
Dr Mehdi Toloo
Academic and research departments
Department of Business Transformation, Faculty of Arts and Social Sciences.Biography
Mehdi Toloo is a Senior Lecturer (Associate Professor) in Business Analytics at Surrey Business School, UK. He also holds a Full Professor position in Systems Engineering and Informatics at the Technical University of Ostrava, Czech Republic. Before that, he was a Full Professor in Operations Management at Sultan Qaboos University, Muscat, Oman. Areas of interest include Operational Analytics, Operations Research/Management, Decision Analysis, Performance Evaluation, Multi-Objective Programming, and Mathematical Modelling. He has contributed to numerous international conferences as a chair, keynote speaker, presenter, track/session chair, workshop organizer, and member of the scientific committee.
Mehdi has lots of experience in leading and collaborating on many successful research projects: (1) Performance evaluation in the presence of unclassified factors, Czech Science Foundation, Czech Republic, 2019-2022. Budget: 172,000 € (Principal Investigator), (2) Economies of Scope in Network Data Envelopment Analysis Models, Czech Science Foundation, Czech Republic, 2017-2019. Budget: 126,000 €, (Principal Investigator), (3) Multiple Criteria Decision Making Modelling: Novel Weighting Methods and Hybrid Approaches, Czech Science Foundation, Czech Republic, 2017-2018. Budget: 70,000 €, (4) Selective Measures in DEA: Theory and Applications, Czech Science Foundation, Czech Republic, 2016-2018. Budget: 106,000 €, (Principal Investigator), (5) Examining Allocative Efficiency Through Network Data Envelopment Analysis, Czech Science Foundation, Czech Republic, Budget: 65,000 €, (6) Research Team for Modelling of Economic and Financial Processes at VŠB-TU Ostrava, Technical University of Ostrava, Ostrava, Czech Republic. European Social Project, 2013-2015. Budget: 1,180,000 €.
Mehdi acts as an editor for Computers & Industrial Engineering (ELSEVIER), Decision Analytics (ELSEVIER), Healthcare Analytics (ELSEVIER), Journal of Business Logistics (WIELY), RAIRO-Operations Research (EDP Sciences), Mathematics (MDPI), and Central European Journal of Operations Research (SPRINGER)
He is an author/editor of several books including:
- Multi-Objective Combinatorial Optimization Problems and Solution Methods, ELSEVIER, ISBN: 978-0-12-823799-1, 2022.
- Optimization Problems in Economics and Finance, series on advanced economic issues (SAEI), Vol. 40. Ostrava: VSB-TU Ostrava, ISBN: 978-80-248-3837-3, 2015.
- Data Envelopment Analysis with selected models and applications, series on advanced economic issues (SAEI), Vol. 30, Ostrava: VSB-TU Ostrava, ISBN: 978-80-248-3738-3, 2014.
- Operations Research II, Modaresan Sharif, ISBN:978-964-187-609-0, 2012.
- Solution Manual of Problems in Operations Research, Azarakhsh, ISBN: 964-6294-68-5.
- MATHEMATICA Applications in Calculus, Azarakhsh, ISBN: 964-6294-72-2.
- 100 Programs in PASCAL, Azad University Press,
- 101 Programs in C++, Azad University Press, ISBN: 978-964-6493-83-4.
- GAMS User Guide with DEA Models, Nasher Kotob Daneshgahi, IBN: 978-600-510-42-5.
- Introduction to Scientific Computing, Scholars’ Press ISBN: 978-3639511161.
- Visual FOXPRO User Guide, Azarakhsh, ISBN: 964-6294-33-2. (Translated to Persian)
- EXCEL for Beginners, Azarakhsh, ISBN: 964-6294-33-2. (Translated to Persian)
- Introduction to Operations Research, 6th Edition, Azarakhsh, ISBN: 64-6294-53-7. (Translated to Persian)
- Introduction to Operations Research, 7th Edition, Nasher Daneshgahi, ISBN: 978-964-01-1317-2. (Translated to Persian)
- Schaum’s Outline of Operations Research, University of Tehran Press, ISBN: 978-964-01-1317-2. (Translated to Persian)
Book chapters:
- Multi-Objective Combinatorial Optimization Problems and Solution Methods, Chapter 01, Multiobjective combinatorial optimization problems: social, keywords, and journal maps, ELSEVIER, ISBN: 978-0-12-823799-1, 2022.
- Multi-Objective Combinatorial Optimization Problems and Solution Methods, Chapter 10, Finding efficient solutions of the multicriteria assignment problem, Academic Press, ELSEVIER, ISBN: 978-0-12-823799-1, 2022.
