Optimal feedback production for a single-echelon supply chain

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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1431-1444
Number of pages14
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number6
Publication statusPublished - 1 Nov 2006


  • Dynamical system in optimization and economics
  • Feedback control
  • Mathematical modeling
  • Optimal feedback synthesis

ASJC Scopus subject areas

  • General Mathematics
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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