Finite Simulation Budget Allocation for Ranking and Selection

We consider a simulation-based ranking and selection (R&S) problem under a fixed budget setting. Existing budget allocation procedures focus either on asymptotic optimality or on one-step-ahead allocation efficiency. Neither of them depends on the fixed simulation budget, the ignorance of which could lead to an inefficient allocation, especially when the simulation budget is finite. In light of this, we develop a finite-budget allocation rule that is adaptive to the simulation budget. Theoretical results show that the budget allocation strategies are distinctively different between a finite budget and a sufficiently large budget. Our proposed allocation rule can dynamically determine the ratio of budget allocated to designs according to different simulation budget and is optimal when the simulation budget goes to infinity, indicating it not only possesses desirable finite-budget properties but also achieves asymptotic optimality. Based on the proposed allocation rule, two efficient finite simulation budget allocation algorithms are developed. In the numerical experiments, we use both synthetic examples and a case study to show the superior efficiency of our proposed allocation rule.