Open Access

Niklas Tuma, Manuel Ostermeier, Alexander Hübner

• Companies commonly outsource transportation logistics to logistics service providers (LSPs) to reduce complexity and leverage economies of scale. The coordination between shippers and LSPs for regional distribution is typically organized through zone-based tariffs, in which shippers propose joint customer deliveries to an LSP. This approach decouples customer allocation and pricing from the delivery sequence, simplifying planning. To minimize costs, shippers must form customer clusters that meet capacity and specific distance constraints, known as detour limits. These detour limits ensure reasonable driving distances within a customer cluster. Despite their widespread application in practice, zone tariffs have received little research attention to date. Early related research either addresses dedicated case applications with a specific single detour limit or relies on exact methods suited only for small instances. In contrast, general real-world applications involve hundreds ofCompanies commonly outsource transportation logistics to logistics service providers (LSPs) to reduce complexity and leverage economies of scale. The coordination between shippers and LSPs for regional distribution is typically organized through zone-based tariffs, in which shippers propose joint customer deliveries to an LSP. This approach decouples customer allocation and pricing from the delivery sequence, simplifying planning. To minimize costs, shippers must form customer clusters that meet capacity and specific distance constraints, known as detour limits. These detour limits ensure reasonable driving distances within a customer cluster. Despite their widespread application in practice, zone tariffs have received little research attention to date. Early related research either addresses dedicated case applications with a specific single detour limit or relies on exact methods suited only for small instances. In contrast, general real-world applications involve hundreds of customers and heterogeneous detour limit options. We address this gap by tailoring an Adaptive Large Neighborhood Search–based matheuristic that features problem-specific operators and two adaptive mechanisms. Combining heuristic tour generation with a set partitioning model, our approach efficiently handles multiple detour limits. Numerical studies, including a case study and benchmark instances with up to 1000 customers, demonstrate the approach’s scalability and effectiveness. This study provides the first comprehensive analysis of how different detour limitations relate and affect routing efficiency as well as zone tariff design, revealing key trade-offs between cost and travel distance. We identify an efficiency threshold with moderate detour values, offering actionable guidance for the design of real-world zone-based tariffs.…