Dr Mehdi Toloo

Senior Lecturer in Business Analytics
BSc, MSc, PhD, docent
+44 (0)1483 683642
21 MS 02



Research interests

Research projects

Research collaborations


Postgraduate research supervision

My teaching

My publications


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.

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.

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.

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, 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.

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