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The shortest path problem (SPP) is a special network structured linear programming problem that appears in a wide range of applications. Classical SPPs consider only one objective in the networks while some or all of the multiple, conflicting and incommensurate objectives such as optimization of cost, profit, time, distance, risk, and quality of service may arise together in real-world applications. These types of SPPs are known as the multi-objective shortest path problem (MOSPP) and can be solved with the existing various approaches. This paper develops a Data Envelopment Analysis (DEA)-based approach to solve the MOSPP with fuzzy parameters (FMOSPP) to account for real situations where input–output data include uncertainty of triangular membership form. This approach to make a connection between the MOSPP and DEA is more flexible to deal with real practical applications. To this end, each arc in a FMOSPP is considered as a decision-making unit with multiple fuzzy inputs and outputs. Then two fuzzy efficiency scores are obtained corresponding to each arc. These fuzzy efficiency scores are combined to define a unique fuzzy relative efficiency. Hence, the FMOSPP is converted into a single objective Fuzzy Shortest Path Problem (FSPP) that can be solved using existing FSPP algorithms.

Data envelopment analysis (DEA) is a prominent technique for evaluating relative efficiency of a set of entities called decision making units (DMUs) with homogeneous structures. In order to implement a comprehensive assessment, undesirable factors should be included in the efficiency analysis. The present study endeavors to propose a novel approach for solving DEA model in the presence of undesirable outputs in which all input/output data are represented by triangular fuzzy numbers. To this end, two virtual fuzzy DMUs called fuzzy ideal DMU (FIDMU) and fuzzy anti-ideal DMU (FADMU) are introduced into proposed fuzzy DEA framework. Then, a lexicographic approach is used to find the best and the worst fuzzy efficiencies of FIDMU and FADMU, respectively. Moreover, the resulting fuzzy efficiencies are used to measure the best and worst fuzzy relative efficiencies of DMUs to construct a fuzzy relative closeness index. To address the overall assessment, a new approach is proposed for ranking fuzzy relative closeness indexes based on which the DMUs are ranked. The developed framework greatly reduces the complexity of computation compared with commonly used existing methods in the literature. To validate the proposed methodology and proposed ranking method, a numerical example is illustrated and compared the results with an existing approach.

Data envelopment analysis (DEA) is a nonparametric frontier assessment method used to evaluate the relative efficiency of similar decision-making units (DMUs). This method provides benchmarking information regarding the removal of inefficiency. In conventional DEA models, the view of the decision maker (DM) is ignored and the performance of each DMU is solely determined by the observations retrieved. The current paper exploits the structural similarity existing between DEA and multiple objective programming to define a model that incorporates the preferences of DMs in the evaluation process of DMUs. Given the potential unfeasibility of the input and output targets selected by the DM, the model defines an interactive procedure that considers minimum and maximum acceptable objective levels. Given the feasible levels located closer to the targets selected by the DM, a program improving upon the feasible allocations is designed so that the suggested benchmark approximates the requirements fixed by the DM as much as possible. A real-life case study is included to illustrate the efficacy and applicability of the proposed hybrid procedure.

As an effective technique to counteract software aging, software rejuvenation is applied in continuously running applications such as web service-based systems. In such systems, web services are allocated depending on the requirements of receivers and the facilities of servers. One of the challenging issues during assignment of web services is how to select the appropriate server to minimize faults. In this paper, we proposed dynamic software rejuvenation in the form of a proactive fault-tolerance technique based on fuzzy system. While including a threshold for the rejuvenation of each web service, we carried out the training phase based on the features of the service providers as well as the receivers’ requirements. The results of simulations revealed that our strategy can mitigate the failure rate of web services by 45, 40, 23, and 12% in comparison with the non-fuzzy, regression-based, Markov-based, and ACOGELS-based web service rejuvenation strategies, respectively.

