Integer tree-based search and mixed-integer optimal control of distribution chains

The use of integer tree-based search and mixed- integer programming is investigated for the purpose of control of multi-item multi-echelon distribution chains. A discrete-time model is considered to describe the dynamics of a generic distribution chain. The decisions on the amounts of goods to transfer are made by referring to a performance index that accounts for transportation, storage, and backlog costs at two levels, i.e., strategic and tactical. As to the strategic level, a worst-case stock replenishment policy is adopted to exploit the uncertain information available on long-term predictions of the customers' demand. The solution of such a problem is obtained by using a top-down tree-based algorithm to select policy parameters such as the delivery cycle times of goods. At the tactical level, the on-line decisions on the transportation of goods are taken basing on model predictive control, which allows one to take into account recent, reliable, short-term predictions of the demand. The tactical optimal decisions are obtained by solving mixed-integer programming problems with fewer variables as compared with the strategic setting. Simulation results are presented to show the effectiveness of the proposed approach.