Data envelopment analysis for resource allocation problems in the presence of radial and non-radial data

Resource allocation is considered to be of great significance for the development of an organization due to its limited resources. This thesis addresses two different aspects of resource allocation problems in data envelopment analysis (DEA) model including centralized resource allocation (CRA) DEA model and inverse DEA model. For each unit, targets are set separately using conventional DEA models whereas based on CRA-DEA models, a centralized decision maker is in charge of all the operating units. In such situation, the decision maker is interested in maximizing the efficiency of particular units at the same time that the aggregate output production is increased or the aggregate input consumption is decreased. The existing data CRA-DEA models are defined only for radial or non-radial data. While it was previously posited that the non-radial CRA-model is helpful in evaluating the targets of units, validation of such a model was completed once the radial inputs and outputs were proposed. It is proposed that there are some variances in the characterizations of the inputs or outputs objects (radial and non-radial inputs and outputs). While the radial inputs have to be decreased proportionately when it is intended to obtain all-outputs, the counterpart inputs need to be reduced non-proportionally. It can be then concluded that combining the two radial and non-radial approaches will yield accurate targets. In an effort to overcome the above mentioned shortcomings of the radial and non-radial CRA-models, firstly, this thesis shows that the two CRA-approaches can be connected to a number of desirable features in the previous ones. The proposed approaches are developed for the cases which consider minimizing of the aggregate input consumption and maximizing of the aggregate output production as radial and non-radial at the same time with outcomes in solving just one instead of n mathematical programing problems. Secondly, this thesis also presents a novel inverse DEA model of efficiency measurement. The proposed inverse model apparently is an aspect of resource allocation problems which is likely to concurrently consider some inputs’ rises (reductions). In order to improve the efficiency scores of some units when there are changes in the output (input) amounts of an efficient unit, the current study will elucidate the inverse DEA model with some advantage over the previous ones. The proposed model is meant for determining the utmost possible input (output) quantities of the efficient unit once its outputs (input) are changed. In this way, the modifications will bring about an increase in some units’ efficiency scores.

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