Input/output weight restrictions, CSOI constraint and efficiency improvement
28 Sep 2016-Benchmarking: An International Journal (Emerald Group Publishing Limited)-Vol. 23, Iss: 7, pp 2080-2091
TL;DR: In this article, the authors developed data envelopment analysis (DEA) models and algorithms for efficiency improvement when the inputs and output weights are restricted and there is fixed availability of inputs in the system.
Abstract: Purpose
The purpose of this paper is to develop data envelopment analysis (DEA) models and algorithms for efficiency improvement when the inputs and output weights are restricted and there is fixed availability of inputs in the system.
Design/methodology/approach
Limitation on availability of inputs is represented in the form of constant sum of inputs (CSOI) constraint. The amount of excess input of an inefficient decision-making unit (DMU) is redistributed among other DMUs in such a way so that there is no reduction in their efficiency. DEA models have been developed to design the optimum strategy to reallocate the excess input.
Findings
The authors have developed the method for reallocating the excess input among DMUs while under CSOI constraint and parameter weight restrictions. It has been shown that in this work to improve the efficiency of an inefficient DMU one needs the cooperation of selected few DMUs. The working of the models and results have been shown through a case study on carbon dioxide emissions of 32 countries.
Research limitations/implications
The limitation of the study is that only one DMU can expect to benefit from the application of these methods at any given time.
Practical implications
Results of the paper are useful in situations when decision maker is exploring the possibility of transferring the excess resources from underperforming DMUs to the other DMUs to improve the performance.
Originality/value
This strategy of reallocation of excess input will be very useful in situations when decision maker is exploring the possibility of transferring the excess resources from underperforming DMUs to the other DMUs to improve the performance. Unlike the existing works on efficiency improvement under CSOI, this work seeks to address the issue of efficiency improvement when the input/output parameter weights are also restricted.
References
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TL;DR: A nonlinear (nonconvex) programming model provides a new definition of efficiency for use in evaluating activities of not-for-profit entities participating in public programs and methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs.
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TL;DR: The CCR ratio form introduced by Charnes, Cooper and Rhodes, as part of their Data Envelopment Analysis approach, comprehends both technical and scale inefficiencies via the optimal value of the ratio form, as obtained directly from the data without requiring a priori specification of weights and/or explicit delineation of assumed functional forms of relations between inputs and outputs as mentioned in this paper.
Abstract: In management contexts, mathematical programming is usually used to evaluate a collection of possible alternative courses of action en route to selecting one which is best. In this capacity, mathematical programming serves as a planning aid to management. Data Envelopment Analysis reverses this role and employs mathematical programming to obtain ex post facto evaluations of the relative efficiency of management accomplishments, however they may have been planned or executed. Mathematical programming is thereby extended for use as a tool for control and evaluation of past accomplishments as well as a tool to aid in planning future activities. The CCR ratio form introduced by Charnes, Cooper and Rhodes, as part of their Data Envelopment Analysis approach, comprehends both technical and scale inefficiencies via the optimal value of the ratio form, as obtained directly from the data without requiring a priori specification of weights and/or explicit delineation of assumed functional forms of relations between inputs and outputs. A separation into technical and scale efficiencies is accomplished by the methods developed in this paper without altering the latter conditions for use of DEA directly on observational data. Technical inefficiencies are identified with failures to achieve best possible output levels and/or usage of excessive amounts of inputs. Methods for identifying and correcting the magnitudes of these inefficiencies, as supplied in prior work, are illustrated. In the present paper, a new separate variable is introduced which makes it possible to determine whether operations were conducted in regions of increasing, constant or decreasing returns to scale in multiple input and multiple output situations. The results are discussed and related not only to classical single output economics but also to more modern versions of economics which are identified with "contestable market theories."
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TL;DR: A sketch of some of the major research thrusts in data envelopment analysis (DEA) over the three decades since the appearance of the seminal work of Charnes et al. is provided.
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