Multi-objective linear plus linear fractional programming problem is an emerging tool for solving problems in different environments such as production planning, financial and corporate planning and healthcare and hospital planning which has attracted many researchers in recent years. This paper presents a method to find a Pareto optimal solution for the multi-objective linear plus linear fractional programming problem through nonlinear membership function. The proposed approach defines a fuzzy goal for each objective through a nonlinear membership function. By means of nonlinear membership function, the multi-objective linear plus linear fractional programming problem transformed into a multi-objective nonlinear programming problem. Applying the linear approximation method, the nonlinear objectives are converted into linear. In order to solve the multi-objective linear programming problem, the fuzzy goal programming model is formulated by minimizing the negative deviational variables. The proposed procedure is illustrated through numerical examples and a real-life application problem. Further, it is compared with the existing methods. Finally, the Euclidean distance function has been used to prove the efficiency of the proposed method.

Exposure to ambient particulate matter (PM) can increase mortality and morbidity in urban area. In this study, annual and seasonal spatial pattern of PM1, PM2.5 and PM10 pollutants were assessed using land use regression (LUR) models in Sabzevar, Iran. The studied pollutants were measured at 26 monitoring stations of different microenvironments in the study area. Sampling was conducted during four campaigns from April 2017 to February 2018. LUR models were developed based on 104 potentially predictive variables (PPVs) subdivided in six categories and 22 sub-categories. The annual mean (standard deviation) of PM1, PM2.5 and PM10 were 36.46 (8.56), 39.62 (10.55) and 51.99 (16.25) μg/m3, respectively. The R2 values and root mean square error for leave-one-out cross validations (RMSE for LOOCV) of PM1 models ranged from 0.23 to 0.79 and 3.43-22.5, respectively. Further, R2 and RMSE for LOOCV of PM2.5 models ranged from 0.56 to 0.93 and 3.66-28.3, respectively. For PM10 models the R2 ranged from 0.31 to 0.82 and the RMSE for LOOCV ranged from 9.16 to 33.9. The generated models can be useful for population based epidemiologic studies and to estimate these pollutants in different parts of the study area for scientific decision making.

Morck, Yeung, and Yu (2000), in their pioneering study of international differences in stock price synchronicity, emphasize the effect of market development on investors' ability to incorporate firm-specific information into prices. We use a unique institutional feature in the Hong Kong market to investigate one of the important tools investors use to do this and hence reduce stock price synchronicity: short selling. Examining the cross-sectional and time-series variation in short-sale constraints in the Hong Kong market, we find that after the removal of short-sale constraints, stock prices become more informative and move less in tandem with the market.

During past few decades, fuzzy decision is an important attention in the areas of science, engineering, economic system, business, etc. To solve day-to-day problem, researchers use fuzzy data in transportation problem for presenting the uncontrollable factors; and most of multi-objective transportation problems are solved using goal programming. However, when the problem contains interval-valued data, then the obtained solution was provided by goal programming may not satisfy by all decision-makers. In such condition, we consider a fixed-charge solid transportation problem in multi-objective environment where all the data are intuitionistic fuzzy numbers with membership and non-membership function. The intuitionistic fuzzy transportation problem transforms into interval-valued problem using (α, β)-cut, and thereafter, it reduces into a deterministic problem using accuracy function. Also the optimum value of alternative corresponds to the optimum value of accuracy function. A numerical example is included to illustrate the usefulness of our proposed model. Finally, conclusions and future works with the study are described., Portuguese Foundation for Science and Technology ("FCT-Fundacao para a Ciencia e a Tecnologia"), through the CIDMA-Center for Research and Development in Mathematics and Applications UID/MAT/ 04106/2019, Spanish Ministry of Economy and Competitiveness, FEDER funds from the European Union TIN2014-55024-P TIN2017-86647-P

This paper is concerned with the solution procedure of a fully fuzzy linear programming (FFLP) problem in which all parameters are represented in terms of triangular fuzzy numbers. According to the...

