Showing papers by "William W. Cooper published in 2000"

A unified additive model approach for evaluating inefficiency and congestion with associated measures in DEA

Abstract: This paper develops a necessary and sufficient condition for the presence of (input) congestion. Relationships between the two congestion methods presently available are discussed. The equivalence between Fare et al. [12] , [13] and Brockett et al. [2] hold only when the law of variable proportions is applicable. It is shown that the work of Brockett et al. [2] improves upon the work of Fare et al. [12] , [13] in that it not only (1) detects congestion but also (2) determines the amount of congestion and, simultaneously, (3) identifies factors responsible for congestion and distinguishes congestion amounts from other components of inefficiency. These amounts are all obtainable from non-zero slacks in a slightly altered version of the additive model — which we here further extend and modify to obtain additional details. We also generate a new measure of congestion to provide the basis for a new unified approach to this and other topics in data envelopment analysis (DEA).

Marginal Rates and Elasticities of Substitution with Additive Models in DEA

Abstract: Marginal rates and elasticities of substitution are derived from the optimal slack values obtained from modified versions of additive DEA models. Projection formulas are used to ensure that all points are on the efficient frontier as required for conformance with assumptions in micro-economics. The models used differ from standard versions in that slack values are allowed to be negative as well as positive in these additive models. This makes movement possible on efficiency frontiers, where improvement in some inputs or outputs requires worsening other inputs or outputs. A new definition is therefore introduced in which efficiency is attained only if the value of the worsenings is exactly offset by the value of the improvements. This includes, but is not restricted to, the case in which all slacks must be zero for full attainment of efficiency—as in standard versions of additive models.

Evaluating Efficiencies of Turbofan Jet Engines: A Data Envelopment Analysis Approach

Abstract: Data envelopment analysis (DEA), a mathematical-programming-basedmethod, has been developed in the operations research and economics literatures for effecting efŽ ciency evaluations. Its use is explained and illustrated with an application to data on turbofan jet engines. Results are compared with standard engineering methods for measuring efŽ ciency. In contrast to the latter, DEA handles data on multiple inputs and multiple outputs that can be used to characterize the performance of each engine. This is accomplished without recourse to any use of prearrangedweights.DEAalsoprovidesinformationonthe sources andamountsof inefŽ ciencies in each inputandoutput of each enginewithout requiring knowledgeof the functional relations that give rise to these estimates. DEA represents an alternative method for evaluating efŽ ciencies. Its purpose is to augment, not replace, traditionalmethods.