Mathematical Optimization Models
Ali Abdi; Seyed Hadi Nasseri
Abstract
Purpose: One of the fundamental problems in the field of supply chain management is the problem of supply chain design. In this problem, the goal is to determine the location for establishing a number of facilities in different geographical areas to cover the demands of customers.
Methodology: In this ...
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Purpose: One of the fundamental problems in the field of supply chain management is the problem of supply chain design. In this problem, the goal is to determine the location for establishing a number of facilities in different geographical areas to cover the demands of customers.
Methodology: In this problem, the static and dynamic network is considered. Suppose the network is static, with the help of the iterated local search algorithm. In that case, the number and location of distribution centers are determined, and customers are assigned to each distribution center. If the network is dynamic, after determining the initial number and location of distribution centers and assigning customers to distribution centers, events related to network dynamics, such as customer decrease, customer increase, and variable size of demands, are investigated by customers. In addition, our proposed method considers the failure modes of network components. Also, the ability to survive the network can be seen in both network modes.
Findings: The results obtained from the experiments were analyzed in terms of evaluation criteria. The results of the experiments show the superiority of the proposed method compared to the CLSC and TSCFL methods.
Originality/Value: By studying the related works in the past in locating facilities in the supply chain network, attention to the design of a multi-level supply chain and the problem of finding facilities has yet to be considered. In addition, facility dynamics and network survivability are not considered at the time of failure. Therefore, in this research, we have tried to reduce the cost by choosing the appropriate location of facilities and assigning customers to each of these facilities. Also, we will design the network so that it can be in a stable state and continue to operate when a network failure occurs.
Mathematical Optimization Models
Fatemeh nikkhoo; Ali Husseinzadeh Kashan; ehsan nikbakhsh; bakhtiar ostadi
Abstract
Purpose: The order picking problem is very important as one of the logistics activities of the warehouse. This problem is defined as collecting orders from different warehouse locations to respond to customers' orders in the shortest possible time. The purpose of this paper is to provide a multi-objective ...
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Purpose: The order picking problem is very important as one of the logistics activities of the warehouse. This problem is defined as collecting orders from different warehouse locations to respond to customers' orders in the shortest possible time. The purpose of this paper is to provide a multi-objective mathematical programming model for integrating the decisions of batching, routing, scheduling of pickers with the problem of packaging in multi-warehouse environment. The objective functions include minimization of the delivery times and total order picking costs.
Methodology: In this research, first by reviewing the literature in the field of order picking, the research gaps of the problem have been identified. Then, taking into account the main constraints of the problem, a multi-objective mathematical model has been formulated for the multi-warehouse order picking problem. To solve the problem, the classic Benders decomposition algorithm and the accelerated Benders decomposition algorithm have been used. To validate and applicability of the proposed model, the data related to the warehouses of a company producing sanitary products in Iran was used as a case study and its results were reported in the article.
Findings: The results of the proposed model indicate that CPLEX is able to solve these problems up to small sizes in an acceptable time. Also, the numerical results show the performance of the Benders decomposition algorithm and the accelerated Benders algorithm as suitable alternatives for solving the model in the large-sized problems. The calculation results obtained from the implementation of the solution methods for the proposed model showed that in terms of the number of iterations and the calculation time, the accelerated Benders algorithm had better results than the classic Benders algorithm.
Originality/Value: In this research, for the first time, the order picking problem with considerations of the integrity of operational decisions has been formulated in the form of a multi-objective mathematical model for a multi-warehouse environment. In this article regarding the solution method, exact solution approaches have been used for the first time considering the structure of the problem. The computation results show that the proposed algorithms are efficient and suitable methods for problem solving.
Mathematical Optimization Models
Elham Basiri
Abstract
Purpose: In this paper, the amount required to increase the reliability of the components of a coherent system is determined so that the cost of this increase is minimized and the reliability of the whole system is not less than the predetermined value.Methodology: In this research, after introducing ...
