Zilla Sinuany-Stern

Review of ranking methods in the data envelopment analysis context

Abstract Within data envelopment analysis (DEA) is a sub-group of papers in which many researchers have sought to improve the differential capabilities of DEA and to fully rank both efficient, as well as inefficient, decision-making units. The ranking methods have been divided in this paper into six, somewhat overlapping, areas. The first area involves the evaluation of a cross-efficiency matrix, in which the units are self and peer evaluated. The second idea, generally known as the super-efficiency method, ranks through the exclusion of the unit being scored from the dual linear program and an analysis of the change in the Pareto Frontier. The third grouping is based on benchmarking, in which a unit is highly ranked if it is chosen as a useful target for many other units. The fourth group utilizes multivariate statistical techniques, which are generally applied after the DEA dichotomic classification. The fifth research area ranks inefficient units through proportional measures of inefficiency. The last approach requires the collection of additional, preferential information from relevant decision-makers and combines multiple-criteria decision methodologies with the DEA approach. However, whilst each technique is useful in a specialist area, no one methodology can be prescribed here as the complete solution to the question of ranking.

Academic departments efficiency via DEA

Abstract This paper presents a case study where academic departments at Ben-Gurion University were evaluated via the Data Envelopment Analysis using the CCR model. Extensive post analyses were performed in several directions. First various sets of data were used to identify efficient and inefficient departments. New efficiency measures are suggested in relation to the reference set included in the analyses of academic departments. We measured the efficiency of departments to other departments within the same school. We applied cluster analyses to divide the departments into several sets; and the discriminant analysis to test the match of the efficiency/inefficiency division of the CCR ratio. We further tested organizational changes where an inefficient department was closed and joins other departments. Finally we compared the CCR model to the pure economic approach—the cost per student ratio.

SCALING UNITS VIA THE CANONICAL CORRELATION ANALYSIS IN THE DEA CONTEXT

Abstract This paper deals with the evaluation of decision making units which have multiple inputs and outputs. A new method (CCA/DEA) is developed where the Canonical Correlation Analysis (CCA) is utilized to provide a full rank scaling for all the units rather than a categorical classification (for efficient and inefficient units) as done by the Data Envelopment Analysis (DEA). The CCA/DEA approach is an attempt to bridge the gap between the frontier approach of DEA and the average tendencies of statistics (econometrics). Nonparametric statistical tests are employed to validate the consistency between the classification from the DEA and the postclassification that was generated by the CCA/DEA.

DEA and the discriminant analysis of ratios for ranking units

The purpose of this study is to develop a new method which provides for given inputs and outputs the best common weights for all the units that discriminate optimally between the efficient and inefficient units as pregiven by the Data Envelopment Analysis (DEA), in order to rank all the units on the same scale. This new method, Discriminant Data Envelopment Analysis of Ratios (DR/DEA), presents a further post-optimality analysis of DEA for organizational units when their multiple inputs and outputs are given. We construct the ratio between the composite output and the composite input, where their common weights are computed by a new non-linear optimization of goodness of separation between the two pregiven groups. A practical use of DR/DEA is that the common weights may be utilized for ranking the units on a unified scale. DR/DEA is a new use of a two-group discriminant criterion that has been presented here for ratios, rather than the traditional discriminant analysis which applies to a linear function. Moreover, non-parametric statistical tests are employed to verify the consistency between the classification from DEA (efficient and inefficient units) and the post-classification as generated by DR/DEA.

Combining ranking scales and selecting variables in the Dea context: the case of industrial branches

Abstract Data Envelopment Analysis (DEA) has been introduced by Charnes et al. (Charnes, A., Cooper, W. W. and Rhodes, E., Measuring the efficiency of decision making units. Eur. J. Oper. Res., 1978, 2, 429–444) based on the Farrell measurement of productive efficiency (J. Royal Statist. Soc., 1957, A120, 253–290). Originally DEA was designed to evaluate the efficiency of decision making units in the public sector (e.g. schools, towns, hospitals and nations) based on their given multiple inputs and outputs which are not measured in unified units (e.g. money). Eventually DEA was used in business and industry (e.g. bank branches). The DEA merely classifies the units into two dichotomic groups, efficient and inefficient. The purpose of our paper is to fully rank the units from the most efficient to the least efficient within the DEA context. For this purpose we use here three recent ranking methods developed within the DEA framework. The multi-ranking approach is utilized for validating the ranks and forming new overall ranking by combining the ranks which statistically fit the DEA classification. In a way this approach bridges between the DEA frontiers approach and the statistical/econometric approach of averages. The motivating example here is the case of ranking Israeli Industrial Branches. In order to determine the appropriate labor variables (number of man hours, average wage, vs total labor cost) we run two versions of the model. In this paper we use various recent scale ranking methods in the DEA (Data Envelopment Analysis) context. Two methods are based on multivariate statistical analysis: canonical correlation analysis (CCA) and discriminant analysis of ratios (DR/DEA), while the third is based on the cross efficiency matrix (CE/DEA) derived from the DEA. This multirank approach is necessary for rank validation of the model. Their consistency and goodness of fit with the DEA are tested by various nonparametric statistical tests. Once we had validated the consistency among the ranking methods, we constructed a new overall rank combining all of them. Actually, given the DEA results, we here provide ranks that complement the DEA for a full ranking scale beyond the mere classification to two dichotomic groups. This new combined ranking method does not replace the DEA, but it adds a post-optimality analysis to the DEA results. In this paper, we combine the ranking approach with stochastic DEA: each approach is in the forefront of DEA. This is an attempt to bridge between the DEA frontier Pareto Optimum approach and the average approach used in econometrics. Furthermore, the quality of this bridge is tested statistically and thus depends on the data. We demonstrate this method for fully ranking the Industrial Branches in Israel. In order to delete unmeaningful input and output variables, and to increase the fitness between the DEA and the ranking, we utilize the canonical correlation analysis to select the meaningful variables. Furthermore, we run the ranking methods on two sets of variables to select the proper combination of variables which best represents labor.