- New Fundamental Technologies in Data Mining, Chapter 23, On Ranking Discovered Rules of Data Mining by Data Envelopment Analysis: Some New Models with Wider Applications, InTech Publisher, ISBN 978-953-307-547-1, 2011.
Research
Research interests
- Operational Analytics
- Business Analytics
- Operations Research/Management
- Performance Evaluation
- Data Envelopment Analysis
- Decision Analysis
- Risk Analysis
- Multiple Criteria Decision Making
- Mathematical Modelling
Research projects
Performance evaluation of a system is the main theme of data envelopment analysis (DEA). Non-parametricity, data-driven modelling and axiomatic framework are the most essential properties of DEA. Indeed, DEA is a mathematical programming approach for assessing the relative efficiency of systems by estimating the best practice in terms of all observations. Performance factors are classified into input and output groups and the efficiency of a system is defined as the ratio of a weighted sum of its outputs to a weighted sum of its inputs. In some applications, there are some unclassified factors, which can simultaneously play input and output roles. The main aim of our research project is to get around DEA implementation problems when unclassified factors are available. With unclassified factors, we need to revisit the axiomatic framework of DEA, extend some non-oriented DEA models, handle data irregularities, and develop some DEA models with the inclusion of weight. We aim to scrutinize the properties and validity of the proposed models from both theoretical and practical standpoints.
The aim of the project is to investigate the ability of particular models for network systems, especially two-stage ones, to estimate suitable measures of efficiency. Then, the DEA models which are available for determining the existence of economies of scope will be analyzed. The special aim of the project is to present an approach by which the existence of economies of scope for two-stage production systems can be studied. To reach the aim the team will: (i) create a comprehensive report on the results of models of economies of scope using DEA and two-stage systems using network DEA and also analyze and compare the recent models; (ii) validate formulated models towards more complicated decision-making units involving various internal processes.
Data Envelopment Analysis (DEA) 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 (DMU) in comparison with other units. 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. In this project, some new DEA models are formulated for selecting performance measures. For this aim, we (i) extend some selecting approaches (ii) extend them to accommodate some special data sets (iii) formulate some new hybrid models to consider both selective and flexible measures (iv) develop some multiplicative DEA models associated with the selecting approaches.
Due to global competitive conditions and economic crises, significant changes in product processing play an increasingly important role in maintaining a competitive and effective position over organizations. Based on the theory of traditional Data Envelopment Analysis (DEA), the DEA approach represents a convenient way to analyze the efficiency of a set of Decision Making Units (DMUs), and the order of them taking into account their level of efficiency. The project adopts DEA to identify the key factors of efficiency evaluation in network organizations. Within the project, the ability of particular integrated network DEA (NDEA) models to estimate allocative efficiency scores will be analyzed. Newly developed models will represent an effective way to identify existing issues and their causes in network organizations, and thus determine the degree of changes required for optimal utilization of resources in order to increase the efficiency score of the organization. Conclusions and validity of the NDEA method's results will be verified in real situations in the Moravian-Silesian Region.
Research collaborations
Multiple Criteria Decision Making Modelling: Novel Weighting Methods and Hybrid Approaches, Czech Science Foundation, Czech Republic, ČACR project number: 17- 22662S, 2017-2018.
Research Team for Modelling of Economic and Financial Processes at VŠB-TU Ostrava, , Technical University of Ostrava, Ostrava, Czech Republic. European Social Project CZ.1.07/2.3.00/20.0296, 2013-2015.
Supervision
Postgraduate research supervision
- E. K. Mensah, Robust Optimization in Data Envelopment Analysis: Extended Theory and Applications, Department of Economics, University of Insubria, Varese, Italy, 2019.
- H. Naseri, Stochastic Noise and Heavy-Tailed (Stable) Distribution in DEA, Department of Industrial Engineering, Islamic Azad University, Science and Research, Tehran, Iran, 2018.
- E. Keshavarz, Solving the multi-objective network flow optimization problems by a DEA methodology, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2015.
- A. Mahmoodirad, Modeling and solving a multi-product fixed charge solid transportation problem in a supply chain by meta-heuristics, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2015.
- A. Masoumzade, Increasing discriminating power in DEA, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2014.
- S. Nalchigar, A new methodology to develop and evaluate context-aware recommender systems based on data mining, Department of Information Technology Management, University of Tehran, Iran, 2014.
- S. Banihashemi, Optimization modelling of portfolio and sensitivity analysis supply chains, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2014.