Pythagorean fuzzy set as an extension of fuzzy set has been presented to handle the uncertainty in real-world decision-making problems. In this work, we formulate a shortest path (SP) problem in an interval-valued Pythagorean fuzzy environment. Here, the costs related to arcs are taken in the form of interval-valued Pythagorean fuzzy numbers (IVPFNs). The main contributions of this paper are fourfold: (1) the interval-valued Pythagorean fuzzy optimality conditions in directed networks are described to design of solution algorithm. (2) To do this, an improved score function is used to compare the costs between different paths with their arc costs represented by IVPFNs. (3) Based on these optimality conditions and the improved score function, the traditional Dijkstra algorithm is extended to find the cost of interval-valued Pythagorean fuzzy SP (IVPFSP) and corresponding IVPFSP. (4) Finally, a small sized telecommunication network is provided to illustrate the potential application of the proposed method.

In the article, Veeramani and Sumathi [10] presented an interesting algorithm to solve a fully fuzzy linear fractional programming (FFLFP) problem with all parameters as well as decision variables as triangular fuzzy numbers. They transformed the FFLFP problem under consideration into a bi-objective linear programming (LP) problem, which is then converted into two crisp LP problems. In this paper, we show that they have used an inappropriate property for obtaining non-negative fuzzy optimal solution of the same problem which may lead to the erroneous results. Using a numerical example, we show that the optimal fuzzy solution derived from the existing model may not be non-negative. To overcome this shortcoming, a new constraint is added to the existing fuzzy model that ensures the fuzzy optimal solution of the same problem is a non-negative fuzzy number. Finally, the modified solution approach is extended for solving FFLFP problems with trapezoidal fuzzy parameters and illustrated with the help of a numerical example.

Data envelopment analysis (DEA) is generally used to evaluate past performance and multi objective linear programming (MOLP) is often used to plan for future performance goals. In this study, we establish an equivalence relationship between MOLP problems and combined-oriented DEA models using a direction distance function designed to account for desirable and undesirable inputs and outputs together with uncontrollable variables. This equivalence model can be effectively used to support interactive processes and performance measures designed to establish future performance goals while taking into account the preferences of decision makers (DMs). In particular, it allows DMs to consider different efficiency improvement strategies when subject to budgetary restrictions. The applicability of the proposed method and the efficacy of the procedures and algorithms are demonstrated using a case study where the performance of high schools in the City of Philadelphia is evaluated.

We investigate the relation between fundamental idiosyncratic volatility and stock returns idiosyncratic volatility using data from 56 countries over 1980-2014. We find a strong positive relation between fundamental idiosyncratic volatility and idiosyncratic volatility of returns. This association, however, seems to be entirely concentrated in the developed economies and we find no effect in the emerging markets. Specifically, fundamental idiosyncratic volatility does not lead to more idiosyncratic return volatility in countries with poor legal institutions and weak shareholder protection laws.

R is a mathematical and object-oriented open source programming language designed first for statistical computing. But, this software is powerful for dealing with optimization models. Variety of optimization moles such as linear, non-linear, integer, binary, and quadratic problems can be considered to be solved in this software. In this chapter some basic definition about R and required commands used in writing DEA models with R codes will be presented. All the commands are review sequentially according to their concepts. Also, for each command some numerical examples are also provided for clarifing the usage of commands for the readers.

As a powerful assessment tool, DEA is very famous in variety of areas. Different applications are performed using EA models for relative evaluations. Being familiar with DEA models and their characteristics is necessary as a mathematical tool for evaluation. In this chapter at first some basic models of DEA technique are briefly reviewed and introduced literally and mathematically. Then, R codes of these models along with numerical examples are provided for readers.

Using data envelopment analysis as a mathematical performance evaluation tool is much more serious for researchers and practitioners. Different data envelopment analysis models are now introduced in different fields. In addition to the classic performance evaluation models in data envelopment analysis, developed models such as super-efficiency, returns to scale, progress and regress models, and so on have been introduced in this technique that help different aspects of analytics and decision making units in performance evaluation. In this chapter, such developed DEA models are formulated, and then the corresponding R codes for these models are provided.

