A numerical method in optimal production of hybrid stochastic production systems via multi-time scales

A hybrid stochastic production system involving fast model and slow model is formulated with multi-time scales. One time scale is 1, the processing time scale, which is frequency and represents fast model. The other time scale is ε^-1, system failure time scale, which is infrequency and indicates slow model of the system. On different time scale, the original system is decomposed into two subsystems. Based on the two subsystems, the optimal control policy of the system is gotten by using approximation numerical technique. Simulation illustrates and confirms the method.