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Title: Optimal feedback production for a single-echelon supply chain
Authors: Wong, KH
Chan, CK 
Lee, HWJ 
Keywords: Dynamical system in optimization and economics
Feedback control
Mathematical modeling
Optimal feedback synthesis
Issue Date: 2006
Publisher: Amer Inst Mathematical Sciences
Source: Discrete and continuous dynamical systems - series b, 2006, v. 6, no. 6, p. 1431-1444 How to cite?
Journal: Discrete and Continuous Dynamical Systems - Series B 
Abstract: The dynamics of a supply chain have been modelled by several authors, yet no attempt has ever been made for finding the vendor's optimal production policy when facing such dynamics. In this paper, we model the dynamics of a supply chain as an infinite-horizon time-delayed optimal control problem. By approximating the time interval [0, ∞) by 0, Tf, we obtain an approximated problem P(Tf) which can be easily solved by the control parametrization method. Moreover, we can show that the objective function of the approximated problem converges to that of the original problem as Tf → ∈. Lastly, we also extend our method to solving a stochastic problem where the demand is a stochastic process with white noise input. Several examples for both the deterministic and the stochastic problems are solved to illustrate the efficiency of our method. In these examples, some important results relating the production rate to the demand are developed.
ISSN: 1531-3492
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