Stability and optimization of a multi-stage production system

The authors study the control of a multistage production system by a base-stock policy. Such a policy is determined by a set of parameters, one for each stage. The authors derive and analyze estimates of derivatives of costs with respect to these parameters. Derivative estimates can be used to find optimal parameters. For the analysis of steady-state derivates estimates, the stability of the system is examined. Conditions are given under which it has a unique stationary distribution to which it converges from all initial stages. Conditions are also given under which it forms a Harris ergodic Markov chain. The attendant regenerative structure helps establish the convergence of steady-state derivative estimates