The conventional DEA models such as CCR and BBC models require precise input and output data, which may not always be available in real world applications. However, in real life problems, inputs and outputs are often imprecise. To deal with imprecise data, the notion of fuzziness has been introduced in DEA and so the DEA has been extended to fuzzy DEA (FDEA). In this chapter, the main approaches for solving FDEA models are classified into five groups and the mathematical approaches of each category are described briefly. Then, R codes for each FDEA model are provided. Finally, numerical examples are provided to illustrate the main advantages of R in FDEA models.

Data Envelopment Analysis (DEA) is a mathematical based programing technique for performance evaluation of a set of Decision Making Units (DMUs). This technique is widely used for assessing different systems with different inputs and outputs in different fields. In this chapter some basic definition of mathematical modeling with DEA technique will be reviewed and introduced. The definitions of efficiency, relative efficiency, effectiveness, and productivity are given. It will be shown how basic DEA models on basis of different Production possibility sets (PPSs) can be formulated. Also, some characteristics of envelopment and multiplier models will be discussed. Finally, the main concepts of fuzzy set theory are introduced.

The shortest path (SP) problem is a network optimization problem with a wide range of applications in business and engineering. Conventional network problems assume precise values for the weights of the edges. However, these weights are often vague and ambiguous in practical applications. Several heuristics have been proposed to find the shortest path (SP) weight and the corresponding SP on a network with fuzzy arc weights. These heuristics largely use α -cuts and the least squares method. We propose an artificial bee colony (ABC) algorithm to solve the fuzzy SP (FSP) problems with fuzzy arc weights. The performance of the proposed ABC algorithm is compared with the performance of other competing algorithms with two SP problems taken from the literature. We present a wireless sensor network (WSN) problem and demonstrate the applicability of the proposed method and exhibit the efficiency of the procedures and algorithms.

In the real world, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables.

The aim of this chapter is to study linear programming problem with fuzzy coefficients as one of the convenient model of fuzzy linear programs. In this way, we first introduce a general form of Fuzzy Number Linear programming (FNLP) problems and then give the fundamental concepts which are useful in throughout of the chapter.

One of the most interesting models of the linear programming in uncertainty environment is the flexible linear programming problem. It is shown that by using a suitable membership function for their constraints we can obtain an equivalent linear programming problem with fuzzy variables (FVLP).

Since the fuzziness may appear in many ways for the parameters of linear programming models, hence the definition of fuzzy linear programming is not unique. One of these models is Semi-Fully Fuzzy Linear Programming (SFFLP) problem where the coefficients in the objective function, the right hand side vector and the decision variables are a kind of fuzzy numbers, simultaneity. This chapter is assigned to these type of problems.

Fuzzy sets theory has been applied to many disciplines such as control theory and management sciences, mathematical modeling, industrial applications and etc. We usually face some difficulties when a such real-world problems are formulated into a mathematical programming problem. One of the difficulties is caused by the uncertainty in knowledge, information and/or decision makers preferences.

Exposure to ambient particulate matter (PM) can increase mortality and morbidity in urban area. In this study, annual and seasonal spatial pattern of PM

The transportation problem (TP) is an important network-structured LP problem that arises in several contexts and can be applied to a wide variety of situations, such as scheduling, production, investment, deciding plant location and inventory control. The central concept in the TP is to determine the minimum total transportation cost of a commodity for satisfying the demand at destinations using the available supply at the origins. Generally, transportation problems are solved with the assumption that th transportation costs, supply and demand are specified precisely. However, in many cases, the decision maker does not possess exact information about the coefficients for the transportation problem. If the information is vague, that is, if it lacks precision, the corresponding coefficients or elements defining the problem can be formulated using fuzzy sets, giving rise to fuzzy TPs (FTPs). In this chapter, we first classify FTPs into four main groups and then discuss the solution methodologies for each one.

