Chiang Kao

• National Cheng Kung University

The efficiency calculated from the conventional slacks-based measure (SBM) model is the minimum in terms of efficiency scores, and the corresponding target point requires more effort for an inefficient decision making unit (DMU) to become efficient. To find the closest target point to the assessed DMU, several models have been proposed via calculat...

Data envelopment analysis is a technique widely used to measure the relative efficiency of a set of decision making units and for ranking alternatives based on the measured efficiency. When there are data that need to be estimated, a group of experts is consulted. The opinions of the experts can be aggregated at either the data level, based on whic...

The data envelopment analysis technique produces higher efficiency scores for the assessed decision making units (DMUs) when more input/output factors are considered. This feature generates an intuitively unreasonable result in which the efficiency of a DMU measured considering the accompanying undesirable outputs is greater than or equal to that m...

Hospitals comprise different types, including, for example, internal medicine hospitals, obstetrics/gynecology hospitals, and general hospitals, and physicians have specialties related to these types. Since a specialty may be supportive to some specialties and independent of some others, hospitals composed of certain departments may be more product...

Hospitals have different departments for treating specific diseases. Some hospitals are specialized into one department while others are diversified into many departments. Since many inputs for different departments can be shared, running a diversified hospital is probably less costly than running several specialized hospitals separately due to eco...

Conventional radial efficiency measurement models in data envelopment analysis are unable to produce appropriate efficiency scores for production units lying outside the cone generated by the convex hull of the extreme efficient production units. In addition, in the case of production technologies with variable returns to scale, the efficiency scor...

Cross efficiency is a concept for solving the problem of incomparability among the efficiencies of a set of decision making units (DMUs) calculated from different weights in data envelopment analysis, and is helpful for ranking. Conventional cross efficiency is a radial measure, and the radial measure has some weaknesses. First, it is not able to p...

One objective of the efficiency measurement of multi-division systems is to find the least efficient divisions such that making improvements to them will increase the efficiency of the system most effectively. To accomplish this task, it is desirable to find the relationship between the system and division efficiencies. This issue has been addresse...

Conventional data envelopment analysis (DEA) models for measuring efficiency are developed for positive data. However, difficulties are encountered when data has negative values. Several models have been proposed to calculate efficiency in the presence of negative data. While efficiencies can be calculated from these models, most of them are biased...

Undesirable outputs are generally by-products of producing desirable ones, and they can thus be reduced only with an accompanying reduction in the latter. To capture this notion, the shadow price of the undesirable output must be negative, as opposed to positive for the desirable output. Based on this condition, this paper proposes a data envelopme...

Decomposing the system efficiency of a network production system into the component division efficiencies helps identify the divisions that affect the performance of the system the most, and making improvements in these increases the system efficiency more effectively. This paper proposes a slacks-based measure (SBM) model to decompose the system e...

While the real world is stochastic in nature, in many cases deterministic data envelopment analysis (DEA) models are used to measure the relative efficiency of a set of production units for simplicity. However, deterministic DEA models are not able to differentiate efficient units. More seriously, the decision maker will be over-confident with the...

Network systems have two basic structures, series and parallel, and a network system can be transformed into a series system of subsystems, where each has a parallel structure composed of a number of divisions. The efficiency of the system can thus be expressed as the product of those of the subsystems, and the efficiency of each subsystem is a wei...

The slacks-based measure (SBM) is a data envelopment analysis (DEA) technique that has been widely used in measuring the efficiency of a system treated as a whole unit. When the internal structure of a system is considered, different ways of modeling the intermediate products that link the component divisions based on the production possibility set...

The data envelopment analysis (DEA) technique uses the most favorable weights for each decision making unit (DMU) to calculate efficiency. The resulting efficiency scores are thus incomparable and difficult to discriminate. This phenomenon is more prominent for network systems, which involves the ranking of the component divisions, in addition to t...

In the production process physical inputs are consumed to produce physical outputs. All the data are therefore positive real numbers, and the conventional DEA models are based on this requirement. However, in many applications the inputs and outputs may not be physical factors, and thus the data are not necessarily positive real numbers. For exampl...

