Solution techniques for the inter-modal pickup and delivery problem in two regions

This work addresses the routing problem faced by transportation carriers and postal services that transport small parcels in large quantities. By splitting the territory into regions, these service providers can adapt a three-part network structure and solve a pickup and delivery problem with long-hauls without direct shipments between regions. That is, bilateral cross-city and cross-country requests must be met while also fulfilling capacity and time window constraints. To address this challenge, this work limits the problem to two regions and thereby can identify the correlations and synchronization between different modes. The proposed solution approach decomposes the problem into two subproblems: a long-haul assignment that can be solved exactly, and a short-haul routing problem that must be solved heuristically. The result is an efficient matheuristic, whose quality is confirmed through a comparison with findings from previous literature; it is viable in terms of solution quality and computation time. Long-haul flexibility also influences short-haul routing cost, such that improvements of up to 22% are possible merely by increasing long-haul flexibility but not long-haul cost. Finally, realistic instances are solved based on the inter-library loan system comparing the influence of selecting train or truck on the SH routing costs.