Modeling, Design and Optimization of Demand Responsive Services, such as Ridesharing, Ride-haling, Carsharing, Feeders, ADA Paratransit, Innovative Transit/Logistic Solutions
- Applications – Vehicle Routing Problems
- Ridesharing/Ride-haling/Carsharing: These services have the potential to change the future, in particular when paired with the rise of Autonomous Vehicle Technologies. The math models associated with them are complex and attract the attention of the optimization research community. Finding stable solutions with fair cost allocation will be the key for attracting more customers.
- Transit for low density areas: Urban sprawl is one of the most evident phenomena characterizing the development of urban areas in the last few decades. My research interest and objective are to look for innovative transit designs which would efficiently provide feasible and sustainable solution to to the “first/last mile” problem.
- ADA Paratransit: These services have been experiencing a tremendous growth in the last decades and their demand is expected to further expand. However, they struggle to operate efficiently, heavily relying on subsidies to maintain their large operations. Paratransit operations are a typical practical application for the well known NP-Hard Pickup and Delivery Problem with Time Windows (PDPTW), a variant of the Vehicle Routing Problem (VRP), which can also be expanded to Multiple Depots (MDVRP or MDPDPTW). I am interested in the design, optimization and operations of these services.
- Methodological Approaches
- Continuous Approximations: I am inclined to model complex systems using continuous approximations whenever reasonable and justifiable. The main purpose of this approach is to obtain analytical insights of complex decision problems with as little information as possible. These approximate models are easier for humans to comprehend and they provide elegant, handy but also potentially powerful tools to help solving many complicated decision problems. The challenge resides in recognizing when the tradeoff between modeling approximations and usefulness of the results is acceptable.
- Algorithm Development: Computers are extremely fast, but they are also “brainless”. I am interested in the development of algorithms and heuristics, especially within the scheduling context, to solve complex problems in reasonable time.
- Optimization Modeling and Cuts Development: Most optimization problems involving integer variables are too hard to solve, because of their NP-completeness. Research aiming to fine tune their formulation adding effective constraints is significant. A constraint is classified as valid if it reduces the size of the relaxed feasible region, ideally making it the convex hull of the integer feasible solutions. Another category of constraints are the so called “logic cuts”. Their purpose is to reduce the feasible region by eliminating dominated integer feasible solutions and they can be indeed very effective in significantly shrinking the feasible region and considerably reducing the CPU time in the search for optimality.
- Simulation: I use simulation extensively usually as a test tool for running experiments.