Producing in a Manufacturing System with Minimum Average Cost

We deal with a single or parallel machine manufacturing system with convex cost of holding and backlogging and develop a new rigorous analysis to address the problem. We provide the results needed for the vanishing discount approach used for aour analysis. In particular, we show that one can go from any point in the state space to any other point in a finite time. The Hamilton-Jacobi-Bellman (HJB) equation is specified for the average cost problem and a verification theorem for optimality over the class of admissible controls is given. We show that the HJB equation has a viscosity solution, which turns out in this case to be also a classical solution