Dr Mehdi Toloo

Reader (Associate Professor) in Business Analytics
BSc, MSc, PhD, docent
+44 (0)1483 684650
17 MS 02



Research interests

Research projects

Research collaborations


Postgraduate research supervision



Majid Azadi, Mehdi Toloo, Fahimeh Ramezani, Reza Farzipoor Saen, Farookh Khadeer Hussain, Hajar Farnoudkia (2023)Evaluating efficiency of cloud service providers in era of digital technologies, In: Annals of operations research Springer Nature

The rapid growth of advanced technologies such as cloud computing in the Industry 4.0 era has provided numerous advantages. Cloud computing is one of the most significant technologies of Industry 4.0 for sustainable development. Numerous providers have developed various new services, which have become a crucial ingredient of information systems in many organizations. One of the challenges for cloud computing customers is evaluating potential providers. To date, considerable research has been undertaken to solve the problem of evaluating the efficiency of cloud service providers (CSPs). However, no study addresses the efficiency of providers in the context of an entire supply chain, where multiple services interact to achieve a business objective or goal. Data envelopment analysis (DEA) is a powerful method for efficiency measurement problems. However, the current models ignore undesirable outputs, integer-valued, and stochastic data which can lead to inaccurate results. As such, the primary objective of this paper is to design a decision support system that accurately evaluates the efficiency of multiple CSPs in a supply chain. The current study incorporates undesirable outputs, integer-valued, and stochastic data in a network DEA model for the efficiency measurement of service providers. The results from a case study illustrate the applicability of our new system. The results also show how taking undesirable outputs, integer-valued, and stochastic data into account changes the efficiency of service providers. The system is also able to provide the optimal composition of CSPs to suit a customer's priorities and requirements.

Mehdi Toloo, Soroosh Nalchigar (2011)On Ranking Discovered Rules of Data Mining by Data Envelopment Analysis: Some Models with Wider Applications, In: New Fundamental Technologies in Data Miningpp. 425-442 InTech

The convergence of computing and communication has resulted in a society that feeds on information. There is exponentially increasing huge amount of information locked up in databases—information that is potentially important but has not yet been discovered or articulated (Whitten & Frank, 2005). Data mining, the extraction of implicit, previously unknown, and potentially useful information from data, can be viewed as a result of the natural evolution of Information Technology (IT). An evolutionary path has been passed in database field from data collection and database creation to data management, data analysis and understanding. According to Han & Camber (2001) the major reason that data mining has attracted a great deal of attention in information industry in recent years is due to the wide availability of huge amounts of data and the imminent need for turning such data into useful information and knowledge. The information and knowledge gained can be used for applications ranging from business management, production control, and market analysis, to engineering design and science exploration. In other words, in today’s business environment, it is essential to mine vast volumes of data for extracting patterns in order to support superior decision-making. Therefore, the importance of data mining is becoming increasingly obvious. Many data mining techniques have also been presented in various applications, such as association rule mining, sequential pattern mining, classification, clustering, and other statistical methods (Chen & Weng, 2008).

Mehdi Toloo, Iman Rahimi, Siamak Talatahari (2022)Multi-Objective Combinatorial Optimization Problems and Solution Methods Academic Press

Multi-Objective Combinatorial Optimization Problems and Solution Methods discusses the results of a recent multi-objective combinatorial optimization achievement that considered metaheuristic, mathematical programming, heuristic, hyper heuristic and hybrid approaches. In other words, the book presents various multi-objective combinatorial optimization issues that may benefit from different methods in theory and practice. Combinatorial optimization problems appear in a wide range of applications in operations research, engineering, biological sciences and computer science, hence many optimization approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic and algebraic techniques. This book covers this important topic as computational optimization has become increasingly popular as design optimization and its applications in engineering and industry have become ever more important due to more stringent design requirements in modern engineering practice.

M Toloo, S Ghorbani, Z Molaee (2011)Ranking DMUs on the benchmark line with equal shadow prices, In: Proceedings of the 40th International Conference on Computers & Industrial Engineering (CIE-40)pp. 1-4 Institute of Electrical and Electronics Engineers (IEEE)

Data envelopment analysis (DEA) with considering the best condition for each decision making unit (DMU) assesses the relative efficiency for it and divides a homogenous group of DMUs into two categories: efficient and inefficient, but traditional DEA models can not rank efficient DMUs. Although some models were introduced for ranking efficient DMUs, Franklin Lio & Hsuan peng (2008), proposed a common weights analysis (CWA) approach for ranking them. These DMUs are ranked according to the efficiency score weighted by the common set of weights and shadow prices. This study shows there are some cases that shadow prices of efficient DMUs are equal, hence this method is not applicable for ranking them. Next, we propose a new method for ranking units with equal shadow prices.

Adel Hatami-Marbini, Aliasghar Arabmaldar, Mehdi Toloo, Ali Mahmoodi Nehrani (2022)Robust non-radial data envelopment analysis models under data uncertainty, In: Expert Systems with Applications207118023 Elsevier

Russell measure (RM) and enhanced Russell measure (ERM) are popular non-radial measures for efficiency assessment of decision-making units (DMUs) in data envelopment analysis (DEA). Input and output data of both original RM and ERM are assumed to be deterministic. However, this assumption may not be valid in some situations because of data uncertainty arising from measurement errors, data staleness, and multiple repeated measurements. Interval DEA (IDEA) has been proposed to measure the interval efficiencies from the optimistic and pessimistic viewpoints while the robustness of the assessment is questionable. This paper draws on a class of robust optimisation models to surmount uncertainty with a high degree of robustness in the RM and ERM models. The contribution of this paper is fivefold; (1) we develop new robust non-radial DEA models to measure the robust efficiency of DMUs under data uncertainty, which are adjustable based upon conservatism levels, (2) we use Monte-Carlo simulation in an attempt to identify an appropriate range for the budget of uncertainty in terms of the highest conformity of ranking results, (3) we introduce the concept of the price of robustness to scrutinise the effectiveness and robustness of the proposed models, (4) we compare the developed robust models in this paper with other existing approaches, both radial and non-radial models, and (5) we explore an application to assess the efficiency of the Master of Business Administration (MBA) programmes where data uncertainties in-fluence the quality and reliability of results.

Mahdi Mahdiloo, Amir E. Andargoli, Mehdi Toloo, Charles Harvie, Thach-Thao Duong (2023)Measuring the digital divide: A modified benefit-of-the-doubt approach, In: Knowledge-Based Systems261110191 Elsevier

In this paper, a modified composite index is developed to measure digital inclusion for a group of cities and regions. The developed model, in contrast to the existing benefit-of-the-doubt (BoD) composite index literature, considers the subindexes as non-compensatory. This new way of modeling results in three important properties: (i) all subindexes are taken into account when assessing the digital inclusion of regions and are not removed (substituted) from the composite index, (ii) in addition to an overall composite index (aggregation of the subindexes), partial indexes (aggregated scores for each subindex) are also provided so that weak performances can be detected more effectively than when only the overall index is measured, and (iii) compared with current BoD models, the developed model has improved discriminatory power. To demonstrate the developed model, we use the Australian digital inclusion index as a real-world example.

Mehdi Toloo, Kaoru Tone, Mohammad Izadikhah (2023)Selecting slacks-based data envelopment analysis models, In: European Journal of Operational Research308(3)pp. 1302-1318 Elsevier

Data envelopment analysis (DEA) is a well-known data-driven mathematical modeling approach that aims at evaluating the relative efficiency of a set of comparable decision making units (DMUs) with multiple inputs and multiple outputs. The number of inputs and outputs (performance factors) plays a vital role for successful applications of DEA. There is a statistical and empirical rule in DEA that if the number of performance factors is high in comparison with the number of DMUs, then a large percentage of the units will be determined as efficient, which is questionable and unacceptable in the performance evaluation context. However, in some real-world applications, the number of performance factors is relatively larger than the number of DMUs. To cope with this issue, selecting models have been developed to select a subset of performance factors that lead to acceptable results. In this paper, we extend a pair of optimistic and pessimistic approaches, involving two alternative individual and summative selecting models, based on the slacks-based model. We mathematically validate the proposed models with some theorems and lemmas and illustrate the applicability of our models using 18 active auto part companies in the largest stock exchange in Iran.