Multi-objective transportation problem (MOTP) under intuitionistic fuzzy (IF) environment is analysed in this paper. Due to the fluctuation of market scenario, we assume that the transportation cost, the supply and the demand parameters are not always precise. Hence, the parameters are imprecise, i.e., they are IF numbers. Considering the specific cut interval, the IF transportation cost matrix is converted to interval cost matrix in our proposed problem. Again, using the same concept, the IF supply and the IF demand of the MOTP are reduced to the interval form. Then the proposed MOTP is changed into the deterministic MOTP, which includes interval form of the objective functions. Two approaches, namely intuitionistic fuzzy programming and goal programming, are used to derive the optimal solutions of our proposed problem, and then the optimal solutions are compared. A numerical example is included to illustrate the feasibility and the applicability of the proposed problem. Finally, we present the conclusions with the future scopes of our study.

In this chapter, the non-simplex based approaches for solving several kinds of LPPs with fuzzy parameters are explored. In such approaches, the fuzzy constraints are first converted to crisp ones based on arithmetic operations on fuzzy numbers and then the standard methods are used for solving the crisp problems. Such approaches increase the number of functional constraints and thus directly affect the computational time of the simplex method.

The aim of this chapter is to study the simplex based approaches for solving several kinds of LP problems with fuzzy parameters. In the LP problems with fuzzy parameters that can be solved by the use of simplex approaches, some or all parameters of the problems under consideration may be fuzzy numbers and the inequalities may be interpreted in terms of fuzzy rankings. Here, we first classify such fuzzy LP problems into five general groups and then discuss the solution methodologies for each one.

Fuzzy sets as defined by Zadeh (Inf. Con. 8(3):338–353, 1965 [1]) provide a useful, effective and operative tool for handling imprecise data. It not only provides a powerful representation of measurement uncertainty, but also gives a meaningful representation of vague concepts expressed in natural language. The purpose of this chapter is to review the basic definitions and results on fuzzy sets, fuzzy numbers, fuzzy arithmetic and fuzzy ranking methods.

In the article (Sudhagar and Ganesan in Optim Eng 10.1007/s11081-012-9202-6) Sudhagar and Ganesan presented an algorithm to solve a fuzzy transportation problem without converting it into a crisp transportation problem based upon score method of ranking fuzzy numbers. Using an example we show that their method will not always lead to a fuzzy optimal solution. Specially, we give a non negative fuzzy solution for the numerical example solved by them which has less total fuzzy transportation cost.

Data Envelopment Analysis (DEA) and Multiple Objective Linear Programming (MOLP) are widely used for performance assessment in organizations. Although DEA and MOLP are similar in structure, DEA is used to assess and analyze past performance and MOLP is used to predict future performance. Several equivalence models between output-oriented DEA models and MOLP models have been proposed in the literature. However these models are not applicable to performance evaluation problems with undesirable outputs. We propose an interactive method for solving output-oriented DEA models with undesirable outputs. We show that the output-oriented BCC model of Seiford and Zhu [47] can be equivalently stated as the maximization of the minimum of several objectives over the production possibility set, which in turn is a scalarization of a multi-objective linear program. We then employ the well-known Zionts-Wallenius procedure to solve the multi-objective optimization problem. We present an example to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedures and algorithms.

In this paper, an efficient approach is presented to solve fully fuzzy linear fractional programming problems. In this approach, first by Alpha-cuts on the objective function and the constraints, the problem is transforming into a bi-objective linear programming problem, and then the resulting problem is converted into two crisp linear programming problems. A numerical example is presented to illustrate the proposed approach. The obtained results demonstrate the acceptable performance of the proposed solution approach.

In recent Data envelopment analysis (DEA) literature, many researchers have examined systems with a two-stage network structure and its pitfalls. In these studies, two-stage network systems operations for converting inputs into outputs have been performed in two stages, meanwhile the intermediate products were considered as the outputs from the first stage and as inputs to the second stage. This duality in dealing with intermediate products imposes restrictions on the pricing of these products. In this paper by focusing on the convexity axiom, we define a new production possibility set. The main contributions of this paper are fourfold: (1) we propose models for evaluating the overall efficiency measure of decision making units (DMUs) in a two-stage network structure based on the convex hull in intermediate products; (2) we propose a procedure to determine the target unit of each inefficient DMU; (3) we explain how to calculate the divisional efficiency; (4) we demonstrate the feasibility and richness of the obtained solutions in the context of two examples.