Network systems have different structures, and most of them can be described by general mathematical models, with the system efficiency being able to be decomposed into the division efficiencies, as discussed in the preceding chapters. In this chapter we will discuss two types of system with symmetrical structures, assembly and disassembly, which a...

In measuring the efficiency of a DMU one can consider it as a closed plant, and the evaluator stands outside of the plant counting the quantity of materials and number of workers entering to manufacture products. After a period of time, the evaluator counts the quantity of products sent out of the plant. From the inputs consumed and the outputs pro...

The primary purpose of network DEA studies is to open the black box of a system, taking the operations of its component divisions into consideration when measuring its efficiency. Scholars thus endeavor to identify and classify the structures of the general network system, so that they can be analyzed in a systematic manner.

The simplest network structure is that of two divisions, in that the operations of the system are divided into two parts, performed by the two divisions. This type of system was first noticed by Charnes et al. (1986) in studying the performance of US Army recruitment. They found that army recruitment actually had two stages, creating awareness thro...

The DEA methodology concerns the efficiency measurement of production systems that apply multiple inputs to produce multiple outputs. Under normal conditions, it is desirable to have less input consumed and more output produced, because this leads to higher efficiencies. With regard to inefficient DMUs, improvement targets can be obtained to make t...

Ever since the industrial revolution, people have been working to use the smallest effort to produce the largest output, so that resources, including human, are utilized more efficiently. Manufacturing companies develop standards to help achieve this, such as the number of items that should be produced with one unit of a certain type of input, in o...

The DEA technique measures efficiency in a relative manner, in that the performances of the DMUs in a group are compared with each other. The efficient ones may not be efficient when compared with the DMUs of other groups. Similarly, the inefficient ones may become efficient when compared with those of other groups. The efficiency measures for DMUs...

There are two basic structures in network analysis that are the basis for studying general network structures, series and parallel. For the former the divisions of a system are arranged in sequence, one after another, in that the outputs of one division are the inputs of the next. In general, a division can start its operation only after its preced...

The preceding three chapters discuss how to measure the efficiency of a DMU based on the production frontier constructed from the peer DMUs. The production possibility set is assumed to be convex. In the classical production theory, production is separated into three stages, as depicted in Fig. 5.1 (Ferguson and Gould 1986). At the beginning, the o...

The basic two-stage system discussed in the preceding chapter describes a production type where all intermediate products produced by the first division are consumed by the second division for production. Specifically, no intermediate products flow out of the system, and the second division does not consume other inputs supplied from outside, excep...

The preceding two chapters discussed systems with two divisions connected in series. Intuitively, the two-stage system should be able to be extended to multiple stages to suit more general cases. As a matter of fact, many real world systems have a multi-stage structure, with assembly lines as typical examples, where raw materials go through a numbe...

The efficiency measurements discussed thus far focus on static models, which either assume that the inputs are fully used for producing outputs in the specified period of time, or assume steady-state production, where capital or other quasi-fixed inputs are fixed. There is thus no time interdependence between the input utilization and output realiz...

Theoretically, network systems can have numerous structures. In practice, however, only a limited number of them exist, and most of them can be classified into one of those discussed in the preceding chapters, including series, parallel, hierarchical, assembly and disassembly, with only a few left unclassified. Since series, parallel, and hierarchi...

The multiplier and envelopment models in data envelopment analysis (DEA) have a primal-dual relationship, and produce the same efficiency measure for a decision making unit (DMU). In addition to measuring efficiency, the multiplier model is able to identify the production frontier facets defined by the DMUs being evaluated, and the envelopment mode...

While management scientists were developing methods to measure efficiency based on the definition of productivity, economists were tackling the same problem using the production function. In the former, efficiency is measured as the ratio of aggregate output to aggregate input, which, from the input point of view, is equal to the smallest amount of...

