A mathematical optimization model for cluster-based single-depot location-routing e-commerce logistics problems

This study proposes a mathematical optimization model for a two-echelon location-routing problem in the last-mile delivery e-commerce environment. The e-commerce firm delivers each customer's demand at home or through delivery points. Customers could be unavailable when the vehicle arrives at their homes. In this case, the vehicle must visit the allocated delivery points for the unavailable customer. There are several scenarios from all-present to all-absent customers. A mathematical model is proposed with six inequalities to reduce the model's complexity. In addition, two scenario reduction methods are introduced to deal with the exponential growth of the number of scenarios. We generate twelve numerical instances to evaluate the performance of the model, the scenario reduction methods, and the proposed inequalities. The model produces valid solutions. Also, the scenario reduction methods are helpful for decision-makers in the e-commerce context by reducing the number of scenarios and decreasing the complexity of managing unavailable customer scenarios.