Data envelopment analysis (DEA) is a widely used technique for measuring the relative efficiencies of decision-making unit (DMUs) with multiple inputs and multiple outputs. In many applications, ranking of DMUs is an important and essential procedure to decision makers in DEA, especially when there are extremely efficient DMUs. Basic DEA models usually give the same efficiency score for some DMUs. Hence, it is necessary to rank of all extreme DMUs. The main purpose of this study is to propose an appropriate method in order to overcome the drawbacks in several methods for ranking DMUs based on the DEA concept. In the present paper, we propose a model for ranking extreme efficient DMUs in DEA by super efficiency technique and Euclidean norm (l2-norm). The presented method in this paper is able to overcome the existing obstacles in some methods. As regards, the proposed model is into nonlinear programming form, a linear model is suggested to approximate the nonlinear model.

Linear programming (LP) is a widely used optimization method for solving real-life problems because of its efficiency. Although precise data are fundamentally indispensable in conventional LP problems, the observed values of the data in real-life problems are often imprecise. Fuzzy sets theory has been extensively used to represent imprecise data in LP by formalizing the inaccuracies inherent in human decision-making. The fuzzy LP (FLP) models in the literature generally either incorporate the imprecisions related to the coefficients of the objective function, the values of the right-hand-side, and/or the elements of the coefficient matrix. We propose a new method for solving FLP problems in which the coefficients of the objective function and the values of the right-hand-side are represented by symmetric trapezoidal fuzzy numbers while the elements of the coefficient matrix are represented by real numbers. We convert the FLP problem into an equivalent crisp LP problem and solve the crisp problem with the standard primal simplex method. We show that the method proposed in this study is simpler and computationally more efficient than two competing FLP methods commonly used in the literature.

Data Envelopment Analysis (DEA) is a mathematical programming technique for identifying efficient Decision Making Units (DMUs) with multiple inputs and multiple outputs. DEA provides a technical efficiency score for each DMU, a technical efficiency reference set with peer DMUs, and a target for the inefficient DMU. The target unit informs the Decision Maker (DM) of the amount (%) by which an inefficient DMU should decrease its inputs and/or increase its outputs to become efficient. However, the conventional DEA models generally do not consider the DM’s preference structure in identifying the target units. Several equivalence models between the output-oriented DEA and Multiple Objective Linear Programming (MOLP) models have been proposed in the literature to take the DMs’ preferences into consideration. However, these models are not able to identify target units when undesirable outputs are produced with desirable outputs in the production process. In this study we obtain a new link between a BCC model and the weighted minimax reference point of the MOLP formulation that simultaneously and interactively considers the increase in the total desirable outputs and the decrease in the total undesirable outputs. We present a pilot study for the North Atlantic Treaty Organization (NATO) enlargement problem to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedures and algorithms.

The changing economic conditions have challenged many financial institutions to search for more efficient and effective ways to assess their operations. Data Envelopment Analysis (DEA) is a widely used mathematical programming approach for comparing the inputs and outputs of a set of homogenous Decision Making Units (DMUs) by evaluating their relative efficiency. The traditional DEA treats DMUs as black boxes and calculates their efficiencies by considering their initial inputs and their final outputs. As a result, some intermediate measures are lost in the process of changing the inputs to outputs. In this study we propose a three-stage DEA model with two independent parallel stages linking to a third final stage. We calculate the efficiency of this model by considering a series of intermediate measures and constraints. We present a case study in the banking industry to exhibit the efficacy of the procedures and demonstrate the applicability of the proposed model.

