Hierarchical model for production planning in the case of uncertain demand

The paper deals with hierarchical production planning for a multiperiod model consisting of an aggregate planning level and a detailed planning level in the case of uncertain demand. At the beginning the detailed demand for the actual planning period is known, whereas for future planning periods only upper and lower bounds of detailed demand are known. On the other hand, the aggregate demand on the product group level is supposed to be deterministic at each planning period over the whole planning horizon. For the aggregate planning level, robust production plans (i.e., aggregate production plans which can be disaggregated to a feasible detailed plan for every possible detailed demand) are proposed and a consistent disaggregation is executed for the detailed planning level. Two sets (static and dynamic) of sufficient conditions for robustness of the aggregate plan as well as dynamic disaggregation conditions are derived. These sufficient conditions are a generalization of the results of Lasserre and Mercé. The performance of the sufficient conditions are demonstrated by a computational study which shows the potential advantage of the approach.