A Branch-and-Cut Algorithm for the Dial-a-Ride Problem
Operations Research
An Exact Algorithm for the Pickup and Delivery Problem with Time Windows
Operations Research
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Unprecedented pace of urbanization and rising income levels have fueled the growth of car ownership in almost all newly formed mega cities. Such growth has congested the limited road space and significantly affected the quality of life in these mega cities. Convincing residents to give up their cars and use public transport is the most effective way in reducing congestion, however, even with sufficient public transport capacity, the lack of last-mile (from the transport hub to the destination) travel services is the major deterrent for the adoption of public transport. Due to the dynamic nature of such travel demands, fixed-size fleets will not be a cost-effective approach in addressing last-mile demands. Instead, we propose a dynamic, incentive-based mechanism that enables taxi ride-sharing for satisfying last-mile travel demands. On the demand side, travelers would register their last-mile travel demands in real-time, and they are expected to receive ride arrangements before they reach the hub, on the supply side, depending on the real-time demands, proper incentives will be computed and provided to taxi drivers willing to commit to the last-mile service. Multiple travelers will be clustered into groups according to their destinations, and travelers belonging to the same group will be assigned to a taxi, while each of them paying fares considering their destinations and also their orders in reaching destinations. In this paper, we provide mathematical formulations for demand clustering and fare distribution. If the model returns a solution, it is guaranteed to be implement able. For cases where it is not possible to satisfy all demands despite having enough capacity, we propose a two-phase approach that identifies the maximal subset of riders that can be feasibly served. Finally, we use a series of numerical examples to demonstrate the effectiveness of our approach.