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.