The output–input ratio and radial distance function measures discussed in the preceding two chapters are essentially the same approach expressed in different forms, bearing the primal-dual relationship. The basic idea is to measure the relative distance between the DMU being evaluated and its projection on the production frontier along the ray from...

This book presents the underlying theory, model development, and applications of network Data Envelopment Analysis (DEA) in a systematic way. The field of network DEA extends and complements conventional DEA by considering not only inputs and outputs when measuring system efficiency, but also the internal structure of the system being analyzed. By...

This paper extends a data envelopment analysis (DEA) model that considers only desirable outputs in measuring efficiencies to incorporate undesirable outputs by requiring the associated multipliers to be negative. It is shown that the proposed model is the ratio-measure counterpart of the difference-measure model existed in the literature. It has t...

A comparison of the efficiency of a production unit at one period with those of other units at another period is challenging, because the bases for calculating efficiency are usually different. The Malmquist productivity index (MPI) is an effective measure that can overcome this difficulty. However, the existing measures of this index have various...

Network data envelopment analysis (DEA) is extended from conventional DEA to explore the internal structure of network production systems so that the efficiencies are measured more appropriately. There are two approaches for discussing the relationships between the system and division efficiencies, efficiency decomposition and efficiency aggregatio...

The conventional Malmquist productivity index (MPI), which ignores the internal structure of a production system when measuring changes in performance between two periods, may produce misleading results. This paper thus takes the operations of the component processes into account in investigating the MPI of parallel production systems. A relational...

Conventional data envelopment analysis (DEA) requires the data to have crisp values, which can be measured precisely. However, there are cases where data is missing and has to be estimated, or the situation has not occurred yet and the data has to be predicted. There are also cases where the factors are qualitative, and thus the data cannot be meas...

The conventional data envelopment analysis (DEA) models for measuring the relative efficiency of a set of decision making units (DMUs), without considering the operations of the component processes, often produce misleading results, and network models have thus been recommended. This paper discusses the development of a network DEA model for system...

Network data envelopment analysis (DEA) concerns using the DEA technique to measure the relative efficiency of a system, taking into account its internal structure. The results are more meaningful and informative than those obtained from the conventional black-box approach, where the operations of the component processes are ignored. This paper rev...

Conventional data envelopment analysis (DEA) treats a system as a whole unit when measuring efficiency, ignoring the operations of the component processes. Network DEA, on the other hand, takes the component processes into consideration, with results that are more representative and can be used to identify inefficient components. This paper discuss...

In measuring the overall efficiency of a set of decision making units (DMUs) in a time span covering multiple periods, the conventional approach is to use the aggregate data of the multiple periods via a data envelopment analysis (DEA) technique, ignoring the specific situation of each period. This paper proposes using a relational network model to...

In order to enable domestic commercial banks to be more competitive globally, the Taiwanese government has twice attempted to financially restructure them, in 2001 and 2004. Different from other studies which use deterministic analyses to measure changes in performance between two periods, this paper adopts probabilistic analysis to take the uncert...

Conventional two-stage data envelopment analysis (DEA) models measure the overall performance of a production system composed of two stages (processes) in a specified period of time, where variations in different periods are ignored. This paper takes the operations of individual periods into account to develop a multi-period two-stage DEA model, wh...

Recently network DEA models have been developed to examine the efficiency of DMUs with internal structures. The internal network structures range from a simple two-stage process to a complex system where multiple divisions are linked together with intermediate measures. In general, there are two types of network DEA models. One is developed under t...

One important objective in measuring efficiency is to find the factors that cause inefficiencies so that its performance can be improved. The conventional data envelopment analysis approach is able to decompose the overall efficiency of a system into the product of the technical and scale efficiencies when the internal structure is ignored. For two...

Conventional data envelopment analysis (DEA) models only consider the inputs supplied to the system and the outputs produced from the system in measuring efficiency, ignoring the operations of the internal processes. The results thus obtained sometimes are misleading. This paper discusses the efficiency measurement and decomposition of general mult...

Linear programming has been widely applied to solving real world problems. The conventional linear programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This chapter discusses the general interval linear programming problems where all the parame...

