Optimal feedback production for a two-level supply chain

Chi Kin Chan, Heung Wing Joseph Lee, K. H. Wong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)


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,Tf], we obtain an approximated problem (P(Tf)) 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,Tf], which is equal to the retailer's optimal production rate in this time interval, he can solve his approximated problem over(P, -) (Tf) to find his optimal production rate throughout [0,Tf]. Several examples have been solved to illustrate the efficiency of the method.
Original languageEnglish
Pages (from-to)619-625
Number of pages7
JournalInternational Journal of Production Economics
Issue number2
Publication statusPublished - 1 Jun 2008


  • Supply chain management
  • Time-delayed optimal control

ASJC Scopus subject areas

  • Economics and Econometrics
  • Industrial and Manufacturing Engineering


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