An approximation approach for optimal production control of manufacturing systems

We consider a switching diffusion model for the dynamics of production, demand, and production capacity in a manufacturing system and define an optimal production control problem of minimizing an infinite-horizon discounted cost. By discretizing the continuous state space we define an associated control of continuous Markov chain (CTMC) problem as an approximation to the original problem. Using a weak convergence approach, we derive some preliminary results on the convergence of the optimal cost of the CTMC problem to that of the original problem as the discretization interval approaches zero