Simulating the evacuation of a small city: the effects of traffic factors

Abstract A behavioral-based simulation model for spontaneous urban evacuation is used to examine the sensitivity of network clearance time to several traffic factors (e.g. interaction with pedestrians, intersection traversing time, and car ownership) and route choice mechanisms (shortest path and myopic behavior). It is a micro traffic simulation model based on stochastic simulation of series of events in a radiological emergency situation. Evacuation time comes closer to reality when interaction with pedestrians and a uniform distribution of intersection traversing time are assumed. More realistic results are also found whenever routes are selected according to the maximal distance from the last car. The sensitivity of clearance time to population growth and car ownership indicates that the model can be easily applied to cities of various sizes.

Generating the Discrete Efficient Frontier to the Capital Budgeting Problem

In this paper, we characterize the capital budgeting problem by two objective functions. One is maximizing the present value of accepted projects and the other is minimizing their risk. As we assume that the weights assigned to these objectives are unspecified, we utilize a Discrete Efficient Frontier DEF approach to represent all the efficient combinations. We found an optimality range for each efficient combination covering the entire possible range of weights zero to one. Furthermore, we present different properties and characteristics of the DEF, and develop two algorithms for constructing the DEF. The first one is a simple heuristic and the second one is an optimal algorithm. We conducted experiments measuring the effectiveness of the heuristic algorithm and the effect of terminating the optimal algorithm before its completion. We have shown that the heuristic algorithm, which is the first phase of the branch-and-bound algorithm, has an average error of about 2%. Furthermore, we have shown that this average error can be reduced by applying only part of the optimal algorithm and terminating it before its actual completion.

The location of a hospital in a rural region: The case of the Negev

Abstract This paper reports on the strategic planning of hospital services in the Negev region of Israel, a sparsely populated region experiencing rapid population growth. One of the questions that concerned the decision-makers was whether to increase the medical services in the area by expanding the existing hospital or by building an additional one. The suggestion to build a new hospital raised questions of location. The purpose of this paper is to address this problem. Objective and subjective approaches were employed in a three-stage procedure in order to find the best location. First the problem was analyzed using established location models to generate a set of candidate locations. In the next stages experts evaluated the alternative locations by employing a subjective multicriteria model—the Analytical Hierarchy Process (AHP). Finally, a recommended solution was presented and analyzed in light of the strategic plan.

A single facility location problem with a weighted maximin-minimax rectilinear distance

Abstract This paper provides an algorithm for locating a single facility in a region, where the objective function is composed of the weighted maximin and minimax rectilinear distances from a set of given demand points. This weighted objective function is applicable when the facility to be located is somewhat desirable but it should not be too close to the demand points, since it also has some undesirable effects. It has been proven in this paper, that it is enough to test for optimality all the intersection points of any two lines forming the equirectilinear distances between any pair of demand points or boundary lines of the region. The algorithm developed here tests these intersection points. The efficient set of points and their optimality range are found. This parametric form of the solution provides an optimal solution for any desired weight.

Evaluating the efficiency of local municipalities in providing traffic safety using the Data Envelopment Analysis.

The purpose of this study was to estimate the relative efficiency of 197 local municipalities in traffic safety in Israel during 2004-2009, using Data Envelopment Analysis (DEA). DEA efficiency is based on multiple inputs and multiple outputs, when their weights are unknown. We used here inputs reflecting the resources allocated to the local municipalities (such as funding), outputs include measures that reflect reductions in accidents (such as accidents per population), and intermediate variables known as safety performance indicators (SPI): measures that are theoretically linked to crash and injury reductions (such as use of safety belts). Some of the outputs are undesirable. Using DEA, the local municipalities were rank-scaled from the most efficient to the least efficient and required improvements for inefficient municipalities were calculated. We found that most of the improvements were required in two intermediate variables related to citations for traffic violations. Several DEA versions were used including a two-stage model where in the first stage the intermediate variables are the outputs, and in the second stage they are the inputs. Further analyses utilizing multiple regressions were performed to verify the effect of various demographic parameters on the efficiency of the municipalities. The demographic parameters tested for each local municipality were related to the size, age, and socio-economic level of the population. The most significant environmental variable affecting the efficiency of local municipalities in preventing road accidents is the population size of the local authority; the size has a negative effect on the efficiency. As far as we could determine, this is the first time that the DEA is used to measure the efficiency of local municipalities in improving traffic safety.