A scalable combinatorial benders decomposition for the Stochastic Dial-a-Ride Problem

Nowadays, Demand-Responsive Transport companies can help the elderly or disabled citizens in their everyday journeys as well as provide an important link between big cities and their outer suburbs. In practice, many of those trips are scheduled in advance but many others are asked on the fly (online) by the users while the drivers are already on their routes. To answer those online requests, dispatching centers often rely on fast heuristics based on some myopic objectives. However, this deteriorates the flexibility of the dispatch over time. This paper shows the potential of a thorough optimization of the planning of the vehicles at the start of the day under the hypothesis that the transport company is able to forecast the requests that will arrive during the service. Our objective is to design an initial set of routes for the vehicles that maximizes the expected acceptance rate of future requests, since the ones scheduled in-advance are mandatory. In this prospect, we propose a Combinatorial Benders Decomposition framework to solve the so-called Stochastic Dial-a-Ride Problem. A key ingredient for the success of this solver is the use of a clustering-based initialization of the Master Problem. The computational results show the effectiveness of this approach when applied to instances extracted from the literature as well as from actual services provided by Padam Mobility, an international company in Shared Mobility Systems. The proposed method provides a substantial performance gain though traditional heuristics are kept to manage online insertions afterward.