In this paper, the authors propose a two-level hierarchical optimization model for an institution (say an enterprise) to allocate resources among its departments. The top decision maker (the board or the general manager) of the institution makes a decision on how to allocate resources to n departments. In the lower level, the head (the manager) of each department is requested to estimate the maximum benefit the department will gain if it consumes a certain amount of resources, possibly obtained from the top decision-maker. In the top level, the top decision-maker allocates resources to n departments by solving an optimization problem in which the information of the expected maximum benefits of the n departments are involved. An incentive strategy is also suggested to support the top decision-maker in inducing the lower-level decision makers of the departments to provide the information truthfully. Under a very mild assumption, the authors prove that an allocation decision made by the top decision-maker with the method presented in this paper is optimal. An example is given to illustrate this model.
