We consider fixed-budget ranking and selection (R&S). This is a popular decision model in simulation optimization, with the goal of maximizing the probability of correctly selecting the best design among a finite set of alternatives within a given simulation budget. Existing R&S methods basically assume that the simulation noises of the designs follow normal distributions with known variances. We argue that the assumption of known variances is problematic, which will cause the derived sample allocation rules to underestimate the sampling uncertainty. In this research, we solve the fixed-budget R&S problem with unknown sampling variances. We follow the framework of the optimal computing budget allocation (OCBA) and establish optimality conditions, develop selection algorithms and characterize theoretical properties of the selection algorithms for this problem. In particular, Ryzhov (2016) made a conjecture about the optimality conditions of this problem. This research shows that this conjecture is partially correct, and fills in the missing parts of this conjecture.

Siyang Gao received the B.S. degree in Mathematics from Peking University in 2009 and the Ph.D. degree in Industrial Engineering from University of Wisconsin-Madison in 2014. Dr. Gao is the Associate Head and an Associate Professor with the Department of Systems Engineering, City University of Hong Kong. His research is devoted to simulation optimization, machine learning and their applications in healthcare management. His work has appeared in Operations Research, Manufacturing & Service Operations Management, INFORMS Journal on Computing, Production and Operations Management, IEEE Transactions on Automatic Control, Automatica, etc. He is a recipient of the Best Conference Paper Award at the IEEE Conference on Automation Science and Engineering in 2019, Best Paper Award at the International Conference on Logistics and Maritime Systems in 2019, and the Best Young Faculty Paper Award at the International Research Conference on Systems Engineering and Management Science in 2018. Dr. Gao is currently serving as an Associate Editor of the journals IEEE Transactions on Automation Science and Engineering and Journal of Simulation.