In microeconomics, a production function is a mathematical function that transforms all combinations of inputs of an entity, firm or organization into the output. Given the set of all technically feasible combinations of outputs and inputs, only the combinations encompassing a maximum output for a specified set of inputs would constitute the production function. Data Envelopment Analysis (DEA), which has initially been originated by Charnes, Cooper and Rhodes in 1978, is a well-known non-parametric mathematical method with the aim of estimating the production function. In fact, DEA evaluates the relative performance of a set of homogeneous decision making units with multiple inputs and multiple outputs.This book covers some basic DEA models and disregards more complicated ones, such as network DEA, and mainly stresses the importance of weights in DEA and some of their applications. As a result, this book mainly considers the multiplier form of DEA models to extend some new approaches, however, the envelopment forms are introduced in some possible approaches. This book also aims at dealing with some innovative uses of binary variables in extended DEA model formulations. The auxiliary variables enable us to formulate Mixed Integer Programming (MIP) DEA models for addressing the problem of finding a single efficient and ranking efficient DMUs. In some cases, the status of input(s) or output(s) measure is unknown and binary variables are utilized to accommodate these flexible measures. Furthermore, the binary variables approach tackles the problem of selecting input or output measures.The book also stresses the mathematical aspects of selected DEA models and their extensions so as to illustrate their potential uses with applications to different contexts, such as banking industry in the Czech Republic, financing decision problem, technology selection problem, facility layout design problem, and selecting the best tennis player. In addition, the majority of the extended models in this book can be extended to some other DEA models, such as slacks-based measures, hybrids, non-discretionary, and fuzzy DEA which are applicable in some other contexts.This research-based book contains six chapters as follows:The first chapter (General Discussion) starts with a simple numerical example to explain the concept of relative efficiency and to clarify the importance of input and output weights in measuring the efficiency score. Then these basic concepts are extended to some more complex cases. Efficient frontiers and projection points are illustrated by means of some constructive and insightful graphs.The second chapter (Basic DEA Models) presents both envelopment and multiplier forms of the DEA models in the presence of multiple inputs and multiple outputs. However, this book mainly focuses on the multiplier form of DEA models. In addition, this chapter illustrates the role of each axiom to construct the production possibility set (PPS). It is also concerned with some DEA models to deal with pure input data as long as with pure output data sets. Apart from basic input- and output-oriented DEA models with different returns to scale, the chapter includes a model that combines both orientations. Three various case studies involving banking industry, technology selection, and asset financing are provided in this section. In chapter 3 (GAMS Software), we briefly introduce General Algebraic Modeling System (GAMS) software, a modelling system for linear, nonlinear and mixed integer optimization problems for solving DEA models. Chapter 4 (Weights in DEA) treats the weights in DEA and their importance along with various weight restrictions and common set of weights (CSW) approaches. The chapter includes Assurance Region (AR) and Assurance Region Global (ARG) methods to restrict weight flexibility in DEA. Two DEA models with different types of efficiency, i.e. minsum and minimax, with their integrated versions are introduced in this chapter. The evaluation of facility layout design problem is addressed as a numerical example.Chapter 5 (Best Efficient Unit) considers CSW and binary variable approaches as the main tool for developing models that have the capability to find the most efficient DMU and also rank DMUs. We cover WEI/WEO data sets along with multiple input and multiple output data sets. Some epsilon-free DEA models are introduced to overcome the problem of finding a set of positive weights. The problem of finding the most cost-efficient under certain and uncertain input prices is also discussed. Two real data sets involving professional tennis players and a Turkish automotive company are rendered to validate the approaches in this chapter.  Chapter 6 (Data Selection in DEA) closes the book by considering the data selection problem in DEA and presenting some modifications of the standard DEA models to accommodate flexible and selective measures. To deal with these problems, two multiplier and envelopment DEA models are developed where each model contains two alternative approaches: individual and integrated models. The individual approach classifies flexible measures and identifies selective measures for each DMU, and the aggregate approach accommodates these measures using integrated DEA models. We present three case studies to examine and validate the approaches in this chapter.Evidently, my deepest gratitude and love go to my family, Laleh and Arad, for supporting me in writing this book. Ronak Azizi saved me a lot of trouble by tackling all formatting issues in Microsoft. Last, but certainly not least, I would like to extend my thanks to my friend, Dr Adel Hatami-Marbini, for helping me with editing the book and for invaluable ideas and comments.This publication has been elaborated in the framework of the project “Support research and development in the Moravian-Silesian Region 2013 DT 1 - International research teams“ (02613/2013/RRC). Financed from the budget of the Moravian-Silesian Region.

Kristiaan Kerstens, Jafar Sadeghi, Mehdi Toloo, Ignace Van de Woestyne (2022)Procedures for ranking technical and cost efficient units: With a focus on nonconvexity, In: European journal of operational research300(1)pp. 269-281 Elsevier B.V

•Infeasibility under the super-efficiency problem aggravates under nonconvexity.•New super-efficiency cost frontier is feasible under constant returns to scale•Super-efficiency cost frontier may be infeasible under variable returns to scale.•The super-efficiency decomposition is new in the literature.•New cost super-efficiency model under incomplete price data is proposed. This contribution extends the literature on super-efficiency by focusing on ranking cost-efficient observations. To the best of our knowledge, the focus has always been on technical super-efficiency and this focus on ranking cost-efficient observations may well open up a new topic. Furthermore, since the convexity axiom has both an impact on technical and cost efficiency, we pay a particular attention to the effect of nonconvexity on both super-efficiency notions. Apart from a numerical example, we use a secondary data set guaranteeing replication to illustrate these efficiency and super-efficiency concepts. Two empirical conclusions emerge. First, the cost super-efficiency notion ranks differently from the technical super-efficiency concept. Second, both cost and technical super-efficiency notions rank differently under convex and nonconvex technologies.

Adel Hatami-Marbini, Mehdi Toloo, Mohamad Reza Amini, Adel Azar (2022)Extending a fuzzy network data envelopment analysis model to measure maturity levels of a performance based-budgeting system: A case study, In: Expert systems with applications200116884 Elsevier Ltd

•Propose a framework for measuring a maturity level of performance-based budgeting.•Develop a parallel network data envelopment analysis model.•Consider the hierarchical configuration of performance indicators.•Use fuzzy sets theory to deal with vagueness and ambiguity.•Present a case study to demonstrate the applicability of the developed framework. Performance-based budgeting (PBB) aims to formulate and manage public budgetary resources to improve managerial decisions based on actual performance measures of agencies. Although the PBB system has been overwhelmingly applied by various agencies, the progress and maturity of its implementation process are not satisfactory at large. Therefore, it warrants to find, evaluate and improve the performance of organisations in relation to implementing a PBB system. To do so, the composite indicators (CIs) have been proposed to aggregate multiple indicators associated with the PBB system, but their employment is contentious as they often lean on ad-hoc and troublesome assumptions. Data envelopment analysis (DEA) methods as a powerful and established tool help to contend with key limitations of CIs. Although the original DEA method ignores an internal production process, the knowledge of the internal structure of the PBB systems and indicators is of importance to provide further insights when assessing the performance of PBB systems. In this paper, we present a budget assessment framework by breaking a PBB system into two parallel stages including operations performance (OP) and financial performance enhancement (FPE) to open up the black-box structure of the system and consider the indicator hierarchy configuration of each stage. In situations of the hierarchical configuration of indicators, we develop a multilayer parallel network DEA-based CIs model to measure the PBB maturity levels of the system and its stages. It is shown that the discrimination power of the proposed multilayer model is better than the existing models with one layer and in situations of relatively small number of DMUs the model developed in this paper can be a good solution to the dimension reduction of indicators. Moreover, this research leverages fuzzy logic to surmount the subjective information that is often available in collecting indicators of the PBB systems. The major contribution of this research is to examine a case study of a PBB maturity award in Iran, as a developing country with a myriad of financial challenges, to adopt a PBB maturity model as well as point towards the efficacy and applicability of the proposed framework in practice.

