Optimal Feedback Production for a Supply Chain

Abstract

In this chapter, we modeled the dynamics of a supply chain considered by several authors. An infinite-horizon, time-delayed, optimal control problem was thus obtained. By approximating the time interval [0, ¥] by [0, Tf ], we obtained an approximated problem (P(Tf )) which could be easily solved by the control parameterization method. Moreover, we could show that the objective function of the approximated problem converged to that of the original problem as Tf ® ¥. Several examples have been solved to illustrate the efficiency of our method. In these examples, some important results relating the production rate to demand rate have been developed.