- L.P. Navas, Application of DEA to public sectors of Colombia with some extensions of model development, Department of Industrial Engineering, Universidad de los Andes, Bogotá, Colombia, 2018.
- M. Barat, Quantitative data in data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2006.
- M. Ahmadzadeh, Using lexicographic parametric programming for identifying efficient units in data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2006.
- E. Sabertahan, A new framework in solving data envelopment analysis models, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2006.
- S. Bahiraee, Evaluation of information technology investment: a data envelopment analysis approach, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2006.
- E. Sarfi, Performance measuring and data categorizing in data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2007.
- N. Aghaee, Overall efficiency and effectiveness measuring in data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2007.
- M. Yekkalam Tash, Decomposition in data envelopment analysis: a relational network, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2008.
- M. Shadab, Data envelopment analysis based on auctions, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2008.
- S. Ghorbani, Ranking of units on the DEA frontier with common set of weights, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2008.
- A. Hashemi, Balanced score card and data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2008.
- S. Soleimani Nadaf, Two-level optimization and data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2010.
- S. Ranjbar, Two-stage processes in data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2010.
- Z. Dinarvand, Classifying inputs and outputs based on distance function, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2011.
- E. Falatouri, Data mining and data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2011.
- M. Maleklou, Evaluation of credits risk using data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2011.
- A. Zandi, Neural network and its application in data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2011.
- Z. Molaee, Presenting data envelopment analysis graphically, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2011.
- L. Narimisa, Multi-objective problems and data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2011.
- H. Gharaee, SBM models in two-stage network structures, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2011.
- N. Chalambari, Two-stage network structures in DEA: a game theory approach, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2011.
- S. Hassan Nejad, Ratio data in data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2011.
- Z. Khoshhal, Supplier selection using data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2011.
- V. Choobkar, Undesirable input and output modelling in efficiency analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2005.
- S. Sadeghi, A model for decision making ranking with sum-zero profit and comparing with some ranking models, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2005
- M. Mirsadeghpoor, Network DEA: evaluating the efficiency of organization with complex internal structure, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2006
- M. Sahraee, Models for performance evaluation and cost efficiency with price uncertainty and its application to banks braches assessment, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2006
- Gh. Rozbehi, Interval efficiency measurement with imprecise data, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2007
- Kh. Nasrollahzadeh, Optimal paths and costs of adjustment in dynamic DEA models and application, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2007.
- S. Joshaghani, Centralized resource allocation models: a data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2008.
- H. Saleh, A fuzzy DEA/AR approach to the selection of flexible manufacturing System, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2008
- S. Nalchigar, A new framework for ranking associate rules of data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2009.
- M. Izadkhah, Integrating DEA-oriented performance assessment and target setting using interactive MOLP methods, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2010.
- P. Madhooshi, The improved OWA model and determining the most preferred OWA Operator, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2010.
- S. Rahmatfam, Cross-efficiency and determination of ultimate cross efficiency weights, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2010.
- S. Mamizadeh, Supply chain management in data envelopment analysis, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2010.
- R. Motefaker Fard, Measurement of multi-period aggregative efficiency, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2010.
- E. Keramati, Some extensions about integrating DEA-oriented performance assessment, Department of Mathematics and Statistics, Islamic Azad University, Central Tehran Branch, Tehran, Iran, 2011.
My teaching
- Fundamental of Computer, Foundation of Algorithms, Data Structure, Programming with Pascal, Programming with C, Advanced Programming with Visual Basic, Microsoft Excel, Microsoft Access, Mathematica, MATLAB, Operations Research, Calculus, Graph Theory, Statistic and Probability. Faculty of Basic Sciences, Islamic Azad University, Tehran, Iran, 1999-2013,
- Microsoft Excel, Microsoft PowerPoint, Microsoft Access, Mathematica, Operations Research, Faculty of Management, University of Tehran, Tehran, Iran, 2001-2011,
- Operations Research, Faculty of Economics, VSB-TU Ostrava, Czech Republic, 2016-2017,
- Statistics for Business, School of Management, University of Turin, Italy, 2018.
- Mathematics for Business and Finance, School of Management, University of Turin, Italy, 2019.
- Mathematics for Business and Finance, Faculty of Business, University of Economics, Prague, Czech Republic, 2019.
- Statistics for Business, Department of Operations Management & Business Statistics, Sultan Qaboos University, Oman, 2020.
- Time Series Forecasting for Business, Department of Operations Management & Business Statistics, Sultan Qaboos University, Oman, 2020
- Applied Optimization Methods, Department of Operations Management & Business Statistics, Sultan Qaboos University, Oman, 2020.
