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

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.

[1]  Suresh P. Sethi.  Some Insights into Near-Optimal Plans for Stochastic Manufacturing Systems , 1997 .

[2]  M. K. Ghosh,et al.  Ergodic Control of Switching Diffusions , 1997 .

[3]  S.P. Sethi,et al.  Minimum average-cost production plan in a multi-product stochastic manufacturing system , 1996, Proceedings 1996 IEEE Conference on Emerging Technologies and Factory Automation. ETFA '96.

[4]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[5]  Yves Dallery,et al.  Partial Characterization of Optimal Hedging Point Policies in Unreliable Two-Part-Type Manufacturing Systems , 1998, Oper. Res..

[6]  W. Fleming,et al.  Risk-Sensitive Control on an Infinite Time Horizon , 1995 .

[7]  Qing Zhang,et al.  Hierarchical Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost: Asymptotic Optimality and Error Bounds , 1998 .

[8]  A. Sharifnia,et al.  Production control of a manufacturing system with multiple machine states , 1988 .

[9]  Wendell H. Fleming,et al.  Risk-Sensitive Production Planning of a Stochastic Manufacturing System , 1998 .

[10]  Panganamala Ramana Kumar,et al.  Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems , 1988, Oper. Res..

[11]  Qing Zhang,et al.  Finite state markovian decision processes with weak and strong interactions , 1996 .

[12]  Suresh P. Sethi,et al.  Asymptotic optimal controls in stochastic manufacturing systems with machine failures dependent on production rates , 1994 .

[13]  Suresh P. Sethi,et al.  Optimal Production Planning in a Multi-Product Stochastic Manufacturing System with Long-Run Average Cost , 1998, Discret. Event Dyn. Syst..

[14]  Qing Zhang,et al.  Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost , 1997 .

[15]  Michel Loève,et al.  Probability Theory I , 1977 .