Thesis Title: Decision Making in the Presence of Subjective Stochastic Constraints

Advisors:  

Dr. Sigrun Andradottir, School of Industrial and Systems Engineering, Georgia Tech 

Dr. Seong-Hee Kim, School of Industrial and Systems Engineering, Georgia Tech 

Committee members:  

Dr. Yajun Mei, School of Industrial and Systems Engineering, Georgia Tech 

Dr. Enlu Zhou, School of Industrial and Systems Engineering, Georgia Tech 

Dr. Chuljin Park, Department of Industrial Engineering, Hanyang University

Date and Time: Friday, October 1, 2021, 9:30 am (EST) 

Meeting URL: https://bluejeans.com/334412469/9302

Meeting ID: 334 412 469 (BlueJeans)  ​

Abstract:  ​

Constrained Ranking and Selection considers optimizing a primary performance measure over a finite set of alternatives subject to constraints on secondary performance measures. When the constraints are stochastic, the corresponding performance measures should be estimated by simulation. When the constraints are subjective, the decision maker is willing to consider multiple constraint threshold values.  In this thesis, we consider three problem formulations when subjective stochastic constraints are present. 

In Chapter 2, we consider the problem of finding a set of feasible or near-feasible systems among a finite number of simulated systems in the presence of subjective stochastic constraints. A decision maker may want to test multiple constraint threshold values for the feasibility check, or she may want to determine how a set of feasible systems changes as constraints become more strict with the objective of pruning systems or finding the system with the best performance. We present indifference-zone procedures that recycle observations for the feasibility check and provide an overall probability of correct decision for all threshold values. Our numerical experiments show that the proposed procedures perform well in reducing the required number of observations relative to four alternative procedures (that either restart feasibility check from scratch with respect to each set of thresholds or with the Bonferroni inequality applied in a conservative way) while providing a statistical guarantee on the probability of correct decision.

Chapter 3 considers the problem of finding a system with the best primary performance measure among a finite number of simulated systems in the presence of subjective stochastic constraints on secondary performance measures. When no feasible system exists, the decision maker may be willing to relax some constraint thresholds. We take multiple threshold values for each constraint as a user’s input and propose indifference-zone procedures that perform the phases of feasibility check and selection-of-the-best sequentially or simultaneously. We prove that the proposed procedures yield the best system in the most desirable feasible region possible with at least a pre-specified probability. Our experimental results show that our procedures perform well with respect to the number of observations required to make a decision, as compared with straightforward procedures that repeatedly solve the problem for each set of constraint thresholds.

In Chapter 4, we consider the problem of finding a portfolio of systems with the best primary performance measure among finitely many simulated systems as stochastic constraints on secondary performance measures are relaxed. By finding a portfolio of the best systems under a variety of constraint thresholds, the decision maker can identify a robust solution with respect to constraints or consider the trade-off between the primary performance measure and the level of feasibility of the secondary performance measures. We propose indifference-zone procedures that perform the phases of feasibility check and selection-of-the-best sequentially and simultaneously. Our proposed procedures show a significant reduction in the required number of observations to achieve the decision compared with applying straightforward procedures repeatedly with respect to each set of constraint thresholds.