Optimization & Operations Research
Mohamed Kouadria; Halim Zeghdoudi; Mohammed El-Arbi Khalfallah
Abstract
This study proposes the New Two-Parameter Weibull–Lindley Distribution (NTPWLD), a flexible lifetime model generated through a transformation of a one-parameter baseline survival function. Owing to its general structure, the NTPWLD accommodates diverse hazard rate shapes, including increasing, ...
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This study proposes the New Two-Parameter Weibull–Lindley Distribution (NTPWLD), a flexible lifetime model generated through a transformation of a one-parameter baseline survival function. Owing to its general structure, the NTPWLD accommodates diverse hazard rate shapes, including increasing, decreasing, and bathtub forms, and captures both light- and heavy-tailed behaviors relevant to survival analysis, engineering reliability, and biomedical applications. The work provides a full mathematical treatment of the distribution, deriving closed-form expressions for its density, distribution, survival, hazard, and quantile functions, along with ordinary and incomplete moments, the moment generating function, mean deviations, and Rényi entropy. Several reliability measures, such as mean residual life and stress–strength reliability, are also obtained. Parameter estimation is examined under various inferential approaches, with particular focus on maximum likelihood estimation. A Monte Carlo simulation study shows that the maximum likelihood estimator performs well across settings, displaying low bias, stability, and consistency. To incorporate uncertainty in lifetime data, fuzzy reliability measures are constructed using Zadeh’s extension principle and α-cut techniques. Applications to two real datasets demonstrate that the NTPWLD provides superior goodness-of-fit compared with several competing models based on AIC, BIC, AICC, and −2 log L, highlighting its practical value in both precise and fuzzy reliability environments.
Optimization & Operations Research
Jafar Pourmahmoud; Ahad Abbasi; Alireza Ghaffari-Hadigheh
Abstract
Data Envelopment Analysis (DEA) is a well-established methodology for assessing the efficiency of decision-making units. In complex systems comprising multiple interconnected subsections, Network DEA provides a structured framework for efficiency evaluation. However, ...
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Data Envelopment Analysis (DEA) is a well-established methodology for assessing the efficiency of decision-making units. In complex systems comprising multiple interconnected subsections, Network DEA provides a structured framework for efficiency evaluation. However, traditional DEA models rely on the assumption of deterministic data, which inadequately reflects the inherent uncertainty present in real-world scenarios. Traditional uncertainty-handling methods, such as fuzzy logic, stochastic models, and interval-based techniques, often fail when there is limited historical data and when expert opinions significantly influence the dataset. To address these limitations, this study introduces an uncertain network DEA model based on Liu’s uncertainty theory, facilitating a more accurate assessment of efficiency under conditions of data imprecision. The proposed model is designed for three interconnected subsections and is further extended into a generalized multi-stage framework, allowing it to adapt to increasingly complex systems. Its effectiveness and practical applicability are demonstrated through two numerical case studies in the banking industry, highlighting its capacity to support decision-making under uncertainty. The findings emphasize the model's potential to enhance efficiency evaluation methods, particularly in environments characterized by limited and uncertain data.
Optimization & Operations Research
Gassan A.M.O. Farah; Abdulaziz Mukhtar; Kailash C. Patidar
Abstract
Malaria continues to represent a significant public health concern in Sudan, with cases rising over 40% from 2015 to 2020. This research investigates how climate change affects malaria transmission patterns using a mathematical model in an ordinary differential equation framework. ...
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Malaria continues to represent a significant public health concern in Sudan, with cases rising over 40% from 2015 to 2020. This research investigates how climate change affects malaria transmission patterns using a mathematical model in an ordinary differential equation framework. The analysis involves calculating the basic reproduction number and evaluating the system's qualitative properties to gain insights into disease dynamics. Additionally, a sensitivity analysis is conducted to evaluate how climatic conditions, e.g., rainfall and temperature, influence key model parameters. Statistical approaches are utilized to estimate parameters and calibrate the model using empirical data from Sudan, ensuring consistency between the model and observed trends. Numerical simulations demonstrate the growing influence of climate variability on the spatial distribution of malaria vectors and the transmission progression over time. The study establishes a strong association between climatic changes and the exacerbation of malaria prevalence in Sudan. These findings emphasize the urgent need for climate-adaptive strategies, including improved vector control, strengthened surveillance systems, and climate-resilient public health interventions, to address the increased risks posed by changing environmental conditions. The research provides valuable insights to inform evidence-based policies aimed at reducing malaria transmission in Sudan and other regions that are experiencing similar challenges due to climate change.