•Our approach addresses the sharing risk problem between government and investors.•It includes constraints that limit the pollution effects on population centers.•It considers social responsibility, economics factors, and benefits of waste recycling. The public–private partnership (PPP) is a practical and standard model that has been at the center of attention over the past two decades. Sharing risk between government and investors has been a challenging issue over the last year. This study formulates a model that aims to define the investors’ longing and allocate risks to the government in a logical range. Besides, in some real-world conditions, foreign investors with lower cost, higher quality, and better technology than domestic investors partner with the government. Under this condition, it is essential to consider the disruption risks because of sanctions and currency price fluctuations. Furthermore, the limited budget of the government for investing in infrastructure projects is intended. In this paper, the government's disruption risks and limited budget are added to the risk-sharing ratio model for the first time in literature. Moreover, the Pythagorean fuzzy sets (PFSs) are applied to cope with the uncertainty of real-world conditions. The PFSs are more potent than classical and intuitionistic fuzzy sets (IFSs) in dealing with uncertainty. The PFSs provide the membership, non-membership, and hesitancy degree for experts to better address the derived uncertainty of real-world conditions. Also, compared with the IFSs, PFSs prepare more space, consequently providing more freedom to address the uncertainty. Finally, a case study is presented to illustrate the applicability and susceptibility of the suggested model. As disruption risks increase, general utility degree, government utility, and investor’s effort decrease, and the guarantee risk ratio by government increases. Note that, investor’s effort decreases because the government is forced to give the unfinished project to the domestic investor; consequently, exclusive terms arise for the domestic investor.

Mehdi Toloo, Emmanuel Kwasi Mensah, Maziar Salahi (2022)Robust optimization and its duality in data envelopment analysis, In: Omega (Oxford)108102583 Elsevier Ltd

•We develop robust equivalents for fractional DEA models.•The proposed models give a proper interpretation of robust efficiency.•The superiorities of our approach models over the existing ones have been investigated.•Duality relation in robust DEA is established according to the “primal worst equal dual best” theorem in robust optimization.•We show an equivalent relation between robust input-and output-oriented models.•We illustrate our proposed models with a study from the largest airports in Europe. Robust Data Envelopment Analysis (RDEA) is a DEA-based conservative approach used for modeling uncertainties in the input and output data of Decision-Making Units (DMUs) to guarantee stable and reliable performance evaluation. The RDEA models proposed in the literature apply robust optimization techniques to the linear and conventional DEA models which lead to the difficulty of obtaining a robust efficient DMU. To overcome this difficulty, this paper tackles uncertainty in DMUs from the original fractional DEA model. We propose a robust fractional DEA (RFDEA) model in both input and output orientation which enables us to overcome the deficiency of existing RDEA models. The linearized models of the fractional DEA are further used to establish duality relations from a pessimistic and optimistic view of the data. We show that the primal worst of the multiplier model is equivalent to the dual best of the envelopment model. Furthermore, we show that the robust efficiency in the input- and output-oriented DEA models are still equivalent in the new approach which is not the case in conventional RDEA models. We finally present a study of the largest airports in Europe to illustrate the efficacy of the proposed models. The proposed RDEA is found to provide an effective management evaluation strategy under uncertain environments.

Mehdi Toloo, Rouhollah Khodabandelou, Amar Oukil (2022)A Comprehensive Bibliometric Analysis of Fractional Programming (1965–2020), In: Mathematics (Basel)10(11)1796

Fractional programming (FP) refers to a family of optimization problems whose objective function is a ratio of two functions. FP has been studied extensively in economics, management science, information theory, optic and graph theory, communication, and computer science, etc. This paper presents a bibliometric review of the FP-related publications over the past five decades in order to track research outputs and scholarly trends in the field. The reviews are conducted through the Science Citation Index Expanded (SCI-EXPANDED) database of the Web of Science Core Collection (Clarivate Analytics). Based on the bibliometric analysis of 1811 documents, various theme-related research indicators were described, such as the most prominent authors, the most commonly cited papers, journals, institutions, and countries. Three research directions emerged, including Electrical and Electronic Engineering, Telecommunications, and Applied Mathematics.

Gholam R. Amin, M. Toloo (2007)Finding the most efficient DMUs in DEA: An improved integrated model, In: Computers & industrial engineering52(1)pp. 71-77 Elsevier

In many applications of DEA finding the most efficient DMUs is desirable. This paper presents an improved integrated DEA model in order to detect the most efficient DMUs. The proposed integrated DEA model does not use the trial and error method in the objective function. Also, it is able to find the most efficient DMUs without solving the model n times (one linear programming (LP) for each DMU) and therefore allows the user to get faster results. It is shown that the improved integrated DEA model is always feasible and capable to rank the most efficient one. To illustrate the model capability the proposed methodology is applied to a real data set consisting of the 19 facility layout alternatives. (c) 2006 Elsevier Ltd. All rights reserved.

Josef Jablonsky, Ali Emrouznejad, Mehdi Toloo (2018)Editorial: Special issue on data envelopment analysis, In: Central European journal of operations research26(4)pp. 809-812 Springer Nature
Mehdi Toloo, Maziar Salahi (2018)A powerful discriminative approach for selecting the most efficient unit in DEA, In: Computers and Industrial Engineering115pp. 269-277 Elsevier

Data envelopment analysis (DEA) is a mathematical approach deals with the performance evaluation problem. Traditional DEA models partition the set of units into two distinct sets: efficient and inefficient. These models fail to get more information about efficient units whereas there are some applications, known as selection-based problems, where the concern is selecting only a single efficient unit. To address the problem, several mixed integer linear/nonlinear programming models are developed in the literature using DEA. The aim of all these approaches is formulating a model with more discriminating power. This paper presents a new nonlinear mixed integer programming model with significantly higher discriminating power than the existing ones in the literature. The suggested model lets the efficiency score of only a single unit be strictly greater than one. It is observed that the discrimination power of the model is high enough for fully ranking all units. More importantly, a linearization technique is used to formulate an equivalent mixed integer linear programming model which significantly decreases the computational burden. Finally, to validate the proposed model and also compare with some recent approaches, two numerical examples are utilized from the literature. Our founding points out the superiority of our model over all the previously suggested models from both theoretical and practical standpoints.

Mehdi Toloo, Madjid Tavana (2017)A novel method for selecting a single efficient unit in data envelopment analysis without explicit inputs/outputs, In: Annals of Operations Research253(1)pp. 657-681 Springer Nature

Data Envelopment Analysis (DEA) is a non-parametric technique for evaluating a set of homogeneous decision-making units (DMUs) with multiple inputs and multiple outputs. Various DEA methods have been proposed to rank all the DMUs or to select a single efficient DMU with a single constant input and multiple outputs [i.e., without explicit inputs (WEI)] as well as multiple inputs and a single constant output [i.e., without explicit outputs (WEO)]. However, the majority of these methods are computationally complex and difficult to use. This study proposes an efficient method for finding a single efficient DMU, known as the most efficient DMU, under WEI and WEO conditions. Two compact forms are introduced to determine the most efficient DMU without solving an optimization model under the DEA-WEI and DEA-WEO conditions. A comparative analysis shows a significant reduction in the computational complexity of the proposed method over previous studies. Four numerical examples from different contexts are presented to demonstrate the applicability and exhibit the effectiveness of the proposed compact forms.

Adel Hatami-Marbini, Mehdi Toloo (2017)An extended multiple criteria data envelopment analysis model, In: Expert Systems with Applications73pp. 201-219 Elsevier

Several researchers have adapted the data envelopment analysis (DEA) models to deal with two inter-related problems: weak discriminating power and unrealistic weight distribution. The former problem arises as an application of DEA in the situations where decision-makers seek to reach a complete ranking of units, and the latter problem refers to the situations in which basic DEA model simply rates units 100% efficient on account of irrational input and/or output weights and insufficient number of degrees of freedom. Improving discrimination power and yielding more reasonable dispersion of input and output weights simultaneously remain a challenge for DEA and multiple criteria DEA (MCDEA) models. This paper puts emphasis on weight restrictions to boost discriminating power as well as to generate true weight dispersion of MCDEA when a priori information about the weights is not available. To this end, we modify a very recent MCDEA models in the literature by determining an optimum lower bound for input and output weights. The contribution of this paper is sevenfold: first, we show that a larger amount for the lower bound on weights often leads to improving discriminating power and reaching realistic weights in MCDEA models due to imposing more weight restrictions; second, the procedure for sensitivity analysis is designed to define stability for the weights of each evaluation criterion; third, we extend a weighted MCDEA model to three evaluation criteria based on the maximum lower bound for input and output weights; fourth, we develop a super-efficiency model for efficient units under the proposed MCDEA model in this paper; fifth, we extend an epsilon-based minsum BCC-DEA model to proceed our research objectives under variable returns to scale (VRS); sixth, we present a simulation study to statistically analyze weight dispersion and rankings between five different methods in terms of non-parametric tests; and seventh, we demonstrate the applicability of the proposed models with an application to European Union member countries.

