Optimal Strategy for Multi-product Inventory System with Supplier Selection by Using Model Predictive Control

Abstract

In this paper, we compute the optimal strategy to control the stock level of a multiproduct inventory system and to select the supplier from several alternatives such that the total cost is minimum by using the model predictive control. The dynamic of this system will be modeled into linear time invariant state space. Furthermore, to control the stock level and to select the supplier in simultaneous way, the model predictive control will be applied which minimizes an objective function subject to a dynamic equation. This dynamic equation presents the dynamic stock level whereas the objective function of this problem presents the total cost of the supplier selection problem as well as the gain between the stock level and the desired level given by the decision maker. We give the numerical simulation for this system by using the model predictive control toolbox in MATLAB then we observe how this model predictive control method generates the optimal strategy to the corresponding response of the stock level. From the simulation results, the model predictive control generates the optimal strategies to control the stock level with minimum total cost and the stock level follows the decision maker desired level.