There are regionally distributed demands for various resources in cloud based large-scale online services. Given fixed resource budget, the service providers need to decide where to place resources to satisfy massive demands from all regions, where demands are usually represented by mean value in given time span. However, in scenarios with a large number of resources, demands are dynamic and stochastic, considering fine-grained demands and adopting stochastic model will further improve resource utilization. Compared with mean demand-based algorithm, considering demand stochasticity in algorithm will increase resource utilization ratio, but also leads to high time complexity. The time complexity of optimal algorithm is linear to total amount of resources, thus may be inefficient when dealing with a large number of resources. Based on nonlinear programming theory, we propose Fast Resource Placement (FRP), an effective resource placement method of high efficiency. In the algorithm, optimal solution is represented by continuous functions of input, and we construct approximation functions to reduce the computation complexity. The preliminary experiments show that in scenarios with general settings, compared with optimal algorithm, FRP can reduce the computation time by three orders of magnitude, and can achieve 99% effect of optimal solution. Therefore, FRP can be used to schedule large number of resources efficiently in time-tense scheduling scenarios.