Diffusion approximation for a controlled stochastic manufacturing system with average cost minimization

The problem of reducing inventory and backlog costs of a single-product machine is solved by using the diffusion approximation method. A solution is needed when there is nonexponential distribution of the times when the machine works or is idle or when there is stochastic demand. A sequence of systems in heavy traffic is built. The limiting system whose optimal control is denoted by a reflecting barrier z* is also presented.