This paper proposes a dynamic data envelopment analysis (DEA) model to measure the system and period efficiencies at the same time for multi-period systems, where quasi-fixed inputs or intermediate products are the source of inter-temporal dependence between consecutive periods. A mathematical relationship is derived in which the complement of the...

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). Recently network DEA models been developed to examine the efficiency of DMUs with internal structures. The internal network structures range from a simple two-stage process to a complex system where multiple divisions are linked together w...

Conventional data envelopment analysis (DEA) treats the production system as a black box when measuring efficiency, ignoring its internal structure. By taking the operations of the component processes of the system into consideration, several network DEA models have been developed. Of these, the slacks-based measure (SBM) approach has attracted muc...

This paper investigates the productivity of the 1000 largest companies in Taiwan – 500 manufacturing and 500 service. For the 523 companies with available data, their average productivity is 1.0845, indicating that the total value of the outputs produced by these companies is greater than that of the inputs consumed. However, there are still approx...

This paper investigates the problem of efficiency measurement for parallel production systems where a number of processes are operating independently within the system, and some input/output data are fuzzy numbers. When all observations have precise values, previous studies found that the system efficiency measured from a relational data envelopmen...

Research performance is difficult to evaluate because most of the criteria are incommensurable, and assessing its improvement over time is even more difficult. This paper assesses the performance improvement in management research in Taiwan between 2006 and 2010 using the Malmquist productivity index (MPI). The criteria for measuring research perfo...

For production systems composed of parallel processes, the system efficiency will more properly represent the aggregate performance of the component processes if the operation of each process is taken into consideration. Several approaches have been proposed for measuring the efficiency of parallel production systems. By requiring the same factor t...

Project selection is an important task for organizations in achieving their missions using limited budgets and resources. Whether or not a project will be approved is also of primary concern to the applicants. This paper predicts whether a project will be approved for cases where the criteria for evaluating it are known while the scoring system is...

Conventional data envelopment analysis (DEA) for measuring the relative efficiency of a set of decision-making units (DMUs) requires the observations to have precise values. When observations are imprecise and represented by interval values, the efficiencies are also expected to reflect interval values. Several methods exist to calculate the interv...

Special Issue Editors: Vincent Charles, Wade D. Cook, and Joe Zhu Foreword This special issue of the Journal of CENTRUM Cathedra (JCC) on data envelopment analysis and its applications to management coincides with the achievement of Triple Crown accreditation by CENTRUM Católica. The Triple Crown denotes business schools that have received accredi...

Two-stage DEA (data envelopment analysis) models show the performance of individual processes, and thus are more informative than the conventional one-stage models for making decisions. This paper extends this approach from deterministic to uncertain situations, where the observations are represented by fuzzy numbers. The extension principle is uti...

Conventional data envelopment analysis (DEA) models are used to measure the technical and scale efficiencies of a system when it is considered as a whole unit. This paper extends the efficiency measurement to two-stage systems where each stage has one process and all the outputs from the first process become the inputs of the second. An input-orien...

Qualitative factors are difficult to mathematically manipulate when calculating the efficiency in data envelopment analysis (DEA). The existing methods of representing the qualitative data by ordinal variables and assigning values to obtain efficiency measures only superficially reflect the precedence relationship of the ordinal data. This paper tr...

The performance of a decision making unit (DMU) can be evaluated in either a cross-sectional or a time-series manner, and data envelopment analysis (DEA) is a useful method for both types of evaluation. In order to eliminate the inconsistency caused by using different frontier facets to calculate efficiency, common-weights DEA models have been deve...

Tolerance allocation is an important problem frequently encountered in the synthesis process, for designers as well as manufacturing engineers. Under the objective of minimizing the manufacturing cost while attaining an acceptable yield, the problem can be formulated as a stochastic program. Owing to the nonlinear nature of the stochastic program,...

Data standardization is a basic task in data analysis when several incommensurable criteria are involved. This paper discusses a data-standardization method for a set of fuzzy numbers that subtracts their minimum from the number to be standardized and divides the result by the difference between their maximum and minimum. Two approaches, i.e., memb...

