Location-Routing Problem for the multi-depot three-echelon network with smart lockers

The surge in online shopping is significantly changing the retail industry and reshaping customer buying behavior. This shift has prompted a move from the conventional Business-to-Business (B۲B) model to the Business-to-Customer (B۲C) one, which requires the handling of smaller items and an increase in the number of drop-off points. This study proposes a location-routing problem within the e-commerce supply chain domain, where customers can be served simultaneously via two different delivery methods: Customer Pick-up (CP) using parcel lockers and traditional Home Delivery (HD). The proliferation of e-commerce makes the last loop of a supply chain expensive and time-consuming. Due to these challenges, this research aims to present a mixed integer linear formulation in order to devise a more efficient distribution system from an economic perspective. Moreover, because of the high-dimensional solution space issues, a simulated annealing algorithm is developed to solve the problem for various sizes of instances. The results of the mathematical approach and meta-heuristic are compared in computational experiments, which demonstrate the effective performance of the aforementioned algorithm in converging toward an optimum or the best-known solution.