35 MULTIPLIER ADJUSTMENT IN DATA ENVELOPMENT ANALYSIS Jorge Azevedo Santos (Universidade de Évora) Luís Cavique Santos (Universidade Aberta) Armando Brito Mendes (Universidade dos Açores). Abstract – Weights restriction is a well-known tech- nique in the DEA field. When those techniques are applied, weights cluster around its new limits, making its evaluation dependent of its levels. This paper introduces a new ap- proach to weights adjustment by Goal Programming tech- niques, avoiding the imposition of hard restrictions that can even lead to unfeasibility. This method results in mod- els that are more flexible. Keywords: Data Envelopment Analysis, Efficiency, Weights Restriction, Evaluation, Goal Programming. I. INTRODUCTION Data Envelopment Analysis (DEA) is a mathemati- cal programming based technique to evaluate the rela- tive performance of organisations. While the main ap- plications have been in the evaluation of not-for-profit organisations, the technique can be successfully applied to other organisations, as a recent evaluation of banks in India has demonstrated [1]. With this paper, we have two objectives in mind. The first one is to present DEA-Data Envelopment Analysis, a technique which may have useful applications in many evaluation contexts, namely when assessing not-for- profit organisations. In addition to allowing the ranking of the organisations traditionally termed decision- making units, DEA also creates the conditions to im- prove performance through target setting and role-model identification. We also briefly describe the technique of deleted domain, also known as Superefficiency. The second objective is to introduce an entirely new way of adjusting multipliers by means of Goal Pro- gramming Techniques. This adjustment is a much more general way of dealing with the incorporation of exoge- nous structure preferences so far relying only in weights restriction techniques, which, in our point of view leads to the concentration of the weights in its upper and lower limits. DEA is suited for this type of evaluation because it enables results to be compared making allowances for factors [2]. DEA makes it possible to identify efficient and inefficient units in a framework where results are considered in their particular context. In addition, DEA also provides information that enables the comparison of each inefficient unit with its "peer group", that is to say, a group of efficient units that are identical with the units under analysis. These role-model units can then be stud- ied in order to identify the success factors that other comparable units can attempt to follow. Thanassoulis et al [3] argue that DEA is preferable to other methods, such as regression analysis, which also make it possible to contextualize results. The present paper is structured as follows. The next section describes the development and fields of applica- tion of the technique, while section III introduces the DEA models followed by a numerical example. In sec- tion IV, we present Superefficiency evaluation, an ex- tension of DEA also known as deleted domain. Section V and VI deal with the graphical solution in the weights space and makes a very short description of the weights restrictions technique respectively. In section VII, a new concept of multiplier adjust- ment is introduced and exemplified through a small data set. In section VIII, a case with artificially generated data is solved to highlight the potentialities of this technique. This paper ends up with a final section with the conclu- sions and directions of future work. Readership not familiar with DEA, may find the brief introduction to the method presented below useful, but for those who wish to follow the matter further there is a good review of DEA in Boussofiane et al [4]. II. HISTORY AND APPLICATIONS OF DEA DEA is a mathematical programming technique pre- sented in 1978 by Charnes, Cooper and Rhodes [5], although its roots may be found as early as 1957 in Far- rel`s seminal work [6]. This technique is usually intro- duced as a non-parametric one, but in fact, it rests on the assumption of linearity [7] and for the original models even in the more stringent assumption of proportional- ity. Its application has been focused mainly on the effi- ciency assessment of not-for-profit organizations, since these cannot be evaluated on the basis of traditional economic and financial indicators used for commercial companies.