A two-step large neighborhood search for a collaborative two-tier city logistics system

The rapid transport of freight is an essential feature of modern societies and an enabling factor for economic trade and growth. Nevertheless, the negative impact of freight transportation in urban areas poses challenges for Logistics Service Providers (LSPs) as well as for municipalities. In this context, a centrally coordinated Two-Tier City Logistics System (2T-CLS), in which LSPs voluntarily agree to collaborate with each other, has the potential to reduce both economic and environmental impact costs. In order to plan such a system, it is important not only to make efficient use of the resources provided but also to have a mechanism that allocates the costs incurred to the individual LSPs. We introduce a mixed-integer linear program (MILP) formulation for the tactical planning of a 2T-CLS involving multiple LSPs that share their resources and customer demands. This MILP comprises a service network design formulation on the first tier and a vehicle routing problem formulation on the second tier, which are connected with each other. To address larger instances, we introduce an Integrative Two-Step Large Neighborhood Search with adaptive components that integrates first and second-tier decisions. In order not only to minimize the costs incurred but also to distribute them fairly, we investigate different problem-specific proportional methods, as well as more advanced game theoretical methods. Numerical experiments show that collaboration leads to average cost savings of 26.91%, which primarily stems from first-tier collaboration.