Numerical solution for optimal production control of unreliable production systems with diffusion terms
含扩散项不可靠生产系统最优生产控制的数值求解

The optimal production control for unreliable stochastic production system always involves in solving a mode-coupled nonlinear partial differential equation, i.e., HJB(Hamilton-Jacobi-Bellman) equation, which is the necessary and sufficient condition of optimal control. Numerical method for stochastic control problems in continuous time is adopted to solve the optimal production control problem involving diffusion terms by constructing Markov chains to approximate the evolution of the system states, and then, the associated HJB equation is transformed into a discrete time Markov decision process(MDP) under local consistence. Based on the MDP, an algorithm including numerical iteration and policy iteration is then proposed. Finally, some numerical examples of production system are presented to illustrate the usefulness of the numerical method.