Mehdi Toloo, Ali Emrouznejad, Placido Moreno (2017)A linear relational DEA model to evaluate two-stage processes with shared inputs, In: Computational and Applied Mathematics36(1)pp. 45-61 Springer

Two-stage data envelopment analysis (DEA) efficiency models identify the efficient frontier of a two-stage production process. In some two-stage processes, the inputs to the first stage are shared by the second stage, known as shared inputs. This paper proposes a new relational linear DEA model for dealing with measuring the efficiency score of two-stage processes with shared inputs under constant returns-to-scale assumption. Two case studies of banking industry and university operations are taken as two examples to illustrate the potential applications of the proposed approach.

Maziar Salahi, Mehdi Toloo (2017)In the determination of the most efficient decision making unit in data envelopment analysis: A comment, In: Computers and Industrial Engineering104pp. 216-218 Elsevier

In order to deal with finding the most efficient unit problem, Lam (2015) recently built a new integrated mixed integer linear programming model which is nearly close to the super-efficiency model. The suggested model involves a non-Archimedean epsilon as the lower bound for the input and output weights. Selecting a suitable value for epsilon is a challenging issue in DEA (Data Envelopment Analysis). Lam (2015) suggested a value for epsilon which guarantees the feasibility of his model; however, this paper illustrates that the model may fail to find the most efficient unit due to unsuitable selected value for epsilon. To cope with this issue, a new model is formulated which provides the maximum epsilon value for the model of Lam (2015). The built model guarantees that when epsilon is maximum, then Lam’s model gives exactly one DMU (Decision Making Unit) as the most efficient unit with the maximum discrimination distance from the other DMUs.

Ales Kresta, Tomas Tichy, Mehdi Toloo (2017)Examination of Market Risk Estimation Models via DEA Approach Modelling, In: Politická Ekonomie65(2)pp. 161-178 Vysoka Skola Ekonomicka

Measuring and managing of financial risks is an essential part of the management of financial institutions. The appropriate risk management should lead to an efficient allocation of available funds. Approaches based on Value at Risk measure have been used as a means for measuring market risk since the late 20th century, although regulators newly suggest to apply more complex method of Expected Shortfall. While evaluating models for market risk estimation based on Value at Risk is relatively simple and involves so-called backtesting procedure, in the case of Expected Shortfall we cannot apply similar procedure. In this article we therefore focus on an alternative method for comprehensive evaluation of VaR models at various significance levels by means of data envelopment analysis (DEA). This approach should lead to the adoption of the model which is also suitable in terms of the Expected Shortfall criterion. Based on the illustrative results from the US stock market we conclude that NIG model and historical simulation should be preferred to normal distribution and GARCH model. We can also recommend to estimate the parameters from the period slightly shorter than two years.

Mehdi Toloo, Maryam Allahyar (2017)A selecting model under constant returns to scale in data envelopment analysis, In: R Nemec, L Chytilova (eds.), PROCEEDINGS OF THE 12TH INTERNATIONAL CONFERENCE ON STRATEGIC MANAGEMENT AND ITS SUPPORT BY INFORMATION SYSTEMS (SMSIS)pp. 350-357 Vsb-Tech Univ Ostrava

Data envelopment analysis (DEA) is a data-oriented mathematical programming approach that evaluates a set of peer decision making units (DMUs) dealing directly with the observed inputs and outputs (performance measures). Empirically, in order to have a logical assessment, there should be a balance between the number of performance measures and the number of DMUs. Accordingly, applying an appropriate method so that one can select some performance measures is very crucial for successful applications. In this paper, we suggest the envelopment form of selecting model under constant returns to scale (CRS) from both individual and aggregate points of view. We also show that applying these selecting models leads to the maximum discrimination between efficient units.

Emmanuel Kwasi Mensah, Mehdi Toloo (2017)Robust DEA for banks' efficiency under uncertainty, In: R Nemec, L Chytilova (eds.), PROCEEDINGS OF THE 12TH INTERNATIONAL CONFERENCE ON STRATEGIC MANAGEMENT AND ITS SUPPORT BY INFORMATION SYSTEMS (SMSIS)pp. 304-311 Vsb-Tech Univ Ostrava

The Data Envelopment Analysis (DEA) has been the benchmarked model for measuring the efficiency of banks over the years. However, inherent noise and uncertainties in the data are hardly considered for robust efficiency scores. The disadvantage is that a small perturbation in the uncertain parameters can lead to high infeasibility of the efficient solutions. This paper introduces a robust DEA into the measurement of banks efficiency. The proposed robust approach is based on the robust counterpart optimization of Ben-Tal & Nemirovski (2000), and it is implemented in the traditional DEA models germane to the performance measurement of banks. A preliminary result from data on banks in the Czech Republic indicates that efficiency scores measured with the robust DEA model provides a true and stable performance measure than the normal DEA model.

Behrouz Arabi, Susila Munisamy, Ali Emrouznejad, Mehdi Toloo, Mohammad Sadegh Ghazizadeh (2016)Eco-efficiency considering the issue of heterogeneity among power plants, In: Energy111pp. 722-735 Elsevier

One of the main objectives in restructuring power industry is enhancing the efficiency of power facilities. However, power generation industry, which plays a key role in the power industry, has a noticeable share in emission amongst all other emission-generating sectors. In this study, we have developed some new Data Envelopment Analysis models to find efficient power plants based on less fuel consumption, combusting less polluting fuel types, and incorporating emission factors in order to measure the ecological efficiency trend. We then applied these models to measuring eco-efficiency during an eight-year period of power industry restructuring in Iran. Results reveal that there has been a significant improvement in eco-efficiency, cost efficiency and allocative efficiency of the power plants during the restructuring period. It is also shown that despite the hydro power plants look eco-efficient; the combined cycle ones have been more allocative efficient than the other power generation technologies used in Iran.

Strategic vendor selection problem (VSP) has been investigated in different purchasing literature during the last two decades. Indeed, senior purchasing managers always deal with such crucial decisions. Manufacturing managers in the global market are faced with challenging and complex tasks very similar to VSP. Increasing outsourcing and opportunity provided by automotive industry to the worldwide markets make these decisions, even more, complex. Various methodologies, from simple weighted scoring methods to complex mathematical programming models, are introduced to tackle the VSP. Data envelopment analysis (DEA) is a non-parametric method in operations research and economics for evaluating the productive efficiency of decision-making units (DMUs). This study utilizes the proposed approach in Toloo and Ertay (2014) to develop a method for finding the most cost efficient DMU when the prices are fixed and known. A case study of an automotive company located in Turkey is adapted from the literature to illustrate the potential application of the suggested approach.

Atefeh Masoumzadeh, Mehdi Toloo, Alireza Amirteimoori (2016)Performance assessment in production systems without explicit inputs: an application to basketball players, In: IMA Journal of Management Mathematics27(2)pp. 143-156 Oxford University Press

A new research issue in the context of production theory is production without explicit inputs. In such systems, input consumption is not important to the decision-maker and the focus is on output production. In the presence of desirable and undesirable outputs, modelling undesirable outputs is an important problem. This paper discusses the problem of weak disposability in the absence of explicit inputs. A linear production technology is constructed axiomatically to handle desirable and undesirable outputs in production systems without explicit inputs. A simple linear formulation of weak disposability in such systems is proposed that enables us to reduce undesirable production outputs.

Mehdi Toloo, Rahele Jalili (2016)LU Decomposition in DEA with an Application to Hospitals, In: Computational Economics47(3)pp. 473-488 Springer

A fundamental problem that usually appears in linear systems is to find a vector satisfying . This linear system is encountered in many research applications and more importantly, it is required to be solved in many contexts in applied mathematics. LU decomposition method, based on the Gaussian elimination, is particularly well suited for spars and large-scale problems. Linear programming (LP) is a mathematical method to obtain optimal solutions for a linear system that is more being considered in various fields of study in recent decades. The simplex algorithm is one of the mostly used mathematical techniques for solving LP problems. Data envelopment analysis (DEA) is a non-parametric approach based on linear programming to evaluate relative efficiency of decision making units (DMUs). The number of LP models that has to be solved in DEA is at least the same as the number of DMUs. Toloo et al. (Comput Econ 45(2):323-326, 2015) proposed an initial basic feasible solution for DEA models which practically reduces at least 50 % of the whole computations. The main contribution of this paper is in utlizing this solution to implement LU decomposition technique on the basic DEA models which is more accurate and numerically stable. It is shown that the number of computations in applying the Gaussian elimination method will be fairly reduced due to the special structure of basic DEA models. Potential uses are illustrated with applications to hospital data set.