A key issue in the preferential voting framework is how voters express their preferences on a set of candidates. In the existing voting systems, each voter selects a subset of candidates and ranks them from most to least preferred. The obtained preference score of each candidate is the weighted sum of votes receives in different places. Thus, one of the most important issues for aggregating preferences rankings is the determination of the weights associated with the different ranking places. To avoid the subjectivity in determining the weights, various models based on Data Envelopment Analysis (DEA) have been appeared in the literature to determine the most favorable weights for each candidate. This work presents a survey on models and methods to assess the weights in voting systems. The existing voting systems are divided into two areas. In the first area it is assumed that the votes of all the voters to have equal importance and in the second area voters are classifies into different groups and assumed that each group is assigned a different voting power. In this contribution, some of the most common models and procedures for determining the most favorable weights for each candidate are analyzed.

This paper proposes a new approach to allow the voters to express their preferences on a set of candidates in ranked voting systems. This approach assumes that the votes of all voters have not equal importance and there is a priority among voters. Here, voters are classified into several groups in terms of their priorities that the vote of a higher category has a greater important than that of lower category. Then, the existing ranking methods are extended to discriminate efficient candidates in our proposed model. Moreover, a new criterion to obtain a total ranking by evaluating different ranking methods based on classical voting system is given. Finally the proposed method is illustrated with an application example and shows to be effective and practical.

In many applications, finding target unit is required, particularly when decision maker (DM) wants to search along the efficient frontier to locate the most preferred solution. Wong et al. [Wong, Y.H., Luque, M., Yang, J.B., 2009. Using interactive multiple objective methods to solve DEA problem with value judgments. Computers and Operations Research 36, 623–636] established an equivalence model between output-oriented dual DEA models and multiple objective linear programming (MOLP). In a similar vein, the aim of this paper is to establish an equivalence model between the general combined-oriented CCR model and multiple objective linear programming and also using Zionts–Wallenius’s method to integrate combined-oriented CCR performance assessment and target setting such that the DM’s preference can be taken into account in an interactive fashion. Our proposed model gives the most preferred solution for DM with trade off analysis on both input and output values of DMUs. The applicability of the proposed equivalence model is illustrated, using a real data set as a case study, which consists of 20 bank branches.

Decision making about the superior method to produce products is essential to growth and dynamism of productive organisations. In this regard, utilising a model to evaluate the comprehensive performance of different manufacturing methods is significant. In addition, defining and finding the suitable indexes of decision making is required to the proper implementation of performance evaluation system. Thus, in this study, it is attempted to select the best production method and to supply material using data envelopment analysis (DEA) technique and analytic hierarchy process (AHP). In this regard, the performance of ball valve production in Petro Nab Sepahan Manufacturing Company is assessed and ranked using these two methods by considering dimensions such as quality, cost and function as well as acquired measures.

Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach.

Evaluating the efficiency and the performance of decision making units (DMUs) at different time periods is one of the most critical and important issues of managers. Data envelopment analysis (DEA) is a powerful non-parametric technique to measure the relative efficiency of a set of DMUs where each DMU consumes multiple inputs to produce multiple outputs. In many DEA applications, DMUs are considered as systems with a two-stage structure. In these situations, two-stage DEA models are used to measure the efficiencies of these systems. In many of such systems, the simultaneous presence of two stages is not necessary for the final product and the shortcoming of one stage is compensated by another stage. Therefore, this paper will use compensatory property of the sum operator and will propose the additive model to measure the multi-period efficiency of these systems under the constant returns to scale (CRS) assumption. In addition, based on the obtained efficiencies, the new efficiency changes Indexes (ECIs) related to the whole system and the first and second stages between two periods will be proposed that have circularity property. Furthermore, ECI of the whole system (and stages) for two periods is defined as the difference between the efficiencies in these periods. Moreover, positive changes (or negative changes), or unchanged in the efficiency of stages will be concluded by the positive changes (or negative changes), or unchanged of the whole system. Finally, the data of 21 non-life insurance industry in Taiwan are used to describe our suggested model that extracted from the extant literature.