A geometric optimization approach to the location and routing problems in modern economy

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With the development of technology, human life has seen major changes throughout the twentieth century and the last two decades in the twenty-first century. New modern ideas and technologies have been continuously adopted into our everyday life. In recent years, an increasing number of people and companies are using unmanned aerial vehicles (UAVs), electric vehicles (EVs), and sharing economy services. The literature of geometric optimization research has been focusing more on the traditional logistics and transportation problems and less on the combination of them with modern technologies. This dissertation aims to study, analyze, and solve different location and routing problems in the context of modern technologies, such as UAVs, EVs, and sharing economy platforms using a geometric optimization approach, which combines optimization with computational geometry. This dissertation studies three different projects in this direction. In the first project, we consider finding the optimal location of several charging stations for EVs in a convex polygonal region to minimize the maximum ratio between the distance traveled by EVs and the distance traveled by the internal combustion engine vehicles (ICEVs). We propose an algorithm to find the optimal solution for the problem of finding the optimal location of one charging station under this setting and then we provide efficient algorithms for finding good sub-optimal solutions when we have several charging stations. In the second project, we study a delivery routing problem where we combine the operation of a delivery truck with UAVs (a.k.a. drones) to serve all demand points in a coordinated system. In this problem, the drone can pick up a package from the truck and deliver it to a demand point and then travel back to the truck for charging its battery or initiating another delivery, while the truck is delivering packages at the same time. In the third project, we study a delivery routing problem where drones are used in a sharing economy platform to deliver packages. A delivery service carries a large batch of packages to a neighborhood using a truck and then crowdsourced drones deliver the packages to their final destinations. The problem is analyzed under different settings and several optimization models and algorithms have been developed to solve it.--Author's abstract