Detection of cost leaders in case of private primary school services

The purpose of this paper is to provide an insight into distinguish cost leaders from the architects of diversification (Porter, 1985) using a non-central principal component analysis (PCA)-based approach. The central theme of this paper is based on the assumption that the operational strategy of a competing firm can be understood by observing its resource consumption and technological practice vis-à-vis its rivals present in the market.

Depending on the previous surveys, two inputs (spending per student and percentage of non-poor income group) and two outputs (average scores attained by students in science group and in language group six private schools, located within the outskirt of Durgapur) were analyzed.

Out of six schools (A, B, C, D, E and F), A, E and F were found efficient; however, the proposed model identifies that out of them, only E and F remain cost efficient. The efficiency scores, due to cost, are very close to the outputs of other three accepted papers.

The input and output vectors have to be non-negative. In case of a negative input (output) set, separate treatment must be applied on them before the application of non-central PCA. Any decision-making unit (DMU) producing an output of 0 will prohibit the use of the non-central PCA.

It can be applied to problems which may or may not be having the information regarding input price for detecting cost-efficient DMUs as in the case of the Banker’s model. Banker’s model remains inconclusive about the fact, whether a DMU is a mere cost leader or it is reigning in both fields. Present model does not have such limitations. Targets to remain cost efficient can be obtained for any competing DMU. Unlike the Banker’s model, the proposed one ascribes unequal weight to the cost of consumption to each resource. This weight vector is determined from the industrial practice. It remains unique in the sense that it relies on few intermediate input variables to measure the performance of a DMU. These variables are dependent on large number of other independent variables, which reflect the extent of its control on the resources to signify the strategic position of it. Moreover, the proposed model offers an ideal frontier of ultimate performers, which provides a very stringent benchmark based on constant return to scale for incorporating those renowned organizations, which operate in various places in West Bengal. However, it also offers lower limits of performance to the strongly efficient performers by using the goal-oriented data envelopment analysis for analyzing the problem on a local basis. The extended model, in addition, is worthy of carrying out SDEA operations.

Under the present scenario, a new model is proposed here to concentrate on the variation present in the market due to specific consumption of resources. All inputs are assumed scarce and desirable for the production of each output (Liu et al., 2010). Thus, a good cost-cutting performance occurs because of an economic use of resources while fulfilling the standards. Unlike Taguchi et al. (1989) and Taguchi (1991), a linear societal loss function, which is solely adhered to the resource consumption, is added here instead of a formal cost function.

The central theme of this paper is as follows: determination of technical efficiency scores for the schools; determination of economic efficiency (with partial information about price); identification of cost leaders and differentiation architects; to prescribe the model of a cost leader so that education can be imparted to a full potential; and to prescribe a non-central PCA and a slack-based optimization model. Superiority in the domain of cost leadership is decided based on the closeness of any DMU from this frontier.