Mehdi Toloo, Seddigheh Babaee (2015)On variable reductions in data envelopment analysis with an illustrative application to a gas company, In: Applied Mathematics and Computation270pp. 527-533 Elsevier

Data envelopment analysis (DEA) is a non-parametric data oriented method for evaluating relative efficiency of the number of decision making units (DMUs) based on pre-selected inputs and outputs. In some real DEA applications, the large number of inputs and outputs, in comparison with the number of DMUs, is a pitfall that could have major influence on the efficiency scores. Recently, an approach was introduced which aggregates collected inputs and outputs in order to reduce the number of inputs and outputs iteratively. The purpose of this paper is to show that there are three drawbacks in this approach: instability due to existence of an infinitesimal epsilon, iteratively which can be improved to just one iteration, and providing non-radial inputs and outputs and then capturing them. In order to illustrate the applicability of the improved approach, a real data set involving 14 large branches of National Iranian Gas Company (NIGC) is utilized.

Amir Ebrahimi Zade, Sasan Barak, Hamidreza Maghsoudlou, Mehdi Toloo (2016)Multi-objective optimization for periodic preventive maintenance, In: Proceedings of the 2015 International Conference on Industrial Engineering and Systems Management (IESM 2015)pp. 173-182 Institute of Electrical and Electronics Engineers (IEEE)

This article investigates a JIT single machine scheduling problem with a periodic preventive maintenance. Also to maintain the quality of the products, there is a limitation on the maximum number of allowable jobs in each period. The proposed bi-objective mixed integer model minimizes total earliness-tardiness and makespan simultaneously. Due to the computational complexity of the problem, multi-objective particle swarm optimization (MOPSO) algorithm is implemented. Also, as well as MOPSO, two other optimization algorithms are used for comparing the results. Eventually, Taguchi method with metrics analysis is presented to tune the algorithms' parameters and a multiple criterion decision making (MCDM) technique based on the technique for order of preference by similarity to ideal solution (TOPSIS) is applied to choose the best algorithm. Comparison results confirmed supremacy of MOPSO to the other algorithms.

Mehdi Toloo, Mona Barat (2015)On considering dual-role factor in supplier selection problem, In: Mathematical Methods of Operations Research82(1)pp. 107-122 Springer

Conventional data envelopment analysis evaluates the relative efficiency of a set of homogeneous decision making units (DMUs), where DMUs are evaluated in terms of a specified set of inputs and outputs. In some situations, however, a performance factor could serve as either an output or an input. These factors are referred to as dual-role factors. The presence of dual-role factor among performance factors gives rise to the issue of how to fairly designate the input/output status to such factor. Several studies have been conducted treating a dual-role factor in both methodological and applied nature. One approach taken to address this problem is to view the dual-role factor as being nondiscretionary and connect it to the returns to scale concepts. It is argued that the idea of classifying a factor as an input or an output within a single model cannot consider the causality relationships between inputs and outputs. In this paper we present a mixed integer linear programming approach with the aim at dealing with the dual-role factor. Model structure is developed for finding the status of a dual-role factor via solving a single model while considering the causality relationships between inputs and outputs. It is shown that the new model can designate the status of a dual-role factor with half calculations as the previous model. Both individual and aggregate points of view are suggested for deriving the most appropriate designation of the dual-role factor. A data set involving 18 supplier selections is adapted from literature review to illustrate the efficacy of the proposed models and compare the new approach with the previous ones.

Mehdi Toloo, Ameneh Zandi, Ali Emrouznejad (2015)Evaluation efficiency of large-scale data set with negative data: an artificial neural network approach, In: Journal of Supercomputing71(7)pp. 2397-2411 Springer

Data envelopment analysis (DEA) is the most widely used methods for measuring the efficiency and productivity of decision-making units (DMUs). The need for huge computer resources in terms of memory and CPU time in DEA is inevitable for a large-scale data set, especially with negative measures. In recent years, wide ranges of studies have been conducted in the area of artificial neural network and DEA combined methods. In this study, a supervised feed-forward neural network is proposed to evaluate the efficiency and productivity of large-scale data sets with negative values in contrast to the corresponding DEA method. Results indicate that the proposed network has some computational advantages over the corresponding DEA models; therefore, it can be considered as a useful tool for measuring the efficiency of DMUs with (large-scale) negative data.

Esmail Keshavarz, Mehdi Toloo (2015)Efficiency status of a feasible solution in the Multi-Objective Integer Linear Programming problems: A DEA methodology, In: Applied Mathematical Modelling39(12)pp. 3236-3247 Elsevier

Efficient solutions in Multi-Objective Integer Linear Programming (MOILP) problems are categorized into two distinct types, supported and non-supported. Many researchers try to gain some conditions to determine whether a feasible solution is efficient, nevertheless there is no attempt to identify the efficiency status of a given efficient solution, i.e. supported and non-supported. In this paper, we first verify the relationships between Data Envelopment Analysis (DEA) and MOILP and then design two distinct practical procedures: the first one specifies whether or not an arbitrary feasible solution is efficient, meanwhile the second one as the main aim of this study, determines the efficiency status of an efficient solution. Finally, as a contribution of the suggested approach, we illustrate the drawback of Chen and Lu's methodology (Chen and Lu, 2007) which is developed for solving an extended assignment problem. (C) 2014 Elsevier Inc. All rights reserved.

You et al. (2013) indicated two errors in Amin and Toloo (2007). The first error was the infeasibility of Amin and Toloo's (2007) model and the second drawback was the lack of a suitable value for the non-Archimedean epsilon in the proposed approach of Amin and Toloo (2007). This paper deals with the raised issues and proves that the model of Amin and Toloo (2007) is always feasible. In addition, we also formulate a new model for finding a suitable value for the epsilon.

Mehdi Toloo, Tomas Tichy (2015)Two alternative approaches for selecting performance measures in data envelopment analysis, In: Measurement65pp. 29-40 Elsevier

Data envelopment analysis seeks a frontier to envelop all data with data acting in a critical role in the process and in such a way measures the relative efficiency of each decision making unit in comparison with other units. There is a statistical and empirical rule that if the number of performance measures is high in comparison with the number of units, then a large percentage of the units will be determined as efficient, which is obviously a questionable result. It also implies that the selection of performance measures is very crucial for successful applications. In this paper, we extend both multiplier and envelopment forms of data envelopment analysis models and propose two alternative approaches for selecting performance measures under variable returns to scale. The multiplier form of selecting model leads to the maximum efficiency scores and the maximum discrimination between efficient units is achieved by applying the envelopment form. Also individual unit and aggregate models are formulated separately to develop the idea of selective measures. Finally, in order to illustrate the potential of the proposed approaches a case study using a data from a banking industry in the Czech Republic is utilized. (C) 2014 Elsevier Ltd. All rights reserved.

Mehdi Toloo, Reza Farzipoor Saen, Majid Azadi (2015)Obviating some of the theoretical barriers of data envelopment analysis-discriminant analysis: an application in predicting cluster membership of customers, In: The Journal of the Operational Research Society66(4)pp. 674-683 Taylor & Francis

Data envelopment analysis-discriminant analysis (DEA-DA) has been used for predicting cluster membership of decision-making units (DMUs). One of the possible applications of DEA-DA is in the marketing research area. This paper uses cluster analysis to cluster customers into two clusters: Gold and Lead. Then, to predict cluster membership of new customers, DEA-DA is applied. In DEA-DA, an arbitrary parameter imposing a small gap between two clusters (η) is incorporated. It is shown that different η leads to different prediction accuracy levels since an unsuitable value for η leads to an incorrect classification of DMUs. We show that even the data set with no overlap between two clusters can be misclassified. This paper proposes a new DEA-DA model to tackle this issue. The aim of this paper is to illustrate some computational difficulties in previous DEA-DA approaches and then to propose a new DEA-DA model to overcome the difficulties. A case study demonstrates the efficacy of the proposed model.

