The Centralized Resource Allocation under Semi-Additive Production Technology in DEA

Centralized resource allocation (CRA) models are usually presented under variable returns to scales (VRS) technology. In these models, the evaluation of the efficiency of the decision-making units (DMUs) is done only on the basis of the observed DMUs. In this paper, we introduce CRA models in semi-additive production technology. In this technology, in addition to the observed DMUs, aggregation of production units is present in the process of performance evaluation using data envelopment analysis (DEA). We prove that we can solve this model only based on observational DMUs in order to reduce the number of calculations. In the following, we develop this model for a general case based on the approach provided by Fang [6]. The proposed models adjust the inputs and outputs to achieve the total input contraction by the central decision-maker (DM). We can only consider adjustments to inefficient DMUs instead of all DMUs in the CRA model. The proposed model maximizes the efficiency of individual DMUs at the same time that total input consumption is minimized or total output production is maximized. We obtain the efficient targets corresponding to all DMUs on the efficiency frontier of semi-additive production technology by solving only one model. We illustrate our approach with an empirical example.