Weight restrictions in DEA: misplaced emphasis?

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract: Measuring productive efficiency is an important research strand within fields of economics, management science and operations research. One definition of efficiency is the proportional scaling needed for observations of an inefficient unit to be projected onto an efficient production function and another definition is a ratio index of weighted outputs on weighted inputs. When linear programming is used to estimate efficiency the two definitions give identical results due to the fundamental duality of linear programming. Empirical applications of DEA using linear programming showed a prevalence of zero weights leading to questioning the consequence for the efficiency score estimate based on the ratio definition. Early literature on weight restrictions is exclusively based on the ratio efficiency. It was stated that variables with zero weights had no influence on the efficiency score, in spite of the alleged importance of the variables. This has been one motivation for introducing restrictions on weights. Another empirical result was that often there were too many efficient units. This problem could also be overcome by introducing weight restrictions. Weight restrictions were said to introduce values for inputs and outputs. The paper makes a critical examinations of these claims based on defining efficiency relative to a frontier production function. Terms of use: Documents in

Critical evaluation of the performance assessment model of Brazilian electricity distribution companies

“…These restrictions come in the form of trade-offs between output and input and are based on Podinovski (2004). Even if we consider that this way of imposing weight restrictions is correct, trade-offs and valuation of inputs and products is combated in Forsund (2012); Also there is the problem of imposition of restrictions on non-controllable variables. It is known that the models in the literature have been proposed for controlled variables and nothing was stated about imposing the weights in non-controllable variables, such as the case of non-technical and quality losses.…”

“…The use of multiple inputs and multiple outputs makes the multidimensional model, where the boundary of production makes up a "shell" on the hyperplane. Forsund (2012) states that the extremely efficient units (those with slacks equal to zero) are vertex points in that hyperplane. So the solution to the shadow price of these units is not necessarily unique, because this unit belongs to more than one side of the production frontier.…”

Optimal Path for Controlling Sectoral CO2 Emissions Among China’s Regions: A Centralized DEA Approach

“…Decision maker preference information can also be incorporated into DEA by employing the multiple criteria decision-making concept [43,44]. A well-known drawback of weight restrictions is the fact that their use in the multiplier model implicitly changes the model of production technology in the envelopment form [45], and that they inappropriately represent the demands of real-world productive activities [46]; in other words, their use makes the traditional meanings of "technical efficiency" and "technologically feasible improvement" become unsubstantiated [47,48]. Comparing to the other research up to now, this paper considers the weights of the outputs and inputs will only be restricted by the constraints used to form environmental production technology, without any user-specified preference restriction on weights.…”

DEA Models with Production Trade-offs and Weight Restrictions

“…Furthermore, the traditional meaning if efficiency as the ultimate and technologically feasible improvement factor generally becomes unsubstantiated (Podinovski 2004a;Førsund 2013).…”