POSTGRADUATE
- Computer Simulation, Fuzzy Sets, Network Flows, Advanced Operations Research, Linear Programming, Integer Programming, Non-Linear Programming, Dynamic Programming, Multi-Criteria Decision Making. Faculty of Basic Sciences, Islamic Azad University, Tehran, Iran, 2005-2013.
- Business Diagnostics, Special Seminar for Diploma Thesis, Faculty of Economics, VSB-TU Ostrava, Czech Republic, 2016-2017.
- Quantitative Methods in Decision Making (QMDM), School of Management, University of Turin, Italy, 2018.
- Special Topics in Operations Management, Sultan Qaboos University, Muscat, Oman, 2020.
- Operational Management, Sultan Qaboos University, Muscat, Oman, 2021.
- Business Modelling and Optimization, Sultan Qaboos University, Muscat, Oman, 2021.
- Operational Analytics, Surrey Business School, University of Surrey, Guildford, UK, 2022.
- Evaluation of Performance and Efficiency (Data Envelopment Analysis), Advanced Linear Programming, Advanced Dynamic Programming, Advanced Non-Linear Programming, Faculty of Basic Sciences, Islamic Azad University, Tehran, Iran, 2010-2013.
- Quantitative Methods of Economic Analysis (QMEA), Faculty of Economics, VSB-TU Ostrava, 2016-present
My publications
Publications
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.
•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.
•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.
•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.
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.
Additional publications
Hatami-Marbini, A., Arabmaldar, Al., Toloo, A., Nehrani, A. M., The price of robustness in non-radial data envelopment analysis models, Expert Systems with Applications, 2022. (Q1, IF 6.954)
Toloo, M., Khodabandelou, R., Oukil, A., A comprehensive bibliometric analysis of Fractional Programming (1965-2020), Mathematics, Vol. 10, 1796, 2022. (Q1, IF 2.258).
Dorfeshan, Y., Taleizadeh, A., Toloo, M., Assessment of risk-sharing ratio with considering budget constraint and disruption risk under a triangular Pythagorean fuzzy environment in public-private partnership projects, Expert Systems with Applications. Vol. 203, 117245, 2022. (Q1, IF 8.665).
Talatahari, A., Azizi, M., Toloo, M., Optimization of large-scale frame structures using fuzzy adaptive quantum inspired charged system search, International Journal of Steel Structures, Vol. 22, 686–707, 2022. (Q4, IF 1.541)
Hatami-marbini, A., Toloo, M., Amini, M., Azar, A., Performance Based-Budgeting Maturity Index: A fuzzy multiple-layer parallel network DEA approach, Expert Systems with Applications, Vol. 200, 116884, 2022. (Q1, IF 6.954)
Toloo, M., Mensah, E.K., Salahi, M., Robust optimization and its duality in data envelopment analysis, OMEGA, Vol. 108, 102583, 2022. (Q1, IF 7.084)
Toloo, M., Taghizadeh Yazdi, M., Mohammadi-Balani, A., Multi-objective centralization-decentralization trade-off analysis for multi-source renewable electricity generation expansion planning: A case study of Iran, Computers & Industrial Engineering, Vol. 164, 107870, 2022. (Q1, IF 5.431)
Kerstens, K., Sadeghi, J., Toloo, M., Van de Woestynex, I., Procedures for Ranking Technical and Cost Efficient Units: With a Focus on Nonconvexity, European Journal of Operational Research, Vol. 300, Issue 1, 269-281, 2022, (Q1, IF 5.334).
Izadikhah, M., Azadi, M., Toloo, M., Khadeer Hussain, F., Sustainably Resilient Supply Chains Evaluation in Public Transport: A Fuzzy Chance-Constrained Two-Stage DEA Approach, Applied Soft Computing, Vol. 113, 107879, 2021, (Q1, IF 6.725)
Wu, X., Ji, Z., Gong, Y., Chen, Y., Toloo, M., Haze emission efficiency assessment and governance for sustainable development based on an improved network data envelopment analysis method, Journal of Cleaner Production, Vol. 317, 128424, 2021 (Q1, IF: 9.239).
