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A multi-periodic, multi-echelon green supply chain network consisting of manufacturing plants, potential distribution centers, and customers is developed. The manufacturing plants can provide the products in three modes including production in regular time, production in over time, or by subcontracting. The problem has three objectives including minimization of the total costs of the green supply chain network, maximization of the average safe inventory levels of the manufacturing plants and the distribution centers and minimization of the environmental impacts of the manufacturing plants in producing, holding and dispatching the products and also the environmental impacts of the distribution centers in holding and dispatching the products. The problem is first formulated as a mixed-integer mathematical model. Then, in order to solve the model, the augmented weighted Tchebycheff method is employed and its performance in producing the Pareto optimal solutions is compared with the goal attainment method.

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Over five decades have passed since the first wave of robust optimization studies conducted by Soyster and Falk. It is outstanding that real-life applications of robust optimization are still swept aside; there is much more potential for investigating the exact nature of uncertainties to obtain intelligent robust models. For this purpose, in this study, we investigate a more refined description of the uncertain events including (1) event-driven and (2) attribute-driven. Classical methods transform convex programming classes of uncertainty sets. The structural properties of uncertain events are analyzed to obtain a more refined description of the uncertainty polytopes. Hence, tractable robust models with a decent degree of conservatism are introduced to avoid the over-protection induced by classical uncertainty sets.

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We present a stochastic dynamic programming approach with Markov chains for optimal control of the forest sector. The forest is managed via continuous cover forestry and the complete system is sustainable. Forest industry production, logistic solutions and harvest levels are optimized based on the sequentially revealed states of the markets. Adaptive full system optimization is necessary for consistent results. The stochastic dynamic programming problem of the complete forest industry sector is solved. The raw material stock levels and the product prices are state variables. In each state and at each stage, a quadratic programming profit maximization problem is solved, as a subproblem within the STDP algorithm.

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Clustering problems with the similarity measure defined by the $𝐿_1$-norm are studied. Characterizations of different stationary points of these problems are given using their difference of convex representations. An algorithm for finding the Clarke stationary points of the clustering problems is designed and a clustering algorithm is developed based on it. The clustering algorithm finds a center of a data set at the first iteration and gradually adds one cluster center at each consecutive iteration. The proposed algorithm is tested using large real world data sets and compared with other clustering algorithms.

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In many problems, it is necessary to take into account monotonic relations. Monotonic (isotonic) Regression (MR) is often involved in solving such problems. The MR solutions are of a step-shaped form with a typical sharp change of values between adjacent steps. This, in some applications, is regarded as a disadvantage. We recently introduced a Smoothed MR (SMR) problem which is obtained from the MR by adding a regularization penalty term. The SMR is aimed at smoothing the aforementioned sharp change. Moreover, its solution has a far less pronounced step-structure, if at all available. The purpose of this paper is to further improve the SMR solution by getting rid of such a structure. This is achieved by introducing a lowed bound on the slope in the SMR. We call it Smoothed Slope-Constrained MR (SSCMR) problem. It is shown here how to reduce it to the SMR which is a convex quadratic optimization problem. The Smoothed Pool Adjacent Violators (SPAV) algorithm developed in our recent publications for solving the SMR problem is adapted here to solving the SSCMR problem. This algorithm belongs to the class of dual active-set algorithms. Although the complexity of the SPAV algorithm is $𝑂(𝑛^2)$, its running time is growing in our computational experiments almost linearly with $𝑛$. We present numerical results which illustrate the predictive performance quality of our approach. They also show that the SSCMR solution is free of the undesirable features of the MR and SMR solutions.

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Many regions in the world are protected against flooding by a dike, which may be either natural or artificial. We deal with a model for finding the optimal heights of such a dike in the future. It minimizes the sum of the investments costs for upgrading the dike in the future and the expected costs due to flooding. The model is highly nonlinear, nonconvex, and infinite-dimensional. Despite this, the model can be solved analytically if there is no backlog in maintenance. If there is a backlog in maintenance, then the optimal solution can be found by minimizing a convex function over a finite interval. However, if the backlog becomes extremely large we show that the model breaks down. Our model has been used in The Netherlands to define legal safety standards for the coming decades.

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Linear programming problems with interval grey numbers have recently attracted some interest. In this paper, we study linear programs in which right hand sides are interval grey numbers. This model is relevant when uncertain and inaccurate factors make difficult the assignment of a single value to each right hand side. Some methods have been developed for solving these problems. In this paper, we propose a new approach for solving interval grey number linear programming problems is introduced without converting them to classical linear programming problems. A numerical example is provided to illustrate the proposed approach.

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This contribution gathers some of the ingredients presented during the Iranian Operational Research community gathering in Babolsar in 2019.It is a collection of several previous publications on how to set up an uncertainty quantification (UQ) cascade with ingredients of growing computational complexity for both forward and reverse uncertainty propagation.

