A stochastic bilevel DEA-based model for resource allocation

Target setting and optimal allocation of limited resources are critical for sustainability and competitiveness of organizations. The process of resource distribution and targeting is usually implemented through a central unit that decides for the resources supplied to the subordinate decision-making units (DMUs) along with DMUs lower bounds of desired efficiency. Moreover, the central unit has the authority to set the overall expected output targets so as to maximize the organizational effectiveness. In this paper, we evaluate the efficiency of organizations using a bilevel network data envelopment analysis (DEA) approach in a stochastic framework. The proposed bilevel DEA model with stochastic conditions optimizes centralized resource allocation and target setting imposing lower bounds on the efficiencies of all DMUs belonging to the organization. Consequently, the total input consumption is minimized and the total output production is maximized at the same time while considering additional bounds and availability constraints for inputs. In the stochastic bilevel model, uncertainty is introduced through the upper level (leader) problem that attempts to maximize organizational effectiveness while in the lower level (follower) problem it evaluates the efficiency of the DMUs. A solution methodology for the bilevel network DEA-based model is presented and numerical results are obtained using data from the literature. The obtained results are compared with those published in other case studies for centralized resource allocation DEA models.