Min-cost route problems for multimodal sustainable logistics cooperation

This article addresses the pressing need for sustainable logistics practices in light of the current global climate emergency. Specifically, we tackle the problem of defining the shortest routes for various carriers in a multimodal logistics network while simultaneously reducing environmental impact. A novel aspect of our approach is that each transport demand from origin to destination is satisfied by considering all the routes within the multimodal network that intersect with the path associated with the transportation request. The primary goal is to minimise the number of circulating vehicles by fully utilising their available cargo capacity. To achieve this, we propose a mixed-integer linear programming model based on a multimodal graph. The objective function comprises various cost components, taking into account the transportation and service costs of different vehicle types (trucks, trains, ships, and aeroplanes). Additionally, the search for the optimal solution incorporates several parameters aligned with the paradigm of cooperative logistics and environmental sustainability. Specifically, pollutant emissions and payload utilisation are factored in through specifically tailored cost coefficients. A total of 3,240 test instances, derived from routes within the Italian multimodal transportation network, were generated and solved to optimality. The results underscore the effectiveness of the proposed model in addressing the aforementioned environmental concerns.