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Singular perturbations in manufacturing
Abstract: "We present an asymptotic analysis for a large class of stochastic optimization problems arising in manufacturing. A typical example of the problems we consider, is a production planning problem with random capacity and demand. In this example we assume that the capacity of the system fluctuates faster than the other quantities. The general model we consider also has a fast controlled Markov process in its state description. Using the difference in the time scales of different quantities, we simplify the problem by 'averaging' out the fast process. Then asymptotically optimal strategies are constructed from the optimal solutions of the limiting problems. The proofs of these results use the theory of viscosity solutions to dynamic programming equations. However, the formal construction of the asymptotically optimal strategies does not require the knowledge of this theory."
- "Abstract: "We present an asymptotic analysis for a large class of stochastic optimization problems arising in manufacturing. A typical example of the problems we consider, is a production planning problem with random capacity and demand. In this example we assume that the capacity of the system fluctuates faster than the other quantities. The general model we consider also has a fast controlled Markov process in its state description. Using the difference in the time scales of different quantities, we simplify the problem by 'averaging' out the fast process. Then asymptotically optimal strategies are constructed from the optimal solutions of the limiting problems. The proofs of these results use the theory of viscosity solutions to dynamic programming equations. However, the formal construction of the asymptotically optimal strategies does not require the knowledge of this theory.""@en
- "Singular perturbations in manufacturing"@en