Optimization Approaches for Mobility and Service Sharing

Abstract

Mobility and service sharing is undergoing a fast rise in popularity and industrial growth in recent years. For example, in patient-centered medical home care, services are delivered to patients at home, who share a group of medical staff riding together in a vehicle that also carries shared medical devices; companies such as Amazon and Meijer have been investing tremendous human effort and money in grocery delivery to customers who share the use of delivery vehicles and staff. In such mobility and service sharing systems, decision-makers need to make a wide range of system design and operational decisions, including locating service facilities, matching supplies with demand for shared mobility services, dispatching vehicles and staff, and scheduling appointments. The complexity of the linking decisions and constraints, as well as the dimensionality of the problems in the real world, pose challenges in finding optimal strategies efficiently. In this work, we apply techniques from Operations Research to investigate the optimal and practical solution approaches to improve the quality of service, cost-effectiveness, and operational efficiency of mobility and service sharing in a variety of applications. We deploy stochastic programming, integer programming, and approximation algorithms to address the issues in decision-making for seeking fast and reliable solutions for planning and operations problems.

This dissertation contains four main chapters. In Chapter 2, we consider a class of vehicle routing problems (VRPs) where the objective is to minimize the longest route taken by any vehicle as opposed to the total distance of all routes. In such a setting, the traditional decomposition approach fails to solve the problem effectively. We investigate the hardness result of the problem and develop an approximation algorithm that achieves the best approximation ratio. In Chapter 3, we focus on developing an efficient computational algorithm for the elementary shortest path problem with resource constraints, which is solved as the pricing subproblem of the column generation-based approach for many VRP variants. Inspired by the color-coding approach, we develop a randomized algorithm that can be easily implemented in parallel. We also extend the state-of-the-art pulse algorithm for elementary shortest path problem with a new bounding scheme on the load of the route. In Chapter 4, we consider a carsharing fleet location design problem with mixed vehicle types and a restriction on CO2 emission. We use a minimum-cost flow model on a spatial-temporal network and provide insights on fleet location, car-type design, and their environmental impacts. In Chapter 5, we focus on the design and operations of an integrated car-and-ride sharing system for heterogeneous users/travelers with an application of satisfying transportation needs in underserved communities. The system aims to provide self-sustained community-based shared transportation. We address the uncertain travel and service time in operations via a stochastic integer programming model and propose decomposition algorithms to solve it efficiently.

Overall, our contributions are threefold: (i) providing mathematical models of various complex mobility and service sharing systems, (ii) deriving efficient solution algorithms to solve the proposed models, (iii) evaluating the solution approaches via extensive numerical experiments. The models and solution algorithms that we develop in this work can be used by practitioners to solve a variety of mobility and service sharing problems in different business contexts, and thus can generate significant societal and economic impacts.