Optimal feedback production for a two-level supply chain

The dynamics of a supply chain has been modelled by several authors, yet very few attempts have been made to find the vendor's optimal production policy when facing such dynamics. In this paper, we consider a two-level supply chain. We first model the dynamics of the retailer's problem as...

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Bibliographic Details
Published in:International journal of production economics 2008-06, Vol.113 (2), p.619-625
Main Authors: Chan, Chi Kin, Lee, H.W.J., Wong, K.H.
Format: Article
Language:English
Subjects:
Optimization
Production controls
Studies
Supply chain management
Supply chains
Time-delayed optimal control
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Summary:The dynamics of a supply chain has been modelled by several authors, yet very few attempts have been made to find the vendor's optimal production policy when facing such dynamics. In this paper, we consider a two-level supply chain. We first model the dynamics of the retailer's problem as an infinite-horizon time-delayed control problem. By approximating the time interval [0,∞) by [0, T f], we obtain an approximated problem ( P( T f)) for the retailer, which can be solved easily by the control parametrization. Next, we extend this model to solving the manufacturer's problem. By assuming that the manufacturer has full knowledge of his demand throughout the time interval [0, T f], which is equal to the retailer's optimal production rate in this time interval, he can solve his approximated problem P ¯ ( T f ) to find his optimal production rate throughout [0, T f]. Several examples have been solved to illustrate the efficiency of the method.
ISSN:0925-5273
1873-7579
DOI:10.1016/j.ijpe.2007.12.012