Toloo, M., An equivalent linear programming form of general linear fractional programming, A duality approach, Mathematics, Vol. 9, 1586, 2021. (Q1, IF 2.258)
Goodarzian, F., Hoseini-Nasab, H., Toloo, M., Fakhrzad, M. Designing a new Medicine Supply Chain Network considering production technology policy using two novel heuristic algorithms, RAIRO - Operations Research, Vol. 55, Issue 2, 2021. (Q3, IF 1.393)
Talatahari, S., Azizi, M., Toloo, M., Fuzzy Adaptive Charged System Search for Global Optimization, Applied Soft Computing, Vol. 109, 107518, 2021 (Q1, IF 6.725)
Arabmaldar, A., Mensah, E., Toloo, M., Robust worst-practice interval DEA with non-discretionary factors, Expert Systems with Applications, Vol. 182, 115256, 2021. (Q1, IF 6.954)
Toloo, M., Keshavarz, E., Hatami-Marbini, A., An Interval Efficiency Analysis with Dual-Role Factors, OR Spectrum, Vol. 43, 255-287, 2021(Q2, IF 1.274).
Babaee, S., Toloo, M., Hermans, E., Shen, Y., A New Approach for Index Construction: The Case of the Road User Behavior Index, Computers & Industrial Engineering, Vol. 152, 106993, 2021, (Ranked A in ABDC Journal Quality List, IF 4.135).
Toloo, M., Ebrahimi, B., Amin, G.R., New DEA models for classifying flexible measures: the role of non-Archimedean Epsilon, European Journal of Operational Research, Vol. 292, Issue 3, 2021, (Ranked A* in ABDC Journal Quality List, IF 5.334).
Tavana, M., Izadikhah, M., Toloo, M., Roostaee, R., A New Non-Radial Directional Distance Model for Data Envelopment Analysis Problems with Negative and Flexible Measures, OMEGA, Vol. 102, 102355, 2021 (Ranked A in ABDC Journal Quality List, IF 5.324).
Tavana, M., Toloo, M., Aghayi, N., Arabmaldar, A., A Robust Cross-Efficiency Data Envelopment Analysis Model in the Presence of Undesirable Outputs, Expert Systems with Applications, Vol. 167, 114117, 2021. (Q1, IF 5.452).
Kazemi, S., Tavana, M., Toloo, M., Zenkevich, N.A., A Common Weights Model for Investigating Efficiency-Based Leadership in the Russian Banking Industry, RAIRO - Operations Research, Vol. 55, Issue 1, 2021. (Q3, IF 1.393)
Izadikhah, M., Azadi, E., Azadi, M., Farzipoor Saeen, R., Toloo, M., Developing a new chance constrained NDEA model to measure performance of sustainable supply chains, Annals of Operations Research, 2020, in press, (Ranked A in ABDC Journal Quality List, IF 2.583).
Salahi, M., Toloo, M., Torabi, N., A new robust optimization approach to common weights formulation in DEA, Journal of the Operational Research Society, Vol. 72, Issue 6, 1390-1402 2021, (Ranked A in ERA Journal Quality List, IF 1.077).
Keshavarz, E., Toloo, M., A hybrid DEA-MADM approach to sustainability assessment, Expert Systems, Vol. 34, e 12347, 2020. (ISI Journal, IF 1.546).
Ebrahimi, B., Tavana, M., Toloo, M., Charles, V., A Novel Mixed Binary DEA Model for Ranking Decision-Making Units with Preference Information, Computers & Industrial Engineering, Vol. 149, 2020, e106720. (Ranked A in ABDC Journal Quality List, Q1, IF 4.355)
Nemati, M., Kazemi Matin, R., Toloo. M., A Two-stage DEA Model with Partial Impacts between Inputs and Outputs: Application in Refinery Industries, Annals of Operations Research, Vol. 295, 285–312, 2020 (Ranked A in ABDC Journal Quality List, IF 2.583).
Tone, K., Toloo, M., Izadikhak, M., A Modified Slacks-Based Measure of Efficiency in Data Envelopment Analysis, European Journal of Operational Research, Vol. 286, Issue 2, 560-571, 2020, (Ranked A* in ABDC Journal Quality List, IF 4.213).
Toloo, M., Hančlova J., Multi-valued measures in DEA in the presence of undesirable outputs, OMEGA, Vol. 94, 1-10, e102041, 2020. (Ranked A in ABDC Journal Quality List, IF 5.341).
Toloo, M., Keshavarz E., Hatami-Marbini, A., Selecting data envelopment analysis models: A data-driven application to EU countries, OMEGA, Vol. 101,102248, 2020 (Ranked A in ABDC Journal Quality List, IF 5.341).
Ebrahimi, B., Toloo, M., Efficiency bounds and efficiency classifications in imprecise DEA: An extension, Journal of the Operational Research Society, Vol. 71, Issue 3, 491-504, 2020, (Ranked A in ERA Journal Quality List, IF 1.754).
Navas, L. P., Montesa, F., Abolghasem, S., Salas, R. J., Toloo, M., Zaramaa, R., Colombian Higher Education Institutions Evaluation, Socio-Economic Planning Sciences, Vol. 71, 100801, 2020. (Q1, IF 2.196).
