Simulation Resource Sharing And Dynamic Decision In Statistical Selection Problems

In this thesis, we study the statistical selection problem in simulation op-timization. This problem has wide applications in various industries, including manufacturing, finance, transportation, telecommunication, airline and aerospace, and health care, and has attracted many interests in recent years. Our work in this thesis has two main contributions. First we extend the optimal computing budget allocation to take account of simulation resource sharing, and secondly, we generalize the problem in dynamic sample allocation and design selection perspec-tive.We first study the problem of optimal computing budget allocation in the case that simulation resource can be shared. This is motivated by many techniques that are widely used in variance reduction, such as common random numbers and the standard clock method in which information and simulation resources are shared when different systems are simulated and compared at the same time. This sharing of computing resources and the potentially different computational requirements for different simulation models are important considerations in allocating simula-tion replications among the candidate designs with the objective of maximizing the probability of selecting the best design. Our formulation of the optimal computing budget allocation problem under this scenario leads to an optimization problem that can be viewed as a generalization of a correlated version considered in earlier work. An approximation to the problem is introduced to allow a tractable solu-tion, for which a heuristic two-stage sequential allocation algorithm is proposed, and several numerical examples are used to illustrate the potential improvements that can be gained.We then consider the statistical selection problem in a general dynamic frame-work comprising both fully sequential sampling allocation and optimal design s-election. The traditional probability of correct selection measure is not sufficient to capture both aspects in this more general framework, so we introduce the in- tegrated probability of correct selection to better characterize the objective. As a result, the usual selection policy of choosing the design with the largest sample mean as the estimate of the best is no longer necessarily optimal. Rather, the optimal selection policy is to choose the design that maximizes the posterior in-tegrated probability of correct selection, which is a function of both the posterior mean and the correlation structure induced by the posterior variance. Because determining the optimal selection policy is generally intractable, we also devise an approximation scheme to efficiently approximate the optimal selection policy. For the allocation policy, we study a myopic policy extending the knowledge gradi-ent policy and an asymptotic policy that is a composition of a sampling statistic and a sequential rule. The optimal computing budget allocation algorithm can be interpreted as a special case of the asymptotically optimal sampling statistics. Numerical examples are provided to illustrate the potential performance improve-ments, especially in small sample behavior.