Wong, K. H.; Chan, Chi Kin; Lee, H. W. J. Optimal feedback production for a single-echelon supply chain. (English) Zbl 1110.37067 Discrete Contin. Dyn. Syst., Ser. B 6, No. 6, 1431-1444 (2006). Summary: 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 \([0,\infty)\) by \(0,T_f\), we obtain an approximated problem \(P(T_f)\) 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 \(T_f\to\infty\). 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. Cited in 1 Document MSC: 37N40 Dynamical systems in optimization and economics 49N35 Optimal feedback synthesis 93A30 Mathematical modelling of systems (MSC2010) 93B52 Feedback control 91B62 Economic growth models 34K35 Control problems for functional-differential equations 90B30 Production models Keywords:dynamical system in optimization and economics; optimal feedback synthesis; mathematical modeling; feedback control PDFBibTeX XMLCite \textit{K. H. Wong} et al., Discrete Contin. Dyn. Syst., Ser. B 6, No. 6, 1431--1444 (2006; Zbl 1110.37067) Full Text: DOI