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

✍ Scribed by Suresh P Sethi; Hanqin Zhang; Qing Zhang

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 275 KB
• Volume: 214
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5602

✦ Synopsis

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.