Mehdi Toloo, Mona Barat, Atefeh Masoumzadeh (2015)Selective measures in data envelopment analysis, In: Annals of Operations Research226(1)pp. 623-642 Springer

Data envelopment analysis (DEA) is a data based mathematical approach, which handles large numbers of variables, constraints, and data. Hence, data play an important and critical role in DEA. Given a set of decision making units (DMUs) and identified inputs and outputs (performance measures), DEA evaluates each DMU in comparison with all DMUs. According to some statistical and empirical rules, a balance between the number of DMUs and the number of performance measures should exist. However, in some situations the number of performance measures is relatively large in comparison with the number of DMUs. These cases lead us to choose some inputs and outputs in a way that produces acceptable results. We refer to these selected inputs and outputs as selective measures. This paper presents an approach toward a large number of inputs and outputs. Individual DMU and aggregate models are recommended and expanded separately for developing the idea of selective measures. The practical aspect of the new approach is illustrated by two real data set applications.

Mehdi Toloo (2015)Alternative minimax model for finding the most efficient unit in data envelopment analysis, In: Computers and Industrial Engineering81pp. 186-194 Elsevier

Data envelopment analysis (DEA) deals with the evaluation of efficiency score of peer decision making units (DMUs) and divides them in two mutually exclusive sets: efficient and inefficient. There are various ranking methods to get more information about the efficient units. Nevertheless, finding the most efficient unit is a scientific challenge and hence has been the subject of numerous studies. Here, the main contribution is an integrated model that is able to determine the most efficient unit under a common condition is developed. The current research formulates a new minimax mixed integer linear programming (MILP) model for fining the most efficient DMU. Three different case studies from different contexts are taken as numerical examples to compare the proposed model with other methods. These numerical examples also illustrate the various potential applications of the suggested model.

Mehdi Toloo, Atefeh Masoumzadeh, Mona Barat (2015)Finding an Initial Basic Feasible Solution for DEA Models with an Application on Bank Industry, In: Computational Economics45(2)pp. 323-336 Springer Nature

Nowadays, algorithms and computer programs, which are going to speed up, short time to run and less memory to occupy have special importance. Toward these ends, researchers have always regarded suitable strategies and algorithms with the least computations. Since linear programming (LP) has been introduced, interest in it spreads rapidly among scientists. To solve an LP, the simplex method has been developed and since then many researchers have contributed to the extension and progression of LP and obviously simplex method. A vast literature has been grown out of this original method in mathematical theory, new algorithms, and applied nature. Solving an LP via simplex method needs an initial basic feasible solution (IBFS), but in many situations such a solution is not readily available so artificial variables will be resorted. These artificial variables must be dropped to zero, if possible. There are two main methods that can be used to eliminate the artificial variables: two-phase method and Big-M method. Data envelopment analysis (DEA) applies individual LP for evaluating performance of decision making units, consequently, to solve these LPs an IBFS must be on hand. The main contribution of this paper is to introduce a closed form of IBFS for conventional DEA models, which helps us not to deal with artificial variables directly. We apply the proposed form to a real-data set to illustrate the applicability of the new approach. The results of this study indicate that using the closed form of IBFS can reduce at least 50 % of the whole computations.

Sasan Barak, Mehdi Toloo (2015)Prioritizing strategies and ranking executive methods by QFD and fuzzy QSPM-Gap analysis, In: R Nemec, F Zapletal (eds.), Proceedings of the 11th International Conference on Strategic Management and its Support by Information Systemspp. 167-175 Technical University of Ostrava, Faculty of Economics

Our peripheral environment is changing rapidly and globalization of organizations has made them more complex. Therefore, organizations should codify their strategic plans and executive methods more accurately. However, some executive methods are not properly fulfilling the organization's strategic priorities. This paper proposes a comprehensive framework in order to evaluate and prioritize strategies and rank executive methods. To do this, firstly, the strategic plans are developed with SWOT (Strength, Weakness, Opportunity, Threat) analysis and then plans are weighted and diminished by using FQSPM-Gap (Fuzzy Quantitative Strategic Planning Matrix) model. Finally, the executive methods of the company are prioritized by QFD (Quality Function Deployment) matrix to accomplish its strategic plans. The model is implemented in a textile and clothing Company.

Esmaiel Keshavarz, Mehdi Toloo (2014)Finding efficient assignments: An innovative DEA approach, In: Measurement58pp. 448-458 Elsevier

Finding and classifying all efficient assignments for a Multi-Criteria Assignment Problem (MCAP) is one of the controversial issues in Multi-Criteria Decision Making (MCDM) problems. The main aim of this study is to utilize Data Envelopment Analysis (DEA) methodology to tackle this issue. Toward this end, we first state and prove some theorems to clarify the relationships between DEA and MCAP and then design a new two-phase approach to find and classify a set of efficient assignments. In Phase I, we formulate a new Mixed Integer Linear Programming (MILP) model, based on the Additive Free Disposal Hull (FDH) model, to gain an efficient assignment and then extend it to determine a Minimal Complete Set (MCS) of efficient assignments. In Phase II, we use the BCC model to classify all efficient solutions obtained from Phase I as supported and non-supported. A 4 x 4 assignment problem, containing two cost-type and single profit-type of objective functions, is solved using the presented approach. (C) 2014 Elsevier Ltd. All rights reserved.

Esmaiel Keshavarz, Mehdi Toloo (2015)Solving the Bi-Objective Integer Programming: A DEA methodology, In: 2014 International Conference on Control, Decision and Information Technologies (CoDIT 2014)pp. 060-064 Institute of Electrical and Electronics Engineers (IEEE)

Finding and classifying all efficient solutions for a Bi-Objective Integer Linear Programming (BOILP) problem is one of the controversial issues in Multi-Criteria Decision Making problems. The main aim of this study is to utilize the well-known Data Envelopment Analysis (DEA) methodology to tackle this issue. Toward this end, we first state some propositions to clarify the relationships between the efficient solutions of a BOILP and efficient Decision Making Units (DMUs) in DEA and next design a new two-stage approach to find and classify a set of efficient solutions. Stage I formulates a two-phase Mixed Integer Linear Programming (MILP) model, based on the Free Disposal Hull (FDH) model in DEA, to gain a Minimal Complete Set of efficient solutions. Stage II uses a variable returns to scale DEA model to classify the obtained efficient solutions from Stage I as supported and non-supported. A BOILP model containing 6 integer variables and 4 constraints is solved as an example to illustrate the applicability of the proposed approach.

Mehdi Toloo (2014)The role of non-Archimedean epsilon in finding the most efficient unit: With an application of professional tennis players, In: Applied Mathematical Modelling38(21-22)pp. 5334-5346 Elsevier

The determination of a single efficient decision making unit (DMU) as the most efficient unit has been attracted by decision makers in some situations. Some integrated mixed integer linear programming (MILP) and mixed integer nonlinear programming (MINLP) data envelopment analysis (DEA) models have been proposed to find a single efficient unit by the optimal common set of weights. In conventional DEA models, the non-Archimedean infinitesimal epsilon, which forestalls weights from being zero, is useless if one utilizes the well-known two-phase method. Nevertheless, this approach is inapplicable to integrated DEA models. Unfortunately, in some proposed integrated DEA models, the epsilon is neither considered nor determined. More importantly, based on this lack some approaches have been developed which will raise this drawback. In this paper, first of all some drawbacks of these models are discussed. Indeed, it is shown that, if the non-Archimedean epsilon is ignored, then these models can neither find the most efficient unit nor rank the extreme efficient units. Next, we formulate some new models to capture these drawbacks and hence attain assurance regions. Finally, a real data set of 53 professional tennis players is applied to illustrate the applicability of the suggested models.

Mehdi Toloo, Ales Kresta (2014)Finding the best asset financing alternative: A DEA-WEO approach, In: Measurement55pp. 288-294 Elsevier

Measurement of performance is an important activity in identifying weaknesses in managerial efficiency and devising goals for improvement. Data envelopment analysis (DEA) is a mathematical quantitative approach for measuring the performance of a set of similar units. Toloo (2013) extended a DEA approach for finding the most efficient unit considering a data set without explicit inputs. The aim of this paper is to develop DEA models without explicit outputs, henceforth called DEA-WEO, to find the most efficient unit when outputs are not directly considered. The suggested models directly utilize the data without the need of adding a virtual output, whose value is equal to for all units. A real data set involving 139 different alternatives for long-term asset financing provided by Czech banks and leasing companies is taken to illustrate the potential application of the proposed approach.

