Hierarchical Production Control in a Stochastic N-Machine Flowshop with Long-Run Average Cost
Journal of Mathematical Analysis and Applications, No. 251, pp. 285-309, 2000
31 Pages Posted: 9 Apr 2008 Last revised: 27 Apr 2008
This paper presents an asymptotic analysis of stochastic manufacturing systems consisting of machines in tandem 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.
A method of shrinking and entire lifting is introduced in order to construct the near optimal controls for the original problem by using near optimal controls of the limiting problem. 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: hierarchical control, manufacturing systems, stochastic dynamic programming, optimal control, long-run average cost
JEL Classification: M11, C61
Suggested Citation: Suggested Citation