Two Echelon Location Routing Problem with Simultaneous Pickup and Delivery: Mixed Integer Programming Formulations and Comparative Analysis

This paper addresses the two-echelon location routing problem with simultaneous pickup and delivery (2E-LRPSPD). The 2E-LRPSPD deals with optimally locating primary and secondary facilities, and integrating goods distribution from depots and collection from customers and secondary depots. To the best of our knowledge there is no previous study on this problem. We propose two mixed integer programming formulations for the 2E-LRPSPD. While the first formulation is a two-index node-based formulation, the second one is a two-index flow-based formulation. Moreover, a family of valid inequalities are adapted from the literature to strengthen the formulations. In order to evaluate the performances of the formulations and valid inequalities, we conduct an experimental study on the instances derived from the literature. The computational results show that the flow-based formulation produces better lower bounds than the node-based formulation on small and medium-size problems.