One of the most difficult tasks in multiple criteria decision analysis (MCDA) is determining the weights of individual criteria so that all alternatives can be compared based on the aggregate performance of all criteria. This problem can be transformed into the compromise programming of seeking alternatives with a shorter distance to the ideal or a...

A recent development in DEA (data envelopment analysis) examines the internal structure of a system so that more information regarding sources that cause inefficiency can be obtained. This paper discusses a network DEA model which distributes the system inefficiency to its component processes. The model is applied to assess the impact of informatio...

Congestion is a wasteful stage of the production process where outputs are reduced due to excessive amount of inputs. This paper investigates three types of models prevailing in the data envelopment analysis literature, i.e., the Färe-family model, the Cooper-family model, and the Wei-Tone model, for measuring the congestion effect. The Färe-family...

This paper surveys 32 renowned Industrial Engineering (IE) journals with regard to authorship for the period of 1996–2005. The findings show that the USA was the top contributing country, accounting for approximately one-third of the total number of articles. The 80/20 rule and the entropy measure consistently identify Issues in Science and Technol...

In the real world there are systems which are composed of independent production units. The conventional data envelopment analysis (DEA) model uses the sum of the respective inputs and outputs of all component units of a system to calculate its efficiency. This paper develops a parallel DEA model which takes the operation of individual components i...

Conventional data envelopment analysis (DEA) for measuring the efficiency of a set of decision making units (DMUs) requires the input/output data to be constant. In reality, however, many observations are stochastic in nature; consequently, the resulting efficiencies are stochastic as well. This paper discusses how to obtain the efficiency distribu...

The conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. In the real world, sometimes the payoffs are not known and have to be estimated, and sometimes the payoffs are only approximately known. This paper develops a solution method for the two-person zero-sum game where the payof...

This paper surveys 56 internationally renowned OR journals published in 1996–2005 with regard to authorship. Our findings show that the USA was the country that contributed the largest amount, approximately one-third, of research results to OR journals. Authors tend to publish papers in their home-country journals. Journal of the Operations Researc...

As the major concerns of the university are teaching and research, this paper describes the study of a nation-wide evaluation of research performance in management for 168 universities in Taiwan. In addition to the popular indicators of SCI/SSCI journal publications and citations, the number of projects funded by the National Science Council of Tai...

Traditional studies in data envelopment analysis (DEA) view systems as a whole when measuring the efficiency, ignoring the operation of individual processes within a system. This paper builds a relational network DEA model, taking into account the interrelationship of the processes within the system, to measure the efficiency of the system and thos...

In efficiency measurement, the input and output factors of similar characteristics can be grouped into input and output categories, respectively, using a weighted-average approach under the data envelopment analysis (DEA) framework to form a two-level DEA model. The resulting two-level model is nonlinear. This note transforms the nonlinear model in...

Universities play an important role in the development of a country in this age of the knowledge economy. As government subsidies to universities have been reducing in recent years, the more efficient use of resources becomes an important issue for university administrators. This paper applies data envelopment analysis (DEA) to assess the relative...

To improve the quality of journals in Taiwan, the National Science Council (NSC) of the Republic of China evaluates journals in the fields of humanities and social sciences periodically. This paper describes the evaluation of 46 management journals conducted by the authors, as authorized by the NSC. Both a subjective approach, with judgments solici...

National competitiveness is a measure of the relative ability of a nation to create and maintain an environment in which enterprises can compete so that the level of prosperity can be improved. This paper proposes a methodology for measuring the national competitiveness and uses the 10 Southeast Asian countries for illustration. The basic idea is t...

The efficiency of decision processes which can be divided into two stages has been measured for the whole process as well as for each stage independently by using the conventional data envelopment analysis (DEA) methodology in order to identify the causes of inefficiency. This paper modifies the conventional DEA model by taking into account the ser...

