Ranking Intervals and Dominance Relations for Ratio-Based Efficiency Analysis

We develop comparative results for ratio-based efficiency analysis, based on the decision making units' (DMUs) relative efficiencies over sets of feasible weight that characterize preferences for input and output variables. Specifically, we determine (i) ranking intervals which indicate the best and worst efficiency rankings that a DMU can attain relative to other DMUs, (ii) dominance structures which convey what other DMUs a given DMU dominates in one-on-one efficiency comparisons, and (iii) efficiency bounds which show how much more efficient a DMU can be relative to a given DMU or a subset of other DMUs. These efficiency results-which reflect the full range of feasible input and output weights-are robust in the sense that they are insensitive to possible outliers and do not necessitate particular returns-to-scale assumptions. We also report a real case study where these results supported the efficiency analysis of the twelve departments at a large technical university. Key words : performance measurement, data efficiency analysis, preference modeling Introduction Inspired by the seminal paper of Because the efficiency scores are computed relative to the efficiency frontier, these scores are potentially sensitive to what DMUs are included in or excluded from the analysis: specifically, the introduction/removal of a single outlier (e.g., an exceptionally efficient DMU that produces more outputs per inputs than the other DMUs) may shift the efficient frontier considerably, which may disrupt the reported efficiency scores for other DMUs and hence perplex the users of efficiency results (see, e.g., Seiford and Zhu, 1998ab; Motivated by the above considerations, we develop efficiency results which allow us to answer questions such as: • What are the best/worst rankings that DMU A can attain in comparison with other DMUs, based on their efficiency ratios

Developing robust composite measures of healthcare quality – ranking intervals and dominance relations for Scottish Health Boards

Although composite indicators are widely used to inform health system performance comparisons, such measures typically embed contentious assumptions, for instance about the weights assigned to constituent indicators. Moreover, although many comparative measures are constructed as ratios, the choice of denominator is not always straightforward. The conventional approach is to determine a single set of weights and to choose a single denominator, even though this involves considerable methodological difficulties. This study proposes an alternative approach to handle incomplete information about an appropriate set of weights and about a defensible denominator in composite indicators which considers all feasible weights and can incorporate multiple denominators. We illustrate this approach for comparative quality assessments of Scottish Health Boards. The results (displayed as ranking intervals and dominance relations) help identify Boards which cannot be ranked, say, worse than 4th or better than 7th. Such rankings give policy-makers a sense of the uncertainty around ranks, indicating the extent to which action is warranted. By identifying the full range of rankings that the organizations under comparison may attain, the approach proposed here acknowledges imperfect information about the “correct” set of weights and the appropriate denominator and may thus help to increase transparency of and confidence in health system performance comparisons

Ranking efficient DMUs using cooperative game theory

The problem of ranking Decision Making Units (DMUs) in Data Envelopment Analysis (DEA) has been widely studied in the literature. Some of the proposed approaches use cooperative game theory as a tool to perform the ranking. In this paper, we use the Shapley value of two different cooperative games in which the players are the efficient DMUs and the characteristic function represents the increase in the discriminant power of DEA contributed by each efficient DMU. The idea is that if the efficient DMUs are not included in the modified reference sample then the efficiency score of some inefficient DMUs would be higher. The characteristic function represents, therefore, the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient units is dropped from the sample. Alternatively, the characteristic function of the cooperative game can be defined as the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient DMUs are the only efficient DMUs that are included in the sample. Since the two cooperative games proposed are dual games, their corresponding Shapley value coincide and thus lead to the same ranking. The more an ef- ficient DMU impacts the shape of the efficient frontier, the higher the increase in the efficiency scores of the inefficient DMUs its removal brings about and, hence, the higher its contribution to the overall discriminant power of the method. The proposed approach is illustrated on a number of datasets from the literature and compared with existing methods

Effective and efficient algorithm for multiobjective optimization of hydrologic models

Practical experience with the calibration of hydrologic models suggests that any single-objective function, no matter how carefully chosen, is often inadequate to properly measure all of the characteristics of the observed data deemed to be important. One strategy to circumvent this problem is to define several optimization criteria (objective functions) that measure different (complementary) aspects of the system behavior and to use multicriteria optimization to identify the set of nondominated, efficient, or Pareto optimal solutions. In this paper, we present an efficient and effective Markov Chain Monte Carlo sampler, entitled the Multiobjective Shuffled Complex Evolution Metropolis (MOSCEM) algorithm, which is capable of solving the multiobjective optimization problem for hydrologic models. MOSCEM is an improvement over the Shuffled Complex Evolution Metropolis (SCEM-UA) global optimization algorithm, using the concept of Pareto dominance (rather than direct single-objective function evaluation) to evolve the initial population of points toward a set of solutions stemming from a stable distribution (Pareto set). The efficacy of the MOSCEM-UA algorithm is compared with the original MOCOM-UA algorithm for three hydrologic modeling case studies of increasing complexity

