is increased from 3 requests and 4 transfer stations to 5 requests and 4 transfer stations. The average computing time is reduced by 40%.