A one-model approach to congestion in data envelopment analysis
Introduction
As noted in [1], two approaches to the analysis of congestion are available in the data envelopment analysis (DEA) literature. See also the exchanges reported in [2], [3]. Because Cooper et al. [1] shows some shortcomings in the approach of Färe et al. [4], we here focus on the development reported in [5] from which we adopt the following definition:
where “DMU” means “decision making unit”—defined as the entity responsible for converting inputs into outputs.Congestion: Evidence of congestion is present in the performance of DMUj=DMU0 when reductions in one or more inputs are associated with increases in one or more outputs—without worsening any other input or outputs. More precisely, congestion is evidenced when the attainment of maximal output requires a reduction in one or more of the input amounts used.
The development that follows will make this definition more precise. For the present, however, we assume that maximal output augmentations will always accompany such input reductions. In short, we assume that movement is effected along a frontier like the one connecting points D and C in Fig. 1. This part of the frontier differs from the “efficient frontier”, which connects A and B in Fig. 1, in accordance with the following definition:
Efficiency (Technical efficiency): Efficiency is achieved by DMU0 if and only if it is not possible to improve some of its inputs or outputs without worsening some of its other inputs or outputs.
This property, we may note, is not present in the frontier connecting B and C in Fig. 1. This segment of the frontier has the property noted in the following definition:
Inefficiency (Technical inefficiency): Technical inefficiency is said to be present in the performance of DMU0 when the evidence shows that it is possible to improve some input or output without worsening some other input or output.
As can be seen in Fig. 1, movements from C back to B result in input reductions but not any output increases. The result therefore differs from movements to C from D which identify input decreases that are associated with output increases and, hence, provide the needed evidence of congestion. Thus, as noted in [5], congestion may be regarded as a particularly severe (separately identifiable) form of technical inefficiency. Remark 1 The term “technical inefficiency” refers to the fact that costs, prices or other such weights for effecting evaluations are not used (or needed) in the analysis. Hence, in this sense, the analysis is “value free” and “objective”. Remark 2 The other, non-frontier, points in Fig. 1 all reflect inefficiencies that are identified by reference to the portion of the frontier that is used to evaluate their performances in the manners discussed below. Remark 3 Other inefficiencies are covered in [4], [6]. See also [4], [7].
Section snippets
The two-model approach
The two currently available approaches to congestion, as described in [1], are attributable to Cooper et al. [8] and Färe et al. [4], [7]. However, as also described in [1], the latter approach suffers from the following two deficiencies: (1) It can identify congestion as being present when this is not the case, and (2) it can fail to identify congestion even when it is present.
To be sure, suggestions for repairing these deficiencies are set forth in the exchange between Cherchye et al. [9] and
The one-model approach
To replace the above two-model approach with a single model, we proceed as follows. First, we note that for an optimal solution (φ*, λ*, s+*, s−*) of (1), we can use si−c=si−*−δi−, in (7) to rewrite (6) as
This model can be regarded as part of a two-stage procedure analogous to the one we described for dealing with the non-Archimedean element ε>0 in (1). Here, however, (8) can be
Summary and conclusion
As these examples have made clear, we can use our one-model approach to analyze congestion. We can also tell whether the DMU0 being analyzed operated on a frontier but we cannot tell whether that portion of the frontier is efficient or inefficient. Concomitantly, we cannot identify the total slack si− or its technical (only) component (see [1]). See also [9], [10] for other properties of these two-model approaches. In any case, the two-model approaches we have used in this analysis were taken
Acknowledgements
W.W. Cooper wishes to express his appreciation to the IC2 Institute of the University of Texas for support of his research. Z.M. Huang would like to acknowledge a President's Faculty Development Grant from Adelphi University for support of his research, and S.X. Li would like to acknowledge a Research Sabbatical Leave Grant from Adelphi University for support of her research. The authors are also grateful to Barnett Parker, Editor-in-Chief of Socio-Economic Planning Sciences, for suggestions
References (12)
- et al.
Comparisons and evaluations of alternative approaches to evaluating congestion in DEA
European Journal of Operational Research
(2001) - et al.
Measuring the efficiency of decision making units
European Journal of Operational Research
(1978) - et al.
Alternative treatments of congestion in DEAa rejoinder to Cooper, Gu and Li
European Journal of Operational Research
(2001) - et al.
Notealternative treatments of congestion in DEA—a response to the Cherchye, Kuosmanen and Post critique
European Journal of Operational Research
(2001) - Färe R, Grosskopf S. When can slacks be used to identify congestion? An answer to Cooper, W. W. Seiford, L, and Zhu, J....
- et al.
Slacks and Congestiona response to comments by Färe and Grosskopf
Socio-Economic Planning Sciences
(2001)
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