Technology development (TD) plays a key role in national competitiveness (NC) by giving a country a competitive edge in our age of information. Lots of researchers have focused on specific areas of TD, such as technology transfer, technology acquisition, and technology management, in most of developed countries. To our knowledge, however, they have...

Conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. This article develops a solution method for the two-person zero-sum game where the payoffs are only approximately known and can be represented by fuzzy numbers. Because the payoffs are fuzzy, the value of the game is fuzzy as w...

In data envelopment analysis (DEA), the input and output data from all of the decision making units (DMUs) to be compared are required. If, for any reason, some data are missing, then the associated DMU must be eliminated to make the approach applicable. This study proposes a fuzzy set approach to deal with missing values. The value of a DMU in an...

This paper proposes a methodology to measure the management performance of the firms of an industry. The idea is to break down the very complicated concept of management into subjects such that the performance of each subject can be measured. The performances of all subjects are then aggregated to form an overall performance of management. The weig...

The conventional data envelopment analysis (DEA) measures the relative efficiencies of a set of decision making units (DMUs) with exact values of inputs and outputs. For imprecise data, i.e., mixtures of interval data and ordinal data, some methods have been developed to calculate the upper bound of the efficiency scores. This paper constructs a pa...

Simulation response optimization has wide applications for management of systems that are so complicated that the performance can only be evaluated by using simulation. This paper modifies the quasi-Newton method used in deterministic optimization to suit the stochastic environment in simulation response optimization. The basic idea is to use the e...

Technology and management are two broad categories of factors that have major influence on the productivity of manufacturing firms. The ratio of the actual productivity of a firm to its maximal productivity is a measure of efficiency. Since the automation technology level and production management achievement of a firm cannot be measured precisely,...

In designing ideal multiple recursive random number (RN) generators (MRGs), the best set of multipliers, in terms of the lattice structure of the RNs produced, is sought. As the order of the MRG increases, the number of possible sets of multipliers to be examined grows exponentially. This paper proposes a genetic algorithm for designing good MRGs....

To construct a regression model for fuzzy numbers, this paper decomposes a fuzzy number into two parts: the position and fuzziness. The former is represented by the elements with membership value 1 and the latter by the entropy of the fuzzy number, both have crisp values. The conventional regression analysis is applied to find the relationship betw...

Transportation models play an important role in logistics and supply chain management for reducing cost and improving service. This paper develops a procedure to derive the fuzzy objective value of the fuzzy transportation problem, in that the cost coefficients and the supply and demand quantities are fuzzy numbers. The idea is based on the extensi...

Network flow problems cover a wide range of engineering and management applications. Many streamlined solution methods have been devised for solving different types of the problems. This paper investigates the network flow problems in that the arc lengths of the network are fuzzy numbers. Based on the integer-solution property of the network flow p...

Data envelopment analysis (DEA) has been used as a tool for evaluating past accomplishments in the banking industry. However, due to a time lag, the results usually arrive too late for the evaluated banking institutions to react timely. This paper makes advanced predictions of the performances of 24 commercial banks in Taiwan based on their financi...

This paper modifies Powell's conjugate direction method for unconstrained, continuous, local optimization problems to adapt to the stochastic environment in simulation response optimization. The main idea underlying the proposed method is to conduct several replications at each trial point to obtain reliable estimate of the theoretical response. To...

Data envelopment analysis is a widely applied approach for measuring the relative efficiencies of a set of decision-making units (DMUs) which use multiple inputs to produce multiple outputs. When some observations are fuzzy, the efficiencies become fuzzy as well. This paper devises a method to rank the fuzzy efficiency scores without knowing the ex...

Regression is a very powerful methodology for forecasting, which is considered as an essential component of successful OR applications. In this paper an idea stemmed from the classical least squares is proposed to handle fuzzy observations in regression analysis. Based on the extension principle, the membership function of the sum of squared errors...

In aggregating the wide range of resources and services pro-vided by the university libraries to produce a single compos-ite index for comparison, two types of weights representing the relative importance of the criteria have been discussed in the literature. One is a priori weights assigned by the experts in a subjective manner before the scores f...