A Mathematical Model for Optimizing Mini-Hub Locations of Distribution Centers in Urban Areas

Logistics play a vital role in the prosperity of today’s cities, but current urban
logistics delivery practices have proven problematic and to be causing various negative
effects in cities. This study proposes an alternative method for delivering cargo with the
leasing of a network of logistics hubs within urban areas for designated daily time intervals
and handcart last-mile deliveries. The objective of the study is the development of a
mathematical programming model for identifying the optimal number and locations of
hubs for serving demand with the minimum cost, as well as the optimal times during the
day for leasing the facilities, while also allocating hubs to customers. The problem is
effectively solved by applying a Lagrangian relaxation and subgradient optimization
approach. Numerical examples and a sensitivity analysis provide evidence of the
robustness of the model and its ability to be effectively applied to address real problems.