Doctoral Dissertations
Date of Award
12-2025
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Major
Industrial Engineering
Major Professor
Jim Ostrowski
Committee Members
James Ostrowski, Mingzhou Jin, Miguel Lejeune, Rebekah Herrman,
Abstract
This dissertation develops models and algorithms for decision-making under uncertainty, with applications ranging from infrastructure protection to freight transportation. A central focus is stochastic optimization problems in which the probability distributions of uncertain outcomes depend on decision variables, a class of problems that presents significant modeling and computational challenges.
The first two papers advance solution methods for decision-dependent uncertainty. The first paper examines a class of two-stage stochastic programs where uncertain component capacities are directly influenced by first-stage decisions. Standard scenario enumeration produces intractable deterministic equivalents with high-degree nonlinearities. To address this challenge, structural properties of the problem are established, and a successive refinement algorithm is introduced that progressively tightens bounds within a branch-and-cut framework. Computational experiments demonstrate that this method significantly outperforms benchmark approaches, with optimal solutions identified before state space growth becomes prohibitive.
The second paper extends these ideas to defender–attacker models. Traditional tri-level formulations assume perfect defense and interdiction, assumptions that oversimplify real-world systems. An imperfect defender–attacker model is introduced in which defense and attack resources only partially influence component reliability, resulting in a stochastic optimization problem with decision-dependent probabilities. To overcome the computational intractability of the deterministic equivalent, a successive refinement algorithm is developed that dynamically refines scenario supports. Results on stochastic maximum flow problems show that the method solves more instances and achieves speedups of up to 66 times, thereby enabling the analysis of imperfect defense and interdiction in complex networks.
The third paper addresses driver assignment in shared truckload (STL) freight transportation, where uncertainty in load forecasts complicates planning. A deterministic optimization model is first formulated to assign drivers to STL bundles, and a heuristic algorithm is developed to improve its computational scalability. Building on this foundation, a two-stage stochastic optimization model is proposed to incorporate both immediate and forecasted future costs. Computational results reveal the rapid growth in complexity with the number of drivers and bundles, highlighting the importance of scalable algorithms. The analysis further shows that the value of accurate forecasts increases with problem size, emphasizing the role of predictive analytics in STL planning.
Recommended Citation
Affar, Samuel O., "Successive Refinement Algorithm for Solving Decision-Dependent Stochastic Programs and Driver Assignment in Shared Truckload Transportation. " PhD diss., University of Tennessee, 2025.
https://trace.tennessee.edu/utk_graddiss/13577