Optimal strategy for supplier selection problem integrated with optimal control problem of single product inventory system with piecewise holding cost

Abstract

In this paper, we formulate a hybrid mathematical model of supplier selection problem integrated with inventory control problem of a single product inventory system with piecewise holding cost. This model will be formulated in a piecewise affine (PWA) form that can be converted into mixed logical dynamic (MLD) form. By using this MLD model, we solve the supplier selection problem and control this inventory system so that the stock level tracks a desired level as the reference trajectory as closed as possible with minimal total cost. We use model predictive control for hybrid system to solve the problem. From the numerical experiment results, the optimal supplier was selected at each time period and the evolution of the stock level tracks the desired level well.