Mehdi Toloo (2014)An epsilon-free approach for finding the most efficient unit in DEA, In: Applied Mathematical Modelling38(13)pp. 3182-3192 Elsevier

Data envelopment analysis (DEA), considering the best condition for each decision making unit (DMU), assesses the relative efficiency and partitions DMUs into two sets: efficient and inefficient. Practically, in traditional DEA models more than one efficient DMU are recognized and these models cannot rank efficient DMUs. Some studies have been carried out aiming at ranking efficient DMUs, although in some cases only discrimination of the most efficient unit is desirable. Furthermore, several investigations have been done for finding the most CCR-efficient DMU. The basic idea of the majority of them is to introduce an integrated model which achieves an optimal common set of weights (CSW). These weights help us identify the most efficient unit in an identical condition. Recently, Toloo (2012) [13] proposed a new mixed integer programming (MIP) model to find the most BCC-efficient unit. Based on this study, we propose a new basic integrated linear programming (LP) model to identify candidate DMUs for being the most efficient unit; next a new MIP integrated DEA model is introduced for determining the most efficient DMU. Moreover, these models exclude the non-Archimedean epsilon and consequently the optimal solution of these models can be obtained, straightforwardly. We claim that the most efficient unit, which could be obtained from all other integrated models, has to be one of the achieved candidates from the basic integrated LP model. Two numerical examples are illustrated to show the variant use of these models in different important cases. (C) 2013 Elsevier Inc. All rights reserved.

Mehdi Toloo (2014)Notes on classifying inputs and outputs in data envelopment analysis: A comment, In: European Journal of Operational Research235(3)pp. 810-812 Elsevier

Cook and Zhu (2007) introduced an innovative method to deal with flexible measures. Toloo (2009) found a computational problem in their approach and tackled this issue. Amirteimoori and Emrouznejad (2012) claimed that both Cook and Zhu (2007) and Toloo (2009) models overestimate the efficiency. In this response, we prove that their claim is incorrect and there is no overestimate in these approaches.

Mehdi Toloo, Tijen Ertay (2014)The most cost efficient automotive vendor with price uncertainty: A new DEA approach, In: Measurement52(1)pp. 135-144 Elsevier

Vendor’s performance evaluation is an important subject which has strategic implications for managing an efficient company. However, there are many important criteria for prospering company. These criteria may contradict together. In other words, while a criterion is improved, the other may worsen. Indeed, similar to manufacturing manager in global market, purchasing manager who has significant practical implications deals with this issue. The vendor selection problem (VSP) is obviously affected by the complexity and uncertainty due to the lack of information associated with related business environment of countries in a global market. On the other hand, in the automotive industry which plays an important role in the worldwide market, these decisions will be exacerbated by increasing the outsourcing and opportunities. There are varieties of techniques, from simple weighted scoring methods to complex mathematical programming, for handling VSP. In this study, we propose a new cost efficiency data envelopment analysis (CE–DEA) approach with price uncertainty for finding the most cost efficient unit. Potential uses are then illustrated with an application to automotive industry involving 73 vendors in Turkey.

Mehdi Toloo (2014)Selecting and full ranking suppliers with imprecise data: A new DEA method, In: International Journal of Advanced Manufacturing Technology74(5-8)pp. 1141-1148 Springer

Supplier selection, a multi-criteria decision making (MCDM) problem, is one of the most important strategic issues in supply chain management (SCM). A good solution to this problem significantly contributes to the overall supply chain performance. This paper proposes a new integrated mixed integer programming ‐ data envelopment analysis (MIP‐DEA) model for finding the most efficient suppliers in the presence of imprecise data. Using this model, a new method for full ranking of units is introduced. This method tackles some drawbacks of the previous methods and is computationally more efficient. The applicability of the proposed model is illustrated, and the results and performance are compared with the previous studies.

Mehdi Toloo (2013)The most efficient unit without explicit inputs: An extended MILP-DEA model, In: Measurement : journal of the International Measurement Confederation46(9)pp. 3628-3634 Elsevier

Data envelopment analysis (DEA) has been a very popular method for measuring and benchmarking relative efficiency of each decision making units (DMUs) with multiple inputs and multiple outputs. DEA and Discriminant Analysis (DA) are similar in classifying units to exhibit either good or poor performance. On the other hand, selecting the most efficient unit between several efficient ones is one of the main issues in multi-criteria decision making (MCDM). Some proponents have suggested some approaches and claimed their methodologies involve discriminating power to determine the most efficient DMU without explicit input. This paper focuses on the weakness of a recent methodology of these approaches and to avoid this drawback presents a mixed integer programming (MIP) approach. To illustrate this drawback and compare discriminating power of the recent methodology to our new approach, a real data set containing 40 professional tennis players is utilized.

Mehdi Toloo (2012)On finding the most BCC-efficient DMU: A new integrated MIP–DEA model, In: Applied Mathematical Modelling36(11)pp. 5515-5520 Elsevier

This paper proposes a new integrated mixed integer programing – data envelopment analysis (MIP–DEA) model to improve the integrated DEA model which was introduced by Toloo & Nalchigar [M. Toloo, S. Nalchigar. A new integrated DEA model for finding most BCC–efficient DMU. Appl. Math. Model. 33 (2009) 597–60]. In this study some problems of applying Toloo & Nalchigar’s model are addressed. A new integrated MIP–DEA model is then introduced to determine the most BCC-efficient decision making unit (DMU). Moreover, it is mathematically proved that the new model identifies only a single BCC-efficient DMU by a common set of optimal weights. To show applicability of proposed models, a numerical example is used which contains a real data set of nineteen facility layout designs (FLDs).

Mehdi Toloo (2012)Alternative solutions for classifying inputs and outputs in data envelopment analysis, In: Computers and Mathematics with Applications63(6)pp. 1104-1110 Elsevier

In conventional data envelopment analysis (DEA) models, a performance measure whether as an input or output usually has to be known. Nevertheless, in some cases, the type of a performance measure is not clear and some models are introduced to accommodate such flexible measures. In this paper, it is shown that alternative optimal solutions of these models has to be considered to deal with the flexible measures, otherwise incorrect results might occur. Practically, the efficiency scores of a DMU could be equal when the flexible measure is considered either as input or output. These cases are introduced and referred as share cases in this study specifically. It is duplicated that share cases must not be taken into account for classifying inputs and outputs. A new mixed integer linear programming (MILP) model is proposed to overcome the problem of not considering the alternative optimal solutions of classifier models. Finally, the applicability of the proposed model is illustrated by a real data set.

Mehdi Toloo, Soroosh Nalchigar (2011)A new DEA method for supplier selection in presence of both cardinal and ordinal data, In: Expert Systems with Applications38(12)pp. 14726-14731 Elsevier

The success of a supply chain is highly dependent on selection of best suppliers. These decisions are an important component of production and logistics management for many firms. Little attention is given in the literature to the simultaneous consideration of cardinal and ordinal data in supplier selection process. This paper proposes a new integrated data envelopment analysis (DEA) model which is able to identify most efficient supplier in presence of both cardinal and ordinal data. Then, utilizing this model, an innovative method for prioritizing suppliers by considering multiple criteria is proposed. As an advantage, our method identifies best supplier by solving only one mixed integer linear programming (MILP). Applicability of proposed method is indicated by using data set includes specifications of 18 suppliers.

Gholam R. Amin, Mehdi Toloo, M. Sheikhan (2010)Input and output scaling in advanced manufacturing technology: theory and application, In: International Journal of Advanced Manufacturing Technology50(50)pp. 1235-1241 Springer Nature

This paper suggests new data envelopment analysis (DEA) models for input and output scaling in advanced manufacturing technology (AMT). For a given group of AMT observations using the traditional DEA models, it is not possible to evaluate the units when a specified input (or specified output) is required to be scaled for all units. The paper provides theoretical results for obtaining the relationship between the original AMT observations and the corresponding scaled data. Also, the paper uses numerical illustrations to show the usefulness of the suggested contribution.

