Determining the Best Performance Time Period of a System

The main purpose of this paper is to determine the best performance time period of a system, consisting some DMUs, among some sequential time periods. This aim is satised by two proposed algorithms, the rst based on global Malmquist Productivity Index and the second is based on PPS frontiers

Using convex preference cones in multiple criteria decision making and related fields

This paper reviews our own and colleagues’ research on using convex preference cones in multiple criteria decision making and related fields. The original paper by Korhonen, Wallenius, and Zionts was published in Management Science in 1984. We first present the underlying theory, concepts, and method. Then we discuss applications of the theory, particularly for finding the most preferred alternative, finding a partial and total rank ordering of alternatives, as well as developing algorithms for solving multi-objective integer and other optimization problems

Robustness of efficiency scores in data envelopment analysis with interval scale data

Our paper focuses on a robustness analysis of efficiency scores in the context of Data Envelopment Analysis (DEA) assuming interval scale data, as defined in A. Dehnokhalaji, P. J. Korhonen, M. Köksalan, N. Nasrabadi and J. Wallenius, “Efficiency Analysis to incorporate interval scale data”, European Journal of Operational Research 207 (2), 2010, pp. 1116–1121. We first show that the definition of the efficiency score used in our paper is a well-defined measure according to Aparicio and Pastor (J. Aparicio and J. T. Pastor, “A well-defined efficiency measure for dealing with closest targets in DEA”, Applied Mathematics and Computation 219 (17), 2013, pp. 9142–9154.). Next, we characterize how robust the efficiency scores are with respect to improvements and deteriorations of inputs and outputs. We illustrate our analysis with two examples: a simple numerical example and a more complex example using real-world data

Convex cone-based partial order for multiple criteria alternatives

In this paper, we consider the problem of finding a preference-based strict partial order for a finite set of multiple criteria alternatives. We develop an approach based on information provided by the decision maker in the form of pairwise comparisons. We assume that the decision maker's value function is not explicitly known, but it has a quasi-concave form. Based on this assumption, we construct convex cones providing additional preference information to partially order the set of alternatives. We also extend the information obtained from the quasi-concavity of the value function to derive heuristic information that enriches the strict partial order. This approach can as such be used to partially rank multiple criteria alternatives and as a supplementary method to incorporate preference information in, e.g. Data Envelopment Analysis and Evolutionary Multi-Objective Optimization

Efficiency analysis to incorporate interval-scale data

We develop an approach to efficiency analysis to enable us to incorporate interval-scale data in addition to ratio-scale data. Our approach introduces a measure of inefficiency and identifies efficient units as is done in Data Envelopment Analysis. The basic idea in our approach is to find the "best" hyperplane separating the units that are better and worse than each unit. "Best" is defined in such a way that the number of not-better units is maximal. The efficiency measure is defined as a proportion of not-better units to all units. The results are invariant under a strictly increasing linear re-scaling of any input- or output-variables. Thus zeroes or negative values do not cause problems for the analysis. The approach is used to analyze the data of the research evaluation exercise recently carried out at the University of Joensuu, Finland.Data Envelopment Analysis Interval-scale Research evaluation

Constructing a strict total order for alternatives characterized by multiple criteria: An extension

The problem of finding a strict total order for a finite set of multiple criteria alternatives is considered. Our research extends previous work by us, which considered finding a partial order for a finite set of alternatives. We merge the preference information extracted from the preference cones and corresponding polyhedral sets, with the information derived from pairwise comparisons of two alternatives, yielding a preference matrix. This preference matrix is used as input to an integer programming model to obtain a strict total order that provides a transitive ranking for the set of alternatives. (c) 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 155-163, 201