Hierarchical Production Control in a Stochastic Manufacturing System with Long-Run Average Cost

• Published in: Journal of mathematical analysis and applications Vol. 214; no. 1; pp. 151 - 172
• Main Authors: Sethi, Suresh P, Zhang, Hanqin, Zhang, Qing
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.10.1997
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1006/jmaa.1997.5602

This paper presents an asymptotic analysis of a stochastic manufacturing system consisting of parallel machines subject to breakdown and repair and facing a constant demand, as the rates of change of the machine states approach infinity. This situation gives rise to a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The long-run average cost for the original problem converges to the long-run average cost of the limiting problem. Open-loop and feedback controls for the original problem are constructed from optimal controls of the limiting problem in a way that guarantees their asymptotic optimality. The convergence rate of the long-run average cost for the original problem to that of the limiting problem is established. This helps in providing an error estimate for the constructed open-loop asymptotic optimal control.