A Study on Efficient Computing Budget Allocation for a Two-Stage Problem

We consider how to allocate simulation budget to estimate the risk measure of a system in a two-stage simulation optimization problem. In this problem, the first stage simulation generates scenarios that serve as inputs to the second stage simulation. For each sampled first stage scenario, the second stage procedure solves a simulation optimization problem by evaluating a number of decisions and selecting the optimal decision for the scenario. It also provides the estimated performance of the system over all sampled first stage scenarios to estimate the system's reliability or risk measure, which is defined as the probability of the system's performance exceeding a given threshold under various scenarios. Usually, such a two-stage procedure is very computationally expensive. To address this challenge, we propose a simulation budget allocation procedure to improve the computational efficiency for two-stage simulation optimization. After generating first stage scenarios, a sequential allocation procedure selects the scenario to simulate, followed by an optimal computing budget allocation scheme that determines the decision to simulate in the second stage simulation. Numerical experiments show that the proposed procedure significantly improves the efficiency of the two-stage simulation optimization for estimating system's reliability.