Date of Award
5-2026
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Industrial Engineering
Committee Chair/Advisor
Hamed Rahimian
Committee Member
Thomas Sharkey
Committee Member
Yongjia Song
Committee Member
Boshi Yang
Abstract
Decision-making under uncertainty pervades modern operations research, yet the classical assumption that model parameters are fixed and known is routinely violated in practice. This dissertation develops theoretical foundations and computational solution methods for chance-constrained programming (CCP), a framework that enforces stochastic constraints with high probability rather than demanding their satisfaction under every scenario. Four interconnected research thrusts are pursued, spanning the risk-averse supply chain optimization, distributionally robust formulations with polyhedral ambiguity sets, geometric cutting-plane methods via intersection cuts, and multistage stochastic programming with joint chance constraints.
The first contribution studies optimal procurement and inventory decisions for a perishable-product supply chain under demand uncertainty. A risk-averse and chance-constrained two-stage stochastic program is formulated using max-CVaR and mean-CVaR objectives, and multiple variants of the L-shaped decomposition, dual and primal, are developed to solve it efficiently. Extensive numerical experiments quantify the value of risk aversion, revealing how varying risk preferences and product shelf-life jointly affect cost distributions and shortage probabilities.
The second contribution addresses distributional ambiguity. When the underlying probability distribution is known only partially, a distributionally robust chance-constrained program (DRCCP) is studied over a polyhedral ambiguity set that subsumes moment-based constraints, total variation distance, and Wasserstein distance. A big-M-free mixed-integer reformulation and a decomposition-based cutting-plane algorithm are derived, and an out-of-sample analysis confirms that DRCCP consistently dominates classical CCP in probability-constraint satisfaction and optimality gap, especially under small sample sizes.
The third contribution introduces a geometric cutting-plane paradigm for CCP with finite discrete distributions. Two families of intersection cuts are developed from the corner-polyhedron framework: a submodular intersection cut that exploits the extended Polymatroid and the extended envelope of the scenario-requirement function as a multi-faceted S-free set, and a modular intersection cut derived from probability covers whose S-free boundary reduces to a single static half-space, admitting closed-form ray-exit distances. Both cut families are extended to two-stage recourse settings via a Farkas-based projection that reduces recourse feasibility to an equivalent non-recourse mixing-set structure. A hybrid switching strategy that initiates with classical mixing inequalities and pivots to intersection cuts upon optimality-gap stagnation, achieves the fastest convergence on large-scale supply chain instances.
The fourth contribution develops a rigorous multistage chance-constrained programming framework for the allocation and sharing of reusable medical resources---specifically mechanical ventilators across U.S. states, under stochastic, time-varying pandemic demand. Joint chance constraints are modeled at the scenario-tree level using binary indicator variables, yielding a multistage stochastic mixed-integer program. The parametric scaled-cut decomposition algorithm is implemented and augmented with feasibility cuts derived from the mixing inequalities, enabling exact solution without big-M reformulations. Provable convergence of the first-stage outer approximation to the convex envelope of the expected cost-to-go function is established. Computational experiments across planning horizons of 3, 6, and 9 stages, up to 300 scenarios, and up to 20 regions confirm that the decomposition approach substantially outperforms the extensive-form formulation solved by a general-purpose MIP solver, and a value of the multistage stochastic solution (VMSS) analysis demonstrates significant improvements in both objective value and expected shortage relative to a two-stage benchmark, with the planning horizon emerging as the dominant driver of the multistage advantage.
Recommended Citation
Pathy, Soumya Ranjan, "Stochastic and Robust Chance-Constrained Programs" (2026). All Dissertations. 4251.
https://open.clemson.edu/all_dissertations/4251