Hierarchical Production Control in Dynamic Stochastic Jobshops with Long-Run Average Cost
Journal of Optimization Theory and Applications, Vol. 106, No. 2, pp. 231-264, August 2000
35 Pages Posted: 9 Apr 2008 Last revised: 27 Apr 2008
We consider a production planning problem for a dynamic jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are assumed to be finite state Markov chains. As the rates of change of the machine states approach infinity, an asymptotic analysis of this stochastic manufacturing systems is given. The analysis results in 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 is shown to converge to the long-run average cost of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem together with an error estimate for the constructed asymptotic optimal control is established.
Keywords: Hierarchical control, manufacturing systems, stochastic dynamic programming, optimal control, long-run average cost
JEL Classification: M11, C61
Suggested Citation: Suggested Citation