The Dial-a-Ride Problem with School Bell Time Adjustment

In this paper, we study a paratransit application in which children are transported every day from their homes to their special schools or medical-social establishments. To optimize this transportation system, the establishments collaborate to propose a joint transportation plan. We propose a new algorithm to jointly build vehicle routes that visit several establishments and simultaneously set the establishments’ opening hours. This algorithm combines a large neighborhood search, the resolution of a route-based model, and the progressive shrinkage of the planning window. It is applied to a real case from the area of Lyon in France, including 34 schools and 575 heterogeneous users served by a heterogeneous fleet of reconfigurable vehicles. On average, we show that in addition to the 10% of saving that can be expected by sharing vehicle routes between schools, 7% of additional savings can be achieved by school bell adjustment. This cost saving also decreases average user ride times and the number of vehicles required, creating longer routes that are more attractive for driver services. Funding: This work was supported by the European Union through the European Regional Development Fund [Grant RA0012500] and by the French Région Auvergne-Rhône-Alpes through the NOMAd project. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1160 .