Optimal and predictive control of distribution chains by using integer tree-based search and mixed-integer programming

The control of multi-item multi-echelon distribution chains is addressed by using integer tree-based search and mixed-integer programming. Basing on a discrete-time model that describes the exchange of goods inside a generic distribution chain, the decisions on the flows are made by referring to a performance index that accounts for transportation, holding, 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 customers' demand. The optimal selection of policy parameters such as delivery cycle times of goods is obtained by using a top-down exploration of a tree with leaves associated with min-max subproblems. A heuristic algorithm is presented to explore the tree for finding a suboptimal solution in a reduced number of steps. Such an algorithm is well-suited to being applied to distribution chains with a dimension that prevents from an exhaustive exploration of the leaves. At the tactical level, the on-line decisions on the transportation of goods are taken by using 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 assess the potential of the proposed approach in terms of both effectiveness and computational efficiency.