A comparison between linear programming model and optimal control model of production-inventory system

Abstract

This study compares two models of the production- inventory system - optimal control and linear programming. We derived the optimality conditions of optimal control model and formulated the linear programming model. A new method to determine the theoretical solution of the boundary value problem has been suggested. Our numerical results suggest that control on the inventory level was realized at the end of the planning period, depending on the optimal control model, while in the linear programming model, it was realized from the beginning of the planning period. Also, the method to determine the theoretical solution of the boundary value problem has proven to be efficient.