The optimal control of production-inventory system

In this paper, we study the optimal production strategy of a production-inventory system with stochastic demand rate. This strategy is called a target level strategy, since it determines an optimal target inventory level and production rate level in the time period. The value function for developing the optimal production strategy is established, and the corresponding equation which is a fully nonlinear equation is derived using the dynamic programming principle (DPP). The uniqueness and comparison principle of the viscosity solutions of related Hamilton-Jacobi-Bellman (HJB) equation are proved. Finally, the numerical illustrative examples are discussed.