Design of a two-echelon last-mile delivery model

Due to high congestion in cities and growing demand for last-mile delivery services, several companies have been implementing two-echelon distribution strategies over the past few years. Notably, the installation of urban transshipment points has gained increasing attention, used by logistics operators to transfer goods from large freight trucks to smaller and more agile vehicles for last-mile delivery. Nevertheless, the main challenge is how to decide the number and location of these facilities under the presence of demand uncertainty. In this paper, we develop a two-stage stochastic program to design two-echelon last-mile delivery networks under demand uncertainty. This approach decomposes the problem into strategic decisions (facility location) and operational decisions (daily distribution of goods). To address large-scale instances, we solve the model through the sample average approximation (SAA) technique and estimate the optimal routing costs (of the SAA counterpart) using a continuous approximation method. Using a real-world case study with more than 1300 customers from New York City, our results provide several managerial insights regarding the mix of transportation modes, facility location, and the impact of allowing the outsourcing of customer demand. We provide extensive validation of the two-stage stochastic program results through a simulation-based approach and the calculation of the value of the stochastic solutions.