With the continuing growth of renewable penetration in power systems, it becomes increasingly challenging to manage the operational uncertainty at near-real-time stage via deterministic scheduling approaches. This paper explores the necessity, benefits and implementability of applying stochastic programming to security constrained economic dispatch (SCED). We formulate a stochastic look-ahead economic dispatch (LAED-S) model for near-real-time power system operation. A concept of uncertainty responses is introduced to assess the power system economic risk with respect to net load uncertainties. This concept offers the system operator a simple yet effective gauge to decide whether a stochastic approach is more desirable than a deterministic one. For an efficient stochastic dispatch algorithm, an innovative hybrid computing architecture is proposed. It leverages the progressive hedging algorithm and the L-shaped method. Numerical experiments are conducted on a practical 5889-bus system to illustrate the effectiveness of the proposed approach.