SUMMARY

An important problem in decision analysis is the evaluation of the difference between two or more different rankings for a set of alternatives. A novel model based on the aggregation technique for combining group member's preferences into one consensus ranking is suggested in this article. The model developed may be used to develop consensus and evolve ranking of alternatives. The application of the model is demonstrated through a case for supplier rating. The advantages of the proposed approach are also highlighted.

A multi-criteria group decisionmaking model for supplier rating

This paper proposes a methodology for evaluating and selecting R&D projects in a collective decision setting, especially useful at sectorial and national levels. It consists of two major phases: Evaluation and Selection. The evaluation process repeatedly uses mathematical programming models to determine the “relative values” of a given R&D project from the viewpoint of the other R&D projects. The selection process of R&D projects is based on these “relative values” and is done through a model-based outranking method. The salient features of the methodology developed are its ability to (1) permit the evaluation of an R&D project from the viewpoint of the other R&D projects without at first imposing a uniform evaluation scheme, and (2) maximize the level of consensus as to which projects should not be retained in the R&D Program being funded, thus minimizing the level of possible resentment in those organizations or departments whose projects are not included in the R&D Program. Also discussed in this paper...

https://www.jstor.org/stable/info/2632540

A methodology for collective evaluation and selection of industrial R&D projects

Enhancing data consistency in decision matrix: Adapting Hadamard model to mitigate judgment contradiction

A preference aggregation method through the estimation of utility intervals

Distance-based and ad hoc consensus models in ordinal preference ranking

This paper examines the problem of rank ordering a set of players or objects on the basis of a set of pairwise comparisons arising from a tournament. The criterion for deriving this ranking is to have as few cases as possible where player i is ranked above j while i was actually defeated by j in the tournament. Such a situation is referred to as a violation. The objective, therefore, is to determine the Minimum Violations Ranking MVR. While there are situations where this ranking would be allowed to contain ties among subsets of objects, we will concern ourselves herein with linear ordering no ties. A series of examples are given where this requirement would seem to be appropriate. In order to put the MVR problem into proper perspective we introduce the concept of a distance on the set of tournaments. A set of natural axioms is presented which any such distance measure should obey, and it is proven that in the presence of these axioms a unique such measure exists. It is then shown that the MVR problem is equivalent to the minimum distance problem, which can be represented in several forms-in particular as a problem of determining the minimum feedback edge set in a graph and as a mixed integer generalized network problem. This opens up a wide scope of possible solution procedures for the MVR problem. An optimal algorithm is presented along with computational results. In addition, various heuristics are discussed including an improved heuristic referred to as the Iterated Kendall method.

On the Minimum Violations Ranking of a Tournament

Cook and Kress Cook, Wade D., Moshe Kress. 1985. Ordinal ranking with intensity of preference. Management Sci.31 1 26-32. present a model for representing ordinal preference rankings, where the voter can express intensity or degree of preference. The consensus of a set of m rankings is that ranking whose distance from this set is minimal. The consensus problem is then shown to be an integer programming problem with a piecewise linear convex objective function. In the present note we prove that the constraint matrix for this integer problem is totally unimodular. In addition, it is shown that the problem can be expressed as an equivalent integer linear programming problem. These two facts allow us to represent the consensus problem as a linear programming model. To further facilitate an efficient solution procedure to the consensus problem, it is shown that the number of columns in the L.P. model can generally be reduced significantly. Computational results on a wide range of problems is presented.

Iqbal Ali

Papers

On the Minimum Violations Ranking of a Tournament

Note-Ordinal Ranking and Intensity of Preference: A Linear Programming Approach