Babazadeh, R., Khalili, M., Toloo, M., A data envelopment analysis method for location optimization of microalgae cultivation: A case study, Waste and Biomass Valorization, Vol. 11, 173-186, 2020. (Q2, IF 2.358).
Toloo, M., Mirbolouki, M., A new project selection method using Data Envelopment Analysis, Computers & Industrial Engineering, Vol. 138, 106119, 2019. (Q1, IF 3.195).
Santos Arteaga, F. J., Tavana, M., Di Caprio, D., Toloo, M., A dynamic multi-stage slacks-based measure data envelopment analysis model with knowledge accumulation and technological evolution, European Journal of Operational Research, Vol. 278, No. 2, 448-462, 2019. (Ranked A* in ABDC Journal Quality List, IF 3.297).
Hatami-Marbini, A., Toloo, M., Data Envelopment Analysis Models with Ratio Data: A revisit, Computers & Industrial Engineering, Vol. 133, 331-338, 2019. (Q1, IF 3.195).
Khezrimotlagh, D., Zhu, J., Cook, W.D., Toloo, M., Data Envelopment Analysis and Big Data, European Journal of Operational Research, Vol. 274, No. 3, 1047-1054, 2019. (Ranked A* in ABDC Journal Quality List, IF 3.297).
Salahi, M., Toloo, M., Hesabirad, Z., Robust Russell and Enhanced Russell Measures in DEA, Journal of the Operational Research Society, Vol. 70, No. 8, 1275-1283, 2019, (Ranked A in ERA Journal Quality List, IF 1.077).
Abolghasem, S., Toloo, M., Amézquita, S., Cross-efficiency evaluation in the presence of flexible measures with an application to healthcare systems, Health Care Management Science, Vol. 22, 512–533, 2019 (Q2, IF 1.306).
Amin, G.R., Al-Muharrami, S., Toloo, M., A combined goal programming and inverse DEA method for target setting in mergers, Expert Systems With Applications, Vol. 115, 412-417, 2019 (Q1, IF 3.928).
Toloo, M., Mensah E.K. Robust optimization with nonnegative decision variables: A DEA approach, Computers & Industrial Engineering, Vol. 127, 313-325, 2019 (Q1, IF 3.195).
Toloo, M., Tavana M., Santos-Arteaga, F. J., An Integrated Data Envelopment Analysis and Mixed Integer Non-Linear Programming Model for Linearizing the Common Set of Weights, Central European Journal of Operations Research, Vol. 27, 887-904, 2019. (ISI Journal, IF 0.659).
Jablonský, J., Emrouznejad, A., Toloo, M., Editorial: Special issue on data envelopment analysis, Central European Journal of Operations Research, Vol. 26, 809-812, 2018 (ISI Journal, IF 0.659).
Toloo, M., Nalchigar, S., Sohrabi, B., Selecting most efficient information system projects in presence of user subjective opinions: a DEA approach, Central European Journal of Operations Research, Vol. 26, No. 4, 2018, (ISI Journal, IF 0.659).
Toloo, M., Allahyar M., A simplification generalized returns to scale approach for selecting performance measures in data envelopment analysis, Measurement, Vol. 121, 327-334, 2018. (Q1, IF 2.359).
Mahdiloo, M., Toloo, M., Duong T., Farzipoor Saen R., Tatham, P., Integrated data envelopment analysis: linear vs. nonlinear model, European Journal of Operational Research, Vol. 268, 255-267, 2018. (Ranked A* in ABDC Journal Quality List, IF 3.297).
Toloo, M., Keshavarz E., Hatami-Marbini, A., Dual-Role Factors for Imprecise Data Envelopment Analysis, OMEGA, Vol. 77, 2018, 15–31. (Ranked A* in ABDC Journal Quality List, IF 4.029).
Akhavan Rahnama, A. H., Toloo, M., Zaidenberg, N. J., An LP-based hyperparameter optimization model for language modeling, The Journal of Supercomputing,, Vol. 74, 2151–2160, 2018. (Q2, IF 1.326).
Toloo, M., Salahi, M., A powerful discriminative approach for selecting the most efficient unit in DEA, Computers & Industrial Engineering, Vol. 115, 269-277, 2018. (Q1, IF 3.195).
Toloo, M., Allahyar M., Hančlova J., A non-radial directional distance method on classifying inputs and outputs in DEA Application to banking industry, Expert Systems With Applications, Vol. 92, 495–506, 2018. (Q1, IF 3.928).
