A* search algorithm for an optimal investment problem in vehicle-sharing systems

We study an optimal investment problem that arises in the context of the vehicle-sharing system. Given a set of locations to build stations, we need to determine i) the sequence of stations to be built and the number of vehicles to acquire in order to obtain the target state where all stations are built, and ii) the number of vehicles to acquire and their allocation in order to maximize the total profit returned by operating the system when some or all stations are open. The profitability associated with operating open stations, measured over a specific time period, is represented as a linear optimization problem applied to a collection of open stations. With operating capital, the owner of the system can open new stations. This property introduces a set-dependent aspect to the duration required for opening a new station, and the optimal investment problem can be viewed as a variant of the Traveling Salesman Problem (TSP) with set-dependent cost. We propose an A* search algorithm to address this particular variant of the TSP. Computational experiments highlight the benefits of the proposed algorithm in comparison to the widely recognized Dijkstra algorithm and propose future research to explore new possibilities and applications for both exact and approximate A* algorithms.Comment: Full version of the conference paper which is accepted to be appear in the proceeding of the The 12th International Conference on Computational Data and Social Networks - SCONET202

MATH 456 Student Project Reports for ValleyBike Operations Optimization

In the fall semester of 2019 UMass Amherst students in Professor Annie Raymond\u27s MATH 456 course used ValleyBike share route data and applied mathematic algorithms to develop recommendations to the system operators and participating communities on how to optimize bike balancing operations, maintenance, station dock allocation, station locations, incentive programs, etc

A* search algorithm for an optimal investment problem in vehicle-sharing systems

We study an optimal investment problem that arises in the context of the vehicle-sharing system. Given a set of locations to build stations, we need to determine i) the sequence of stations to be built and the number of vehicles to acquire in order to obtain the target state where all stations are built, and ii) the number of vehicles to acquire and their allocation in order to maximize the total profit returned by operating the system when some or all stations are open. The profitability associated with operating open stations, measured over a specific time period, is represented as a linear optimization problem applied to a collection of open stations. With operating capital, the owner of the system can open new stations. This property introduces a set-dependent aspect to the duration required for opening a new station, and the optimal investment problem can be viewed as a variant of the Traveling Salesman Problem (TSP) with set-dependent cost. We propose an A* search algorithm to address this particular variant of the TSP. Computational experiments highlight the benefits of the proposed algorithm in comparison to the widely recognized Dijkstra algorithm and propose future research to explore new possibilities and applications for both exact and approximate A* algorithms

Microscopic traffic models, accidents, and insurance losses

The paper develops a methodology to enable microscopic models of transportation systems to be accessible for a statistical study of traffic accidents. Our approach is intended to permit an understanding not only of historical losses but also of incidents that may occur in altered, potential future systems. Through such a counterfactual analysis, it is possible, from an insurance, but also from an engineering perspective, to assess the impact of changes in the design of vehicles and transport systems in terms of their impact on road safety and functionality. Structurally, we characterize the total loss distribution approximatively as a mean-variance mixture. This also yields valuation procedures that can be used instead of Monte Carlo simulation. Specifically, we construct an implementation based on the open-source traffic simulator SUMO and illustrate the potential of the approach in counterfactual case studies

Data-driven fleet load balancing strategies for shared Mobility-on-Demand systems

Mobility on Demand (MoD) systems utilize shared vehicles to supplement or replace mass transit and private vehicles. Such systems include traditional taxis as well as Transportation Network Companies (TNCs) that offer bike and ride sharing. MoD systems face myriad operational challenges, but this dissertation focuses on the data-driven load balancing problem of redistributing vehicles among service regions. This is a difficult resource reallocation problem because customer demands follow a stochastic process subject to dynamic temporal-spatial patterns. The first half of this dissertation considers the load balancing problem for a bike sharing system in which bikes are redistributed among stations via trucks. The objective is to avoid situations in which a user wishes to rent (return) a bike to a station but cannot because the station is empty (full). First, a station and interval-specific inventory level is defined as a function of station capacity and interval demand rates as observed from analyzed data. Second, using a graph network framework, a receding horizon controller is proposed to determine the optimal paths -- over a short period of time -- for the fleet of trucks to take. When calculating the optimal paths the controller considers the current and projected inventory subject to the dynamically changing rent and return rates for every station in the network. The second half of this dissertation tackles the redistribution of an autonomous taxi fleet in which the vehicles themselves are capable of performing load balancing operations across service regions. The objective is to minimize the fraction of customers whose demands are dropped due to vehicle unavailability as well as the fraction of time the vehicles spend on load balancing operations (i.e driving empty). The system is represented by a queuing model and, as such, dynamic programming can find the optimal solution; however, the state-space of the model grows quickly rendering all but a minuscule system impossible to solve. To this end a parametric control is proposed that uses thresholds to dictate redistribution actions and well performing parameters are found via concurrent estimation methods of simulation