A modified multiplier model of BCC DEA to determine cost-based efficiency
Authors: Sarkar Subhadip 
Published: June 2017

Purpose
A cost-oriented data envelopment analysis (DEA) is a non-parametric tool for discriminating the best performers from a number of homogenous decision-making units (DMU) using allocative efficiency, technical efficiency and a cost-based efficiency score. Cost of each resource has been an important input in such cases. However, the purpose of this paper is to propose a method, which, in absence of it, helps to define the targeted output for all DMUs. Eigenvector derived from the first principal component of specific covariance matrix from each allocated outputs is used here for computing such targets. An orthogonal projection of resources to such radial directions is another indicator of a relative economic use of resources. Unlike regular cost-oriented DEA model, the current model proposes a multiplier model of BCC DEA. With the provision of the targeted output set for a DMU, the modified multiplier model measures the orientation of a DMU towards cost. A case study of six schools is incorporated here to identify the superior cost efficient school.

Design/methodology/approach
The problem referred here is concerned about six private pre-primary schools situated in a locality. The financial condition of the population is heterogeneous. The school management has the option to select the group of students according to the richness of the family. Thus, an average richness is taken into account here for each school to understand the motive of providing service to the targeted section of the society. Cost borne by each school per student per month is incorporated here to notice the intention of the school to offer education. The selection of input variables is inspired from the valuable findings of Hillman and Jenkner (2002). According to them in many developing countries, the governments lack either the financial resources or the political will to meet their citizens’ educational needs. Moreover, “Children are entitled to a free, quality basic education. Many children who do attend school receive an inadequate education because of poorly trained, underpaid teachers, overcrowded classrooms, and a lack of basic teaching tools such as textbooks, blackboards, and pens and paper […].” The inclusion of the first input is due to the measurement of willingness of a primary school to impart education. Commenting on the ill-effects, they mentioned “In an ideal world, primary education would be universal and publicly financed, and all children would be able to attend school regardless of their parents’ ability or willingness to pay. The reason is simple: when any child fails to acquire the basic skills needed to function as a productive, responsible member of society, […]. The cost of educating children is far outweighed by the cost of not educating them. Adults who lack basic skills have greater difficulty in finding well-paying jobs and escaping poverty […].” Thus, the second input plays a key role to measure the intention of a primary school to stand them in a good stead serve for the sake of ensuring social benefit. In this regard, two scores refer the outcome of the endeavor of whole system to create better students and to help society to progress.

Findings
The cost-oriented multiplier BCC DEA model is presented here to cite a proof of an existence of an ideal cost frontier originating from an MPSS-based DEA (referred in Sarkar, 2014a). The former model has mentioned that it is not necessary for a CCR efficient DMU to remain cost competent. However, the major drawback of that model was its inability to show the impact of return to scale. In the present model, this problem has been tackled nicely. School A, in this example, under the variable return to scale, can become a cost efficient school. However, the proposed model, in this paper, under constant return to scale, has accepted the ranking, which was proposed before.

Research limitations/implications
Only six schools, situated around Northwest Durgapur, were observed.

Practical implications
The prescribed model iterates how a smaller number of intermediate inputs can be used in DEA to identify benchmark. These variables, which emblem the control through lean approaches, can be representative of a large number of other actual inputs which have already been mentioned by many erstwhile researchers.

Social implications
The selection of input variables is inspired from the valuable findings of Hillman and Jenkner (2002). According to them in many developing countries, the governments’ lack either the financial resources or the political will to meet their citizens’ educational needs. Moreover, “Children are entitled to a free, quality basic education. Many children who do attend school receive an inadequate education because of poorly trained, underpaid teachers, overcrowded classrooms, and a lack of basic teaching tools such as textbooks, blackboards, and pens and paper […].” The inclusion of the first input is due to the measurement of willingness of a primary school to impart education. Commenting on the ill-effects, they mentioned “In an ideal world, primary education would be universal and publicly financed, and all children would be able to attend school regardless of their parents’ ability or willingness to pay. The reason is simple: when any child fails to acquire the basic skills needed to function as a productive, responsible member of society, […]. The cost of educating children is far outweighed by the cost of not educating them. Adults who lack basic skills have greater difficulty in finding well-paying jobs and escaping poverty […].” Thus, the second input plays a key role to measure the intention of a primary school to stand them in a good stead serve for the sake of ensuring social benefit. In this regard, two scores refer the outcome of the endeavor of whole system to create better students and to help society to progress.

Originality/value
The application of the directional distance model (prescribed by Chambers et al., 1998) in the present problem is because the target for each DMU is settled using the non-central PCA. Such a radial direction not only explains a comprehensive variation of the corresponding specific covariance matrix but also provides a cost function, which is orthogonal to it. The targeted output for any DMU is predicted by minimizing the cost function bearing with the respective utilization of resources. The current model allows deriving the radial efficiency score in reference to such targeted goals. The outcome of this model is validated with the outputs of an MPSS-based constant return on scale frontier function described in Sarkar (2014a). Both models show a substantial association in this regard.