Kresta, A., Tichý, T., Toloo, M., Examination of Market Risk Estimation Models via DEA Approach Modelling, Politická ekonomie, Vol. 65, Issue 2, 161-178, 2017. (in Czech Language) (ISI Journal, IF 0.589).
Toloo, M., Emrouznejad, A., Moreno, P., A linear relational DEA model to evaluate two-stage processes with shared inputs, Computational and Applied Mathematics, Vol. 36, 45–61, 2017. (Q2, IF 0.961).
Hatami-Marbini, Toloo, M., An extended multiple criteria data envelopment analysis model, Expert Systems with Applications, Vol. 73, 201-219, 2017. (Q1, IF 3.928).
Salahi, M., Toloo, M., In the determination of the most efficient decision making unit in data envelopment analysis: a comment, Computers & Industrial Engineering, Vol. 104, 216–218, 2017. (Q1, IF 3.195).
Toloo, M., Tavana, M., A Novel Method for Selecting a Single Efficient Unit in Data Envelopment Analysis without Explicit Inputs/Outputs, Annals of Operations Research, Vol. 253, 657–681, 2017, (Ranked A in ABDC Journal Quality List, IF 1.709).
Arabi, B., Munisamy, S., Emrouznejad, A., Toloo, M., Ghazizadeh, M.S., Eco-Efficiency considering the issue of heterogeneity among power plants, Energy, Vol. 111, 722-735, 2016. (Q1, IF 4.25).
Masoumzadeh, A., Toloo, M., Amirteimori, A., Performance assessment in production systems without explicit inputs: An application to basketball players, IMA Journal of Management Mathematics, Vol. 27, 143–156, 2016. (Q2, IF 1.488).
Toloo, M., Jalili, R., LU Decomposition in DEA with an Application to Hospitals, Computational Economics, Vol. 47, 473–488, 2016. (Q2, IF 1.053).
Toloo, M., A Cost Efficiency Approach for Strategic Vendor Selection Problem under Certain Input Prices Assumption, Measurement, Vol. 85, 175–183, 2016. (Q1, IF 2.359).
Toloo, M., Babaee, S., On variable reductions in data envelopment analysis with an illustrative application to a gas company, Applied Mathematics and Computations, Vol. 270, 527–533, 2015. (Ranked A in ERA Journal Quality List, IF 1.738).
Toloo, M., Barat, M., On considering dual-role factor in supplier selection problem, Mathematical Methods of Operations Research, Vol. 82, 107–122, 2015. (Q3, IF 0.762).
Toloo, M., A technical note on 'Erratum to ''Finding the most efficient DMUs in DEA: An improved integrated model'' [Comput. Indus. Eng. 52 (2007) 71-77]', Computers & Industrial Engineering, Vol. 83, 261-263, 2015. (Q1, IF 2.623).
Toloo, M., Zandi, A., Emrouznejad, A., Evaluation efficiency of large-scale data set with negative data: an artificial neural network approach, The Journal of Supercomputing, Vol. 71, 2397–2411, 2015. (Q2, IF 1.326).
Toloo, M., Alternative minimax model for finding the most efficient unit in data envelopment analysis, Computers & Industrial Engineering, Vol. 81, 186-194, 2015. (Q1, IF 3.195).
Toloo, M., Tichy, T., Two alternative approaches for selecting performance measures in data envelopment analysis, Measurement, Vol. 65, 29-40, 2015. (Q1, IF 2.359).
Toloo, M., Masoumzadeh, A., Barat, M., Finding an initial basic feasible solution for DEA models with an application on bank industry, Computational Economics, Vol. 45, Issues 2, 323-326, 2015. (Q2, IF 1.053)
Keshavarz, E., Toloo, M., Efficiency status of a feasible solution in the Multi-Objective Integer Linear programming problems: A DEA methodology, Applied Mathematical Modelling, Vol. 39, 3236–3247, 2015. (Q1, IF 2.617).
Toloo, M., Barat, M., Masoumzadeh, A., Selective measures in data envelopment analysis, Annals of Operations Research, Vol. 226, 523-642, 2015. (Ranked A in ABDC Journal Quality List, IF 1.709)
Toloo, M., Farzipoor, R., Azadi, M., Obviating some of the theoretical barriers of data envelopment analysis discriminant analysis (DEA-DA): an application in predicting cluster membership of customers, Journal of the Operational Research Society, Vol. 66, Issue 4, 674–683, 2015. (Ranked A in ERA Journal Quality List, IF 1.077).