Dominance measuring methods within MAVT/MAUT with imprecise information concerning decision-makers'preferences

Dominance measuring methods are an approach for dealing with complex decision-making problems with imprecise information within multi-attribute value/utility theory. These methods are based on the computation of pairwise dominance values and exploit the information in the dominance matrix in different ways to derive measures of dominance intensity and rank the alternatives under consideration. In this paper we review dominance measuring methods proposed in the literature for dealing with imprecise information (intervals, ordinal information or fuzzy numbers) about decision-makers? preferences and their performance in comparison with other existing approaches, like SMAA and SMAA-II or Sarabando and Dias? method

Dominance relations when both quantity and quality matter, and applications to the\r\ncomparison of US research universities and worldwide top departments in economics

In this article, we propose an extension of the concept of stochastic dominance intensively\r\nused in economics for the comparison of composite outcomes both the quality and the\r\nquantity of which do matter. Our theory also allows us to require unanimity of judgement\r\namong new classes of functions. We apply this theory to the ranking of US research\r\nuniversities, thereby providing a new tool to scientometricians (and the academic\r\ncommunities) who typically aim to compare research institutions taking into account both\r\nthe volume of publications and the impact of these articles. Another application is provided\r\nfor comparing and ranking academic departments when one takes into account both the size\r\nof the department and the prestige of each member.Ranking, dominance relations, citations.

Stand structure and wood production efficiency in Black Hills ponderosa pine

2011 Fall.Includes bibliographical references.Contemporary North American forestry has moved away from management primarily for fiber production toward management for a suite of priorities, including aesthetics, forest health, wildlife habitat, and restoration of pre-settlement conditions. Multi-aged forest stands are better suited to contemporary management priorities than even-aged stands in many instances, largely because stand density can be held in check and regeneration initiated without wholesale removal of the overstory. However, competitive interaction between trees of varying size and inherent physiological differences between small and large trees make it unclear that multi-aged stands produce stemwood volume as efficiently as even-aged stands. In South Dakota's Black Hills National Forest, fiber production remains an important management objective, which raises questions regarding potential impacts to wood production associated with creating multi-aged structures. We used stemwood volume production per unit leaf area as a metric of production efficiency to compare productivity of different sized trees and cohorts of trees within multi-aged stands, as well as to compare productivity of multi-aged to even-aged stands of pure Pinus ponderosa var. scopulorum. Leaf area is a good measure of resource acquisition for productivity analysis both because it is closely related to light capture, and because multi-aged silvicultural systems can use leaf area per unit ground area (leaf area index) as a stocking tool to regulate density of individual cohorts within a stand. Direct measurement of leaf area is currently unfeasible in the context of daily forestry operations. Consequently, an explicit relationship between leaf area and a standard forestry metric is needed to allow managers to allocate leaf area among cohorts within multi-aged stands using available inventory data. A widely-used stocking tool called stand density index (SDI) is highly correlated with leaf area and has been suggested for this purpose. Yet, it is unclear that the relationship between SDI and leaf area is unbiased across cohorts within multi-aged stands. This work sampled 1,824 trees in 21 multi-aged and 10 even-aged stands to address questions of production efficiency and implementation of multi-aged silviculture. We found trees in the smallest cohort in multi-aged stands produced stemwood on average 20% less efficiently than trees in larger cohorts. Growth dominance analysis showed efficiency increased with increasing size for the smallest trees in multi-aged stands, but this relationship was inverted for larger trees. Despite size related efficiency differences between trees in multi-aged stands, there was no statistical difference in production efficiency between stand structures. SDI explained almost 90% of leaf area variation in multi-aged stands, with no statistical difference in the relationship across cohorts. Results suggested no penalty in terms of production efficiency for multi-aged stands compared to their even-aged counterparts. Furthermore, SDI provided an unbiased estimate of leaf area in multi-aged stands, supporting its use as a stocking tool for management of complex stand structures