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Hierarchical Production Control in Dynamic Stochastic Jobshops with Long-Run Average Cost |
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| Authors: | Sethi S P Zhang H Zhang Q |
| Institution: | (1) School of Management, University of Texas at Dallas, Richardson, Texas;(2) Institute of Applied Mathematics, Academia Sinica, Beijing, China;(3) Present address: School of Management, University of Texas at Dallas, Richardson, Texas;(4) Department of Mathematics, University of Georgia, Athens, Georgia |
| Abstract: | 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 |
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