A bi-level formulation for DEA-based centralized resource allocation under efficiency constraints

• We present a bi-level DEA model for centralized resource allocation.
• The model optimizes the firm effectiveness and improves all DMUs’ efficiencies.
• We consider lower bounds on efficiencies of DMUs in the proposed model.
• We prove that the proposed model can be converted to a single level optimization.
• The results show that consideration of efficiency and effectiveness is necessary.

This paper presents a bi-level data envelopment analysis (DEA) model for centralized resource allocation considering lower bounds on efficiencies of decision making units (DMUs). The DMUs are controlled by a central unit which has the authority to allocate limited resources to them so that overall organization effectiveness is maximized. The upper-level model is concerned with determining input resources and output targets as key decision variables while imposing lower bounds on BCC efficiencies of all DMUs evaluated in the lower-level model. The model is optimized for organizational effectiveness (total outputs minus total inputs) while trying to improve the efficiencies of all DMUs. We prove that such a bi-level DEA model can be converted to a single level optimization problem. Numerical results are presented and compared with various examples taken from the literature.