Grocery distribution plans in urban networks with street crossing penalties

Following the emergency caused by the Covid-19 pandemic, there is the need, among other measures, to modify urban mobility plans in order to reduce the use of collective public transport, reducing the crowding of people while also preventing traffic congestion through discouraging the use of private vehicles. From this perspective, retail companies operating within cities must also reorganize themselves, considering both the unpredictable requirements of environmental sustainability and the new mobility needs calling for the promotion of bicycles and electric scooters. In this context, we deal with the need to determine minimum cost routes in urban areas for delivering orders placed through e-channels. More precisely, we face a variant of the green vehicle routing problem of heterogeneous fleets, in which the objective function includes environmental impact cost components that differ by vehicle type. Moreover, as a novel issue, attention must be paid to avoid crossing and passing close to bicycle lanes; therefore, penalties are associated with the transit of vehicles near bicycle lanes. To address this problem, we propose a mixed integer linear programming model and a matheuristic associated with it. The proposed approach is then used to analyze different scenarios derived from the transportation network of the city of Milan, Italy. Milan is one of the smartest cities in Europe from the mobility point of view but also one of the most affected by the Covid-19 pandemic, and the municipality is making a big investment to promote the use of bicycles.