Mehdi Toloo, Babak Sohrabi, Soroosh Nalchigar (2009)A new method for ranking discovered rules from data mining by DEA, In: Expert systems with applications36(4)pp. 8503-8508 Elsevier

Data mining techniques, extracting patterns from large databases have become widespread in business. Using these techniques, various rules may be obtained and only a small number of these rules may be selected for implementation due, at least in part. to limitations of budget and resources. Evaluating and ranking the interestingness or usefulness of association rules is important in data mining. This paper proposes a new integrated data envelopment analysis (DEA) model which is able to find most efficient association rule by solving only one mixed integer linear programming (MILP). Then, utilizing this model, a new method for prioritizing association rules by considering Multiple criteria is proposed. As an advantage, the proposed method is computationally more efficient than previous works. Using an example of market basket analysis, applicability of our DEA based method for measuring the efficiency of association rules with multiple criteria is illustrated. (C) 2008 Elsevier Ltd. All rights reserved.

Mehdi Toloo (2009)On classifying inputs and outputs in DEA: A revised model, In: European Journal of Operational Research198(1)pp. 358-360 Elsevier

Cook and Zhu [Cook, W.D., Zhu, J., 2007. Classifying inputs and outputs in data envelopment analysis. European Journal of Operational Research 180, 692–699] introduced a new method to determine whether a measure is an input or an output. In practice, however, their method may produce incorrect efficiency scores due to a computational problem as result of introducing a large positive number to the model. This note introduces a revised model that does not need such a large positive number.

Mehdi Toloo, Samaneh Joshaghani (2009)Centralized additive model, In: CIE: 2009 INTERNATIONAL CONFERENCE ON COMPUTERS AND INDUSTRIAL ENGINEERING, VOLS 1-3pp. 420-425 Institute of Electrical and Electronics Engineers (IEEE)

While conventional data envelopment analysis (DEA) models set targets separately for each decision making unit (DMU), Lozano and Villa (2004) introduced the concept of "centralized" DEA models, which aim at optimizing the combined resource consumption by all units in an organization rather than considering the consumption by each unit, separately. In these models, there is a centralized decision maker (DM) who supervises all DMUs. The main aim is optimizing total input consumption and output production. In this paper, firstly we present centralized output product model. Then we introduce parametric centralized additive model, which during one phase minimizes total consumption inputs and maximizes total output production simultaneously, in the direction of optimization vector. Some numerical examples of the proposed models and their results are presented.

Mehdi Toloo, Maryam Shadab, Mahta Yekkalam, (2009)Finding the most cost efficient DMU with certain and uncertain input prices, In: CIE: 2009 INTERNATIONAL CONFERENCE ON COMPUTERS AND INDUSTRIAL ENGINEERING, VOLS 1-3pp. 396-401 Institute of Electrical and Electronics Engineers (IEEE)

Cost efficiency (CE) assesses the ability to produce current output at minimal cost. There are some models which are introduced to measure cost efficiency with certain and uncertain input prices. Normally, by using data envelopment analysis (DEA) models, more than one cost efficient decision making units (DMUs) are recognized. The main contribution of this paper consists of development of a model which was proposed by Amin and Toloo (2007) to some models for finding the most cost efficient DMU in various situations of input prices. These models find the most cost efficient DMU by solving only one mixed integer linear programming (MILP) in each case.

Mehdi Toloo, Soroosh Nalchigar (2009)A new integrated DEA model for finding most BCC-efficient DMU, In: Applied Mathematical Modelling33(1)pp. 597-604 Elsevier

In many applications of widely recognized technique, DEA, finding the most efficient DMU is desirable for decision maker. Using basic DEA models, decision maker is not able to identify most efficient DMU. Amin and Toloo [Gholam R. Amin, M. Toloo, Finding the most efficient DMUs in DEA: an improved integrated model. Comput. Ind. Eng. 52 (2007) 71–77] introduced an integrated DEA model for finding most CCR-efficient DMU. In this paper, we propose a new integrated model for determining most BCC-efficient DMU by solving only one linear programming (LP). This model is useful for situations in which return to scale is variable, so has wider range of application than other models which find most CCR-efficient DMU. The applicability of the proposed integrated model is illustrated, using a real data set of a case study, which consists of 19 facility layout alternatives.

Mehdi Toloo, Nazila Aghayi, Mohsen Rostamy-malkhalifeh (2008)Measuring overall profit efficiency with interval data, In: Applied Mathematics and Computation201(1-2)pp. 640-649 Elsevier

This paper presents a framework where data envelopment analysis (DEA) is used to measure overall profit efficiency with interval data. Specifically, it is shown that as the inputs, outputs and price vectors each vary in intervals, the DMUs cannot be easily evaluated. Thus, presenting a new method for computing the efficiency of DMUs with interval data, an interval will be defined for the efficiency score of each unit. As well as, all the DMUs are divided into three groups which are defined according to the interval obtained for the efficiency value of DMUs.

Gholam R. Amin, M. Toloo, B. Sohrabi (2006)An improved MCDM DEA model for technology selection, In: International journal of production research44(13)pp. 2681-2686 Taylor & Francis Group

This paper presents an Improved MCDM Data Envelopment Analysis (DEA) model in order to evaluate the best efficient DMUs in Advanced Manufacturing Technology (AMT). This model is capable of ranking the next most efficient DMUs after removing the previous best one.

Gholam R. Amin, Mehdi Toloo (2004)A polynomial-time algorithm for finding ε in DEA models, In: Computers & Operations Research31(5)pp. 803-805 Elsevier

This paper presents a new algorithm for computing the non-Archimedean ε in DEA models. It is shown that this algorithm is polynomial-time of O(n), where n is the number of decision making units (DMUs). Also it is proved that using only inputs and outputs of DMUs, the non-Archimedean ε can be found such that, the optimal values of all CCR models, which are corresponding to all DMUs, are bounded and an assurance value is obtained.

Mehdi Toloo, Mohammadreza Taghizadeh-Yazdi, Abdolkarim Mohammadi-Balani (2022)Multi-objective centralization-decentralization trade-off analysis for multi-source renewable electricity generation expansion planning: A case study of Iran, In: Computers & Industrial Engineering164107870 Elsevier

Countries need robust long-term plans to keep up with the global pace of transitioning from pollutant fossil fuels towards clean, renewable energies. Renewable energy generation expansion plans can be either centralized, decentralized, or a combination of these two. This paper presents a novel approach to obtain an optimal multi-period plan for generating each type of renewable energy (solar, wind, hydro, geothermal, and biomass) via multi-objective mathematical modeling. The proposed model has integrated with Autoregressive Integrated Moving Average (ARIMA) econometric method to forecast the country’s demand during the planning horizon. The optimal energy mix based on several socio-economic aspects of renewable sources was obtained using the Passive and Active Compensability Multicriteria ANalysis (PACMAN) multi-attribute decision-making method. The model has been solved by a Non-dominated Sorting Genetic Algorithm (NSGA-II) metaheuristic algorithm. Each solution in the Pareto front contains a plan for each electricity generation region under a certain combination of centralization and decentralization strategies.

Siamak Talatahari, Mahdi Azizi, Mehdi Toloo, Milad Baghalzadeh Shishehgarkhaneh (2022)Optimization of Large-Scale Frame Structures Using Fuzzy Adaptive Quantum Inspired Charged System Search, In: International journal of steel structures22pp. 686-707 Korean Society of Steel Construction

In this paper, a metaheuristic-based design approach is developed in which the structural design optimization of large-scale steel frame structures is concerned. Although academics have introduced form-dominant methods, yet using artificial intelligence in structural design is one of the most critical challenges in recent years. However, the Charged System Search (CSS) is utilized as the primary optimization approach, which is improved by using the main principles of quantum mechanics and fuzzy logic systems. In the proposed Fuzzy Adaptive Quantum Inspired CSS algorithm, the position updating procedure of the standard algorithm is developed by implementing the center of potential energy presented in quantum mechanics into the general formulation of CSS to enhance the convergence capability of the algorithm. Simultaneously, a fuzzy logic-based parameter tuning process is also conducted to enhance the exploitation and exploration rates of the standard optimization algorithm. Two 10 and 60 story steel frame structures with 1026 and 8272 structural members, respectively, are utilized as design examples to determine the performance of the developed algorithm in dealing with complex optimization problems. The overall capability of the presented approach is compared with the Charged System Search and other metaheuristic optimization algorithms. The proposed enhanced algorithm can prepare better results than the other metaheuristics by considering the achieved results.

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