Optimization & Operations Research
Narjes Amiri; Hadi Nasseri; Davood Darvishi Salokolaei
Abstract
This paper explores a specific category of optimization management models tailored for wireless communication systems. To enhance the efficiency of managing these systems, we introduce a fuzzy relation multi-objective programming approach. We define the concept of a feasible ...
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This paper explores a specific category of optimization management models tailored for wireless communication systems. To enhance the efficiency of managing these systems, we introduce a fuzzy relation multi-objective programming approach. We define the concept of a feasible index set and present a novel algorithm, termed the feasible index set algorithm, which is designed to determine the optimal lexicographic solution to the problem, demonstrating polynomial computational complexity. Previous studies have indicated that the emission base stations within wireless communication systems can be effectively modeled using a series of fuzzy relation inequalities through max-product composition. This topic is also addressed in our paper. Wireless communication is widely employed across various sectors, encompassing mobile communication and data transmission. In this framework, information is transmitted via electromagnetic waves generated by fixed emission base stations.
Optimization & Operations Research
Narges Hosseinzadeh; Elyas Shivanian; Saeid Abbasbandy
Abstract
This study employs the radial basis function-generated finite difference (RBF-FD) method to address high-dimensional elliptic differential equations under Dirichlet boundary conditions. The method utilizes polyharmonic spline functions (PHSs) combined with polynomials for approximation. ...
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This study employs the radial basis function-generated finite difference (RBF-FD) method to address high-dimensional elliptic differential equations under Dirichlet boundary conditions. The method utilizes polyharmonic spline functions (PHSs) combined with polynomials for approximation. A notable benefit of this approach is that PHSs do not require a shape parameter, simplifying implementation and enhancing numerical stability. The proposed method offers several advantages, including high accuracy, rapid computation, and adaptability to complex geometries and irregular node arrangements. It is particularly effective for high-dimensional problems, providing a mesh-free alternative that scales efficiently with increased complexity. Beyond scientific computing, the method is also applied to financial option pricing, where integro-differential equations are transformed into a series of second-order elliptic partial differential equations (PDEs). Numerical experiments demonstrate that the proposed algorithm significantly outperforms existing RBF-based approaches in both accuracy and efficiency. These strengths make it a robust tool for solving a wide range of PDEs in both regular and irregular domains.
Optimization & Operations Research
Ahmad Sharif
Abstract
In this study, we explore soliton solutions for the conformable time-fractional Boussinesq equation utilizing the three-wave method. To validate the precision of our findings, we discuss specific special cases by adjusting certain potential parameters and also present the ...
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In this study, we explore soliton solutions for the conformable time-fractional Boussinesq equation utilizing the three-wave method. To validate the precision of our findings, we discuss specific special cases by adjusting certain potential parameters and also present the graphical representations of our results. The results achieved in this research align closely with those from previous studies, demonstrating enhanced accuracy and simplicity. Given the extensive applications of this equation in particle physics, understanding its dynamics is crucial. Consequently, employing methods that encompass a broad spectrum of solutions is imperative. The versatility of this method in yielding diverse solutions is evident in the results we have obtained. The solutions derived in this paper are novel and offer greater precision compared to previous works.
Optimization & Operations Research
Reza Akbari; Leader Navaei; Mohammad Shahriari
Abstract
This paper presents an extension of the SEIR mathematical model for infectious disease transmission to a fractional-order model. The model is formulated using the Caputo derivative of order α ∈ (0, 1]. We study the stability of equilibrium points, including ...
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This paper presents an extension of the SEIR mathematical model for infectious disease transmission to a fractional-order model. The model is formulated using the Caputo derivative of order α ∈ (0, 1]. We study the stability of equilibrium points, including the disease-free equilibrium $(E_{f})$, and the infected steady-state equilibrium $(E_{e})$ using the stability theorem of Fractional Differential Equations. The model is also analyzed under certain conditions, and it is shown that the disease-free equilibrium is locally asymptotically stable. Additionally, the extended Barbalat’s lemma is applied to the fractional-order system, and a suitable Lyapunov functional is constructed to demonstrate the global asymptotic stability of the infected steady-state equilibrium. To validate the theoretical results, a numerical simulation of the problem is conducted.
Optimization & Operations Research
Sajad Amirian; Maghsoud Amiri; Mohammad Taghi Taghavifard
Abstract
Integrating sustainability and reliability represents a synergistic approach that can be explored through the problem of a closed-loop supply chain network design (SCND). This study is conducted in three stages: mathematical modeling, model solution using exact methods, ...