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Purpose: In this paper, the amount required to increase the reliability of the components of a coherent system is determined so that the cost of this increase is minimized and the reliability of the whole system is not less than the predetermined value.Methodology: In this research, after introducing the objective and constraint functions in the optimization problem, the Lagrange method is used and then the problem is solved by presenting an algorithm. In this article, several cost functions are considered, and then the results are presented in the general case for a coherent system and then for two special cases, series-parallel and parallel-series systems.Findings: In this article, two numerical examples are presented and solved. In the first example, a bridge structure is evaluated and in the second example, a series-parallel system is studied. In both examples, the required values are determined to increase the reliability of the system components.Originality/Value: This research, using a mathematical model and numerical calculations with the help of R software, examines the optimization problem for a coherent system.
Mathematical Optimization Models
Najme Esmaeil Darjani; Ahmad Assadzadeh; Mohamad Mehdi Barghi Oskoei
Abstract
Purpose: Most tax policies are based on how taxpayers make decisions based on classical economic models. However, studies show that conventional decision-making models, which are designed without socio-psychological foundations and based only on economic components, can not explain the developments and ...
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Purpose: Most tax policies are based on how taxpayers make decisions based on classical economic models. However, studies show that conventional decision-making models, which are designed without socio-psychological foundations and based only on economic components, can not explain the developments and the exact way decision-makers work. Considering that the issue of preventing tax evasion by taxpayers is very important and necessary, in this study, using mathematical modeling and scenario making tools to calculate tax crimes, the theory of behavioral economics and the theory of expected desirability have been compared.Methodology: In this research, using mathematical modeling tools and a questionnaire to calculate tax crimes, the theory of behavioral economics and the theory of expected desirability have been compared.Findings: The results indicate that the amount of crimes calculated in the theory of behavioral economics is closer to crimes in the real world. Therefore, the obtained results are a good justification for choosing the theory of perspective instead of the theory of expected utility, and by adding the parameter of tax ethics, the amount of tax penalty in both theories is reduced.Originality/Value: Since a healthy economy is an economy that is mostly based on taxes and has tried to cover government expenditures through taxes. To achieve this, the country's tax system must be reformed.
Mathematical Optimization Models
Leila Torkzadeh
Abstract
Purpose: Providing an analytical approach to minimize risk to a situation that traders deal with model risk, as a financial risk arises by choosing an approximation model, for the underlying securities status in financial estimates.Methodology: Improving the standard binomial pricing model and using ...
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Purpose: Providing an analytical approach to minimize risk to a situation that traders deal with model risk, as a financial risk arises by choosing an approximation model, for the underlying securities status in financial estimates.Methodology: Improving the standard binomial pricing model and using the equivalence portfolio mechanism in a particular incomplete market situation which traders are uncertain about the actual status space of the stock binomial process.Findings: From a research aspect, a model of approximation was provided and generalized with different hypotheses that minimizes the risk of the model for pricing call options. From an applied practical aspect, the results give to financial institutions the outlook to predict a mechanism to moderate excessive volatilities in the markets related to options.Originality/Value: The study of the model risk is performed by maintaining the simple framework and elegance of the binomial model and then it is proved that by defining the optimality in the sense of minimum mean-square errors, the choice of an optimal approximation model is possible. In addition, the implementation and efficiency of the method for the multi-period model are explained.
Mathematical Optimization Models
Hassan Rashidi
Abstract
Many of the world's top universities have already decided to hold the next semester with e-education. In our country, the forecasts show a red situation for some areas in terms of the prevalence of corona. Also, a number of university students are living in these areas. Therefore, in the planning of ...
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Many of the world's top universities have already decided to hold the next semester with e-education. In our country, the forecasts show a red situation for some areas in terms of the prevalence of corona. Also, a number of university students are living in these areas. Therefore, in the planning of the next semester, more attention should be paid to e-education. It is recommended that the next semester be implemented in two parts, including e-education for 10 weeks and face-to-face training for 3 weeks. In face-to-face training with the needs of the educational and dormitory space, students are divided into two sub-categories (A) and (B) so that it is possible to implement health protocols in universities and dormitories. In this paper, to determine the number of male and female students accommodated in dormitories for both subcategories (A) and (B) in face-to-face training, a mathematical optimization model is proposed in the form of nonlinear programming with integer decision variables. In the objective function of the model, the distribution of students in the educational space and dormitories is done in such a way that it has the maximum possible dispersion (minimum difference), due to the prevention of the spread of corona disease. This model has been implemented for the allocation of student dormitories at Allameh Tabatabai University, and its use can bring positive results for decision makers.