Hierarchical Production Control in a Stochastic Manufacturing System with Long-Run Average Cost
Journal of Mathematical Analysis and Applications, Vol. 214, No. 1, pp. 151-172, 1997
25 Pages Posted: 9 Apr 2008 Last revised: 18 Jan 2009
Abstract
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.
Keywords: Production Planning, Hierarchical Controls, Stochastic Manufacturing System, Long-Run Average Cost, Dynamic Programming, Ergodic Problem, Asymptotic Optimality, Open-Loop Controls, Feedback Controls
JEL Classification: M11, C61
Suggested Citation: Suggested Citation