Keshavarz, E., Toloo, M., Finding efficient assignments: An innovative DEA approach, Measurement, Vol. 58, 448–458, 2014. (Q1, IF 2.218).
Toloo, M., Selecting and full ranking suppliers with imprecise data: A new DEA method, International Journal of Advanced Manufacturing Technology, Vol. 74, Issues 5-8, 1141-1148, 2014. (Q2, IF 2.209).
Toloo, M., Kresta, A., Finding the best asset financing alternative: A DEA-WEO approach, Measurement, Vol. 55, 288-294, 2014. (Q1, IF 2.218).
Toloo, M., The role of non-Archimedean epsilon in finding the most efficient unit: with an application of professional tennis players, Applied Mathematical Modelling, Vol. 38, Issues 21-22, 5334-5346, 2014. (Q1, IF 2.617).
Toloo, M., Ertay, T., The most cost efficient automotive vendor with price uncertainty: A new DEA approach, Measurement, Vol. 52, 135-144, 2014. (Q1, IF 2.218).
Toloo, M., Notes on classifying inputs and outputs in data envelopment analysis: a comment, European Journal of Operational Research, Vol. 235, Issue 3, 810-812, 2014. (Ranked A* in ABDC Journal Quality List, IF 3.297).
Toloo, M., An Epsilon-free Approach for Finding the Most Efficient Unit in DEA, Applied Mathematical Modelling, Vol. 38, Issue. 13, 3182-3192, 2014. (Q1, IF 2.617).
Toloo, M., The most efficient unit without explicit inputs: An extended MILP-DEA model, Measurement, Vol. 46, Issue 9, 3628–3634, 2013. (Q1, IF 2.359).
Toloo, M., Alternative solutions for classifying inputs and outputs in data envelopment analysis, Computers and Mathematics with Application, Vol. 63, Issue 6, 1104–1110, 2012. (Q1, IF 1.531).
Toloo, M., On finding the most BCC-efficient DMU: A new integrated MIP-DEA model, Applied Mathematical Modelling, Vol. 36, Issue 11, 5515–5520, 2012. (Q1, IF 2.617).
Toloo, M., Nalchigar, S., A New Integrated DEA Model for Supplier Selection in Presence of both Cardinal and Ordinal Data, Expert Systems with Applications, Vol. 38, Issue. 12, 14726–14731, 2011. (Q1, IF 3.928).
Amin, G.R., Toloo, M., Sheikhan, M., Input and output scaling in advanced manufacturing technology: theory and application, International Journal of Advanced Manufacturing Technology, Vol. 50, Issue 9-12, 1235–1241, 2010. (Q2, IF 2.209).
Toloo, M., Sohrabi, B., Nalchigar, S., A New Method for Ranking Discovered Rules from Data Mining by DEA, Expert Systems with Applications, Vol. 36, Issue 4, 8503–8508, 2009. (Q1, IF 3.928).
Toloo, M., On classifying inputs and outputs in DEA: A revised model, European Journal of Operational Research, Vol. 198, Issue 1, 358–360, 2009. (Ranked A* in ABDC Journal Quality List, IF 3.297).
Toloo, M., Nalchigar, S., A new integrated DEA model for finding most BCC-efficient DMU, Applied Mathematical Modelling, Vol. 33, Issue 1, 597–604, 2009. (Q1, IF 2.617).
Toloo, M., Aghayi, N., Rostamy-Malkhalifeh, M., Measuring overall profit efficiency with interval data, Applied Mathematics & Computations, Vol. 201, Issue 1-2, 640–649, 2008. (Ranked A in ERA Journal Quality List, IF 1.738).
Amin, G.R., Toloo, M., Finding the most efficient DMUs in DEA: An improved integrated model, Computers & Industrial Engineering, Vol. 52, Issue 1, 71-77, 2007. This paper is introduced as one of the 25 hot top articles. (Q1, IF 3.195).
Amin, G.R., Toloo, M., Sohrabi, B., An Improved MCDM DEA Model to Technology Selection, International Journal of Production Research, Vol. 44, Issue 13, 2681-2686, 2006. (Ranked A in ABDC Journal Quality List, IF 2.325).
Toloo, M., Comment on A Comparison to Parametric and Non-Parametric Distance Functions, European Journal of Operational Research, Vol. 171, Issue 1, 344-345, 2006. (Ranked A* in ABDC Journal Quality List, IF 3.297).
Amin, G.R., Toloo, M., A Polynomial-time Algorithm for Determining the Non-Archimedean Epsilon in DEA models, Computers & Operations Research, Vol. 31, Issue 5, 803-805, 2004. (Ranked A in ERA Journal Quality List, IF 2.6).