PhD Defense by Taylor Leonard
You are cordially invited to the following dissertation defense:
Resource Allocation Optimization Problems In The Public Sector
Prof. George Nemhauser, Industrial & Systems Engineering, Georgia Institute of Technology
Prof. Martin Savelsbergh, Industrial & Systems Engineering, Georgia Institute of Technology
Prof. Alan Erera, Industrial & Systems Engineering, Georgia Institute of Technology
Prof. David Goldsman, Industrial & Systems Engineering, Georgia Institute of Technology
Dr. Jeff Weir, Associate Dept Head of Dept of Operational Sciences, Air Force Institute of Technology
Dr. Andrew Armacost, President, University of North Dakota (June 2020)
Dean of Faculty (Former, 2019), U.S. Air Force Academy
February 12, 2020 @ 10:30am EST
This dissertation consists of three distinct, although conceptually related, public sector topics: the Transportation Security Agency (TSA), U.S. Customs and Border Patrol (CBP), and the Georgia Trauma Emergency Network Commission (GTENC). The topics are unified in their mathematical modeling and mixed-integer programming solution strategies.
In Chapter 2, we discuss strategies for solving large-scale integer programs to include column generation and particle swarm optimization (PSO). In order to solve problems with an exponential number of decision variables, we employ Dantzig-Wolfe decomposition to take advantage of the special subproblem structures encountered in resource allocation problems. In each of the resource allocation problems presented, we concentrate on selecting an optimal portfolio of improvement measures. We use column generation to effectively solve these problems to optimality, but are hindered by the solution time and large CPU requirement. We explore utilizing multi-swarm particle swarm optimization to solve the decomposition heuristically. We also explore integrating multi-swarm PSO into the column generation framework to solve the pricing problem for entering columns of negative reduced cost.
In Chapter 3, we present a TSA problem to allocate security measures across all federally funded airports nationwide. This project establishes a quantitative construct for enterprise risk assessment and optimal resource allocation to achieve the best aviation security. We first analyze and model the various aviation transportation risks and establish their interdependencies. The mixed-integer program determines how best to invest any additional security measures for the best overall risk protection and return on investment. Our analysis involves cascading and inter-dependency modeling of the multi-tier risk taxonomy and overlaying security measurements.
In Chapter 4, we optimize security measure investments to achieve the most cost-effective deterrence and detection capabilities for the CBP. A large-scale resource allocation integer program was successfully modeled that rapidly returns good Pareto optimal results. The model incorporates the utility of each measure, the probability of success, along with multiple objectives. The model accommodates different resources, constraints, and various types of objectives.
In Chapter 5, we analyze the emergency trauma network problem first by simulation. The simulation offers a framework of resource allocation for trauma systems and possible ways to evaluate the impact of the investments on the overall performance of the trauma system. We then explore three different formulations to model the Emergency Trauma Network as a mixed-integer programming model. The first model is a Multi-Region, Multi-Depot, Multi-Trip Vehicle Routing Problem with Time Windows. This is a known expansion of the vehicle routing problem that has been extended to model the Georgia trauma network. We then adapt an Ambulance Routing Problem (ARP) to the previously mentioned VRP. The new ARP also implements more constraints based on trauma level limitations for patients and hospitals. Lastly, the Resource Allocation ARP is constructed to reflect the investment decisions presented in the simulation.