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Here, scalarization techniques for multi-objective optimization problems are addressed. A new scalarization approach, called unified Pascoletti-Serafini approach, is utilized and a new algorithm to construct the Pareto front of a given bi-objective optimization problem is formulated. It is shown that we can restrict the parameters of the scalarized problem. The computed efficient points provide a nearly equidistant approximation of the whole Pareto front. The performance of the proposed algorithm is illustrated by various test problems and its effectiveness with respect to some existing methods is shown.

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Here, we investigate the classical p-median location problem on a network in which the vertex weights and the distances between vertices are uncertain. We propose a programming model for the uncertain p-median location problem with tail value at risk objective. Then, we show that it is NP-hard. Therefore, a novel hybrid modified binary particle swarm optimization algorithm is presented to obtain the approximate optimal solution of the proposed model. The algorithm contains the tail value at risk simulation and the expected value simulation. Finally, by computational experiments, the algorithm is illustrated to be efficient.

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Ant colony optimization (ACOR) is a meta-heuristic algorithm for solving continuous optimization
problems (MOPs). In the last decades, some improved versions of ACOR have been proposed.
The UACOR is a unified version of ACOR that is designed for continuous domains. By adjusting
some specified components of the UACOR, some new versions of ACOR can be deduced. By doing
that, it becomes more practical for different types of MOPs. Based on the nature of meta-heuristic
algorithms, the performance of meta-heuristic algorithms are depends on the exploitation and
exploration, which are known as the two useful factors to generate solutions with different
qualities. Since all the meta-heuristic algorithms with random parameters use the probability
functions to generate the random numbers and as a result, there is no any control over the
amount of diversity; hence in this paper, by using the best parameters of UACOR and making
some other changes, we propose a new version of ACOR to increase the efficiency of UACOR.
These changes include using chaotic sequences to generate various random sequences and also
using a new local search to increase the quality of the solution. The proposed algorithm, the two
standard versions of UACOR and the genetic algorithm are tested on the CEC05 benchmark
functions, and then numerical results are reported. Furthermore, we apply these four algorithms
to solve the utilization of complex multi-reservoir systems, the three-reservoir system of Karkheh
dam, as a case study. The numerical results confirm the superiority of proposed algorithm over
the three other algorithms.
 

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The hub location and revenue management problem are two research topics in the field of network design and transportation. The hub location model designs the structure of the transportation network, while the revenue management model allocates network capacity to different customer categories according to their price sensitivity. Revenue management determines which products to sell to which customers and at what price. On the other hand, due to the limited number of aircraft seats, the revenue management problem has been widely used in the aviation industry. In this study, a robust optimization model is developed for the hub location and revenue management problem. For this purpose, a real-world case study with a central hub and six airports is presented and solved using CPLEX solver in GAMS software. Finally, a sensitivity analysis was performed on the key parameters of the problem, and their effect on the objective functions of the problem was investigated. Results show that the proposed model achieved the feasible solution in reasonable time for real case problem by exact method.

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Location theory is one of the most important topics in optimization and operations research. In location problems, the goal is to find the location of one or more facilities in a way such that some criteria such as transportation costs, customer traveling distance, total service time, and cost of servicing are optimized. In this paper, we investigate the goal Weber location problem in which the location of a number of demand points on a plane is given, and the ideal is locating the facility in the distance Ri , from the i-th demand point. However, in most instances, the solution of this problem does not exist. Therefore, the minimizing sum of errors is considered. The goal Weber location problem with the lp  norm is solved using the stochastic version of the LBFGS method, which is a second-order limited memory method for minimizing large-scale problems. According to the obtained numerical results, this algorithm achieves a lower optimal value in less time with comparing to other common and popular stochastic optimization algorithms. Note that although the investigated problem is not strongly convex, the numerical results show that the SLBFGS algorithm performs very well even for this type of problem.
 

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In this paper, we present a new primal-dual predictor-corrector interior-point algorithm for linear optimization problems. In each iteration of this algorithm, we use the new wide neighborhood proposed by Darvay and Takács. Our algorithm computes the predictor direction, then the predictor direction is used to obtain the corrector direction. We show that the duality gap reduces in both predictor and corrector steps. Moreover, we conclude that the complexity bound of this algorithm coincides with the best-known complexity bound obtained for small neighborhood algorithms. Eventually, numerical results show the capability and efficiency of the proposed algorithm.

