Exact Solution for the Production Planning Problem with Several Regimes Switching over an Infinite Horizon Time

We consider a stochastic production planning problem with regime switching. There are k≥1 regimes corresponding to different economic cycles. The problem is to minimize the production costs and analyze the problem by the value function approach. Our main contribution is to show that the optimal production is characterized by an exact solution of an elliptic system of partial differential equations. A verification result is given for the determined solution.