Min-Max and Predictive Control for the Management of Distribution in Supply Chains

Inventory control for the management of multi-item multi-echelon distribution chains is addressed in a two-level hierarchical framework motivated by strategic and tactical points of view. Toward this end, a discrete-time dynamic model is presented together with various types of constraints to describe a generic distribution chain in detail. As to the strategic level, a worst-case approach is proposed to set up a stock replenishment policy by using the uncertain information available on long-term predictions of customers' demands. The solution of the resulting min-max problem is obtained by using a branch-and-bound algorithm to select policy parameters such as safety stocks and delivery cycle times of goods. The online decisions on the transportation of goods are made at the tactical level instead. In order to accomplish such a task, an approach based on model predictive control is proposed to exploit recent, more reliable, short-term predictions of the demands. Simulation results are presented to show the effectiveness and potential of the proposed methodology.