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This study aims to develop a capacitated hub location-routing model to design a rapid transit network under uncertainty. The mathematical model is formulated by making decisions about the location of the hub and spoke (non-hub) nodes, the selection of the hub and spoke edges, the allocation of the spoke nodes to the hub nodes, the determination of the hub and spoke lines, the determination of the percentage of satisfied origin-destination demands, and the routing of satisfied demand flows through the lines. Capacity constraints are considered in the hub and spoke nodes and also the hub and spoke edges. Uncertainty is assumed for the demands and transportation costs, represented by a finite set of scenarios. The aim is to maximize the total expected profit, where transfers between the lines are penalized by including their costs in the objective function. The performance of the proposed model is evaluated by computational tests and some managerial insights are also provided through the analysis of the resulting networks under various parameter settings.
 

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Due to the importance of vehicle routing for delivering a large number of orders with different restrictions in the world, various optimization methods have been studied in past researches. In this article, a number of researches of recent years have been discussed, then the proposed model is described in 3 phases with the penalty index. This model has the ability to assign orders, route vehicles and determine the number of active vehicles dynamically with the aim of minimizing the total cost of distribution. By examining valid metaheuristic models and using their strengths and weaknesses, and considering multiple limitations, a new model of "dynamic 3-phase optimization" has been designed. The main application of the proposed model is for vehicle routing problems with capacity constraints of fleet number and capacity constraints (maximum and minimum number of orders). Finally, with simulation, the outputs of the model have been analyzed in different conditions . Although the limitation of maximum and minimum capacity is added to the problem, by dynamically considering the number of vehicles and using star clustering (initiative of this research), three social, environmental and economic dimensions were improved. The time for orders to reach customers decreased by 19.3%, fuel consumption and air pollution by 14.9%, and logistics costs by 8.7%. To calculate the final value of system stability, a unique 3D fuzzy model has been used. With the sensitivity analysis, we came to the conclusion that the 3-phase dynamic optimization model has led to a 14.58% improvement in system stability.

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In an uncapacitated facility location problem, the aim is to find the best locations for facilities on a specific network in order to service the existing clients at the maximum total profit or minimum cost. In this paper, we investigate the uncapacitated facility location problem where the profits of the demands and the opening costs of the facilities are uncertain values. We first present the belief degree-constrained, expected value and tail value at risk programming models of the problem under investigation. Then, we apply the concepts of the uncertainty theory to transform these uncertain programs into the corresponding deterministic optimization models. The efficient algorithms
are provided for deriving the optimal solutions the problem under investigation.

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Abstract
Objective: From economic, environmental and social perspectives, the sustainability of the supply chain can give a competitive advantage to organizations. By designing a hybrid discrete event agent-based simulation model based on the simulation-optimization approach and meta-heuristic algorithms, this study has sought to evaluate the sustainability of the supply chain and improve the economic, environmental and social objectives of the supply chain.
Method: First, by identifying supply chain agents, an agent-based simulation model is developed. After designing the hybrid simulation model, the verification and validation phases are performed. By combining the simulation model with meta-heuristic algorithms and using the simulation-optimization approach, the optimal/near-optimal values of the components affecting the sustainability of the supply chain are finally extracted.
Findings: In addition to being able to reflect all the complexities of supply chains, the hybrid simulation optimization approach can also improve the key components affecting the sustainability of the supply chain.
Results: Implementation of sustainable supply chain components without optimizing the key variables of the supply chain can lead to the deterioration of performance and sustainability of the supply chain. The components of the maximum levels of product and inventory maintenance and how to implement environmental and social aspects in all the elements of the supply chain have a direct effect on the chain performance and should have appropriate values in different scenarios.
 

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This paper considers the progressively Type-II censoring and determines the optimal sample size using a Bayesian prediction approach. To this end, two criteria, namely the Bayes risk function of the point predictor for a future progressively censored order statistic and the designing cost of the experiment are considered. In the Bayesian prediction, the general entropy loss function is applied. We find the optimal sample size such that the Bayes risk function and the cost of the experiment do not exceed two pre-fixed values. To show the usefulness of the results, some numerical computations are presented.

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In this article, the modeling and solution of a cryptocurrency capital portfolio optimization problem has been discussed. The presented model, which is based on Markowitz's mean-variance method, aims to maximize the non-deterministic internal return and minimize the cryptocurrency investment risk. A combined PSO and SCA algorithm was used to optimize this two-objective model. The results of the investigation of 40 investment portfolios in a probable state showed that with the increase in the internal rate of return, the investment risk increases. So in the optimistic state, there is the highest internal rate of return and in the pessimistic state, there is the lowest investment risk. Investigations of the investment portfolio in the probable state also showed that more than 80% of the investment was made to optimize the objective functions in 5 cryptocurrencies BTC, ETH, USTD, ADA, and XRP. So in the secondary analysis, it was observed that in the case of investing in the top 5 cryptocurrencies, the average internal rate of return increased by 9.92%, and the average investment risk decreased by 0.1%.