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Integrating sustainability and reliability represents a synergistic approach that can be explored through the problem of a closed-loop supply chain network design (SCND). This study is conducted in three stages: mathematical modeling, model solution using exact methods, and evaluation of the solution methods. In the first stage, a mixed-integer linear programming (MILP) model is developed in a multi-objective, multi-product, and multi-period framework. The objectives of the proposed model aim to maximize profitability, social responsibility, and reliability. In the second stage, two methods, namely Augmented $\varepsilon$-Constraint (AEC) and Normalized Normal Constraint (NNC), are implemented in the GAMS software to solve the model and identify the optimal Pareto solutions. In the third stage, the Shannon Entropy technique is employed to determine the criteria weights, and the VIKOR technique is utilized to select the superior solution method. The overall performance accuracy of the proposed model is measured using four samples from a numerical example with randomly generated data based on the objective function coefficients. The results indicate the presence of a conflict among the three objective functions. Consequently, decision-makers should consider sacrificing some profitability to enhance environmental protection and improve reliability. In terms of three criteria, run time, diversification metric, and general distance, the NNC method is given priority over the AEC method. Even when the criteria are given equal weight, the superiority of the NNC method remains unchanged. The application of the proposed model across different industries represents a significant research direction for future research.
Optimization & Operations Research
Zahra Abbasi; Nasser Akhoundi
Abstract
Product reviews in E-commerce websites such as restaurants, movies, E-commerce products, etc., are essential resources for consumers to make purchasing decisions on various items. In this paper, we model discovering groups with maximum descriptively ...
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Product reviews in E-commerce websites such as restaurants, movies, E-commerce products, etc., are essential resources for consumers to make purchasing decisions on various items. In this paper, we model discovering groups with maximum descriptively from E-commerce website of the form $<i,u,s>$, where $i\in \mathcal{I}$ (the set of items or products), $u\in \mathcal{U}$ (the set of users) and $s$ is the integer rating that user $u$ has assigned to the item $i$. Labeled groups from user's attributes are found by solving an optimization problem. The performance of the approach is examined by some experiments on real data-sets.
Optimization & Operations Research
Davood Darvishi Salookolaei; Sifeng Liu; Parvin Babaei
Volume 2, Issue 2 , December 2017, , Pages 15-32
Abstract
Considering the fact that Iran is situated in an arid and semi-arid region, rainfall prediction for the management of water resources is very important and necessary. Researchers have proposed various prediction methods that have been utilized in such areas as water and meteorology, especially water ...
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Considering the fact that Iran is situated in an arid and semi-arid region, rainfall prediction for the management of water resources is very important and necessary. Researchers have proposed various prediction methods that have been utilized in such areas as water and meteorology, especially water resources management. The present study aimed at predicting rainfall amounts using Grey Prediction Method. It is a novel approach in confrontation with uncertainties in the aquiferous region of Babolrud to serve for the water resources management purposes. Therefore, expressing the concepts of Grey Prediction Methods using the collected data, at a 12-year timeframe of 2006 and 2017, rainfall prediction in 2018 and 2022 were also implemented with three methods GM(1,1), DGM(2,1) and Verhulest models. According to the calculated error and the predictive power, GM(1,1) method is better than other models and was placed within the set of good predictions. Also, we predict that in 2027, there might be a drought. According to the small samples and calculations required in this approach, the method is suggested for rainfall prediction in inexact environments. The authors can use fuzzy grey systems to predict the amount of rainfall in uncertaint environments.
Optimization & Operations Research
Siyamak Firouzian; Mohamad Adabitabar Firozja
Volume 1, Issue 2 , October 2016, , Pages 77-86
Abstract
Graph theory has an important role in the area of applications of networks and clustering. In the case of dealing with uncertain data, we must utilize ambiguous data such as fuzzy value, fuzzy interval value or values of fuzzy number. In this study, values ...
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Graph theory has an important role in the area of applications of networks and clustering. In the case of dealing with uncertain data, we must utilize ambiguous data such as fuzzy value, fuzzy interval value or values of fuzzy number. In this study, values of fuzzy number were used. Initially, we utilized the fuzzy number value fuzzy relation and then proposed fuzzy number-value fuzzy graph on nodes and arcs. In this study, some properties of the graph on fuzzy number-value fuzzy graph were examined. First, we define the Cartesian product, composition, union and join operators on fuzzy number-value fuzzy graphs and then prove some of their properties and and give some examples for every one of definitions. We also introduced the notion of homomorphism, weak isomorphism,weak co-isomorphism, isomorphism, complete, weak complete and compliment on the fuzzy number fuzzy graphs and prove some of their properties and also present some examples for every one of them.
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