Hybrid mathematical model of inventory system with piecewise holding cost and its optimal strategy

In this paper, we formulate a hybrid mathematical model of an inventory system with piecewise holding cost. We write the hybrid model of this system in the piecewise-affine (PWA) form. We use model predictive control method to generate the optimal strategy i.e. the amount of the arriving product shipment so that the inventory level tracks some desired inventory level given by decision maker as close as possible and this inventory system meets the demand with minimum total holding cost. Firstly, we convert the model of the PWA form into mixed logical dynamic (MLD) form and then we apply the model predictive control for hybrid system to this model in the MLD form. We simulate the model with various desired inventory level. From the computational simulation results, we observed that the inventory level follows the given desired inventory level very well.