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Because of the intricate nature of real-world scenarios, experts could encounter many ambiguities throughout the decision-making (DM) process. Adopting a DM strategy in conditions of indeterminacy so that the decision makers are limited to a small number of experts is always helpful in real life. Neutrosophic conception is a convenient technique for handling inconsistent, ambiguous, and uncertain values. This research presents an autocratic DM strategy based on Neutrosophic Sets (NSs) to address these ambiguities. The essential component of the suggested technique is the conversion of diverse management decision and weight matrices into a unified evaluation matrix. Supplier Selection (SS) is a multi-criteria decision-making problem where a limited number of alternative suppliers are evaluated using a limited set of criteria. The suggested methodology based on different score functions is applied to SS issues involving construction materials. The numerical illustrations indicate the success of the introduced method in selecting the best supplier with the least computational complexity. The important point obtained in this research is that adopting a suitable score function appropriate to the characteristics of the data plays an important role in the decision-making process.

Irrigation water management is crucial for agricultural production and livelihood security in many regions and countries throughout the world. Over the past decades, controversial and conflictladen water-allocation issues among competing municipal, industrial and agricultural interests have raised increasing concerns. Particularly, growing population, varying natural conditions and shrinking water availabilities have exacerbated such competitions. Shrinking water availabilities can result in reduced water supplies, while growing population can lead to increased water demands, these two facts can further intensify the water shortage. Stochastic programming methodology is applied in this paper to a capital investment problem in water resources. A framework is offered for the evaluation of electricity generation and water supply for agricultural irrigation. This essessment is conducted through the construction of an appropriate stochastic optimization model. A recursive least squares algorithm is incorp-orated in the model which enablee more accurate estimation of model parameters.

Geometric programming problems are well-known in mathematical modeling. They are broadly used in diverse practical fields that are contemplated through an appropriate methodology. In this paper, a multi-parametric vector α is proposed for approaching the highest decision maker satisfaction. Hitherto, the simple parameter α , which has a scalar role, has been considered in the problem. The parameter α is a vector whose range is within the region of the satisfaction area. Conventionally, it is assumed that the decision maker is sure about the parameters, but, in reality, it is mostly hesitant about them, so the parameters are presented in fuzzy numbers. In this method, the decision maker can attain different satisfaction levels in each constraint, and even full satisfaction can be reached in some constraints. The goal is to find the highest satisfaction degree to maintain an optimal solution. Moreover, the objective function is turned into a constraint, i.e., one more dimension is added to n-dimensional multi-parametric α . Thus, the fuzzy geometric programming problem under this multi-parametric vector α ∈ ( 0 , 1 ] n + 1 gives a maximum satisfaction level to the decision maker. A numerical example is presented to illustrate the proposed method and the superiority of this multi-parametric α over the simple one.

One of the most ‎prevalent problems in linear programming as one of the convenient models in the field of operation research ‎‎environment is Data Envelopment Analysis (DEA), which supports the ‎efficiency of ‎‎Decision-Making Units (DMUs). Usually, accurate data are common; however, in ‎the real world, we are facing an inaccurate ‎situation. In this paper, a new ‎model for assessing DMUs in a fuzzy environment is presented; we ‎consider the inverse DEA ‎model with the variable return to scale with fuzzy numbers for fluctuating ‎data. A case study is given to ‎illustrate its performance.

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 customers' demands.Methodology: The static and dynamic networks are considered to solve the problem. If the network is static, with the help of the iterated local search algorithm, the number and location of distribution centers are determined, and customers are assigned to each. 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 regarding evaluation criteria. The results of the experiments show the superiority of the proposed method compared to the CLSC and TSCFL methods.Originality/Value: The background investigation of the subject indicates that the design of multi-level supply chains and the issue of lesser-addressed facility locations have received less attention. 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.

The supply chain design problem is one of the important problems in supply chain management. In this problem, the goal is to locate several facilities for distribution centers in different geographical areas to cover customer demands. In the model presented in this paper, customer demand is met through distribution centers, while these distribution centers supply products from manufacturing plants. In this paper, a mathematical model of integer linear programming is presented that, in addition to the optimal supply chain network design, considers the facility's location. This model aims to minimize the costs of sending products from the factory to distribution centers, from distribution centers to customers, and establishing distribution centers. To evaluate the proposed model, different network samples were created randomly on small, medium and large scales for experiments. In order to perform the experiments, a linear programming solver (LP Solver) and an iterated local search algorithm were used to compare the performance of each of these methods to find the optimal solution. These experiments show the superiority of the iterated local search algorithm compared to LP Solver in achieving the optimal solution in the shortest runtime for all instances.

Many problems in operations research including problems from management, production planning and scheduling, transportation, location, and many others necessitate decision making in the presence of uncertainty. Therefore, many theories and methodologies have been developed to deal with optimization problems under uncertainty in general. To understand uncertain data envelopment analysis models, the process was started by introducing the definition of uncertain variables, uncertain vectors, fuzzy linear programming (FLP). Selection criteria of an incoming vector in improving uncertain linear programming is established along with its unbounded nature. This paper based on the established theoretical framework proposes an alternative linear programming model that can include some uncertainty information. Finally, input-oriented CCR model with fuzzy variables is developed and an effective approach for measuring efficiency is demonstrated with a numerical example.

Today, human decisions are more than ever based on information. But most of this information is not definitive, and in this situation, logical decision making is very difficult based on this uncertainty. Different methods are used to represent this uncertainty, including the fuzzy numbers. The fuzzy linear programming problem is one of the interesting concepts to be addressed in fuzzy optimization. Fully Fuzzy Linear Programming Problems (FFLP) are issues in which all parameters of the coefficients of the variables in the target functions, the coefficients of the variables in the constraints, the right-hand side of the constraints, and the decision variables in them are fuzzy. In this paper, we show that Definition 2.6 which is used by Ezzati et al. [1], failed to compare any arbitrary triangular fuzzy numbers. We demonstrate that their presented method is not well in general, thus the proposed method finds the fuzzy optimal solution of fully fuzzy linear programming problems by Ezzati et al. [1]. Then a new approach is proposed for solving this FFLP problem. An example is also presented to demonstrate the new method.

Abstract There are many reasons for the growing interest in developing new product projects for any firm. The most embossed reason is surviving in a highly competitive industry which the customer tastes are changing rapidly. A well-managed supply chain network can provide the most profit for firms due to considering new product development. Along with profit, customer satisfaction and production of new products are goals which lead to a more efficient supply chain. As new products appear in the market, the old products could become obsolete, and then phased out. The most important parameter in a supply chain which considers new and developed products is the time that developed and new products are introduced and old products are phased out. With consideration of the factors noted above, this study proposes to design a tri-objective multi-echelon multi-product multi-period supply chain model, which incorporates product development and new product production and their effects on supply chain configuration. The supply chain under consideration is assumed to consist of suppliers, manufacturers, distributors and customer groups. In terms of overcoming NP-hardness of the proposed model and in order to solve the complicated problem, a non-dominated sorting genetic algorithm is employed. As there is no benchmark available in the literature, the non-dominated ranking genetic algorithm is developed to validate the results obtained and some test problems are provided to show the applicability of the proposed methodology and evaluate the performance of the algorithms.

In this paper, dynamic programming for sequencing weighted jobs on a single machine to minimizing total tardiness is focused, to significance of fuzzy numbers field, and importance of that for decision makers who are facing on uncertain data, combination of dynamic programming and fuzzy numbers is applied. A random scheduling problem with fuzzy processing times is given and solved. In addition, algorithm consuming time during solving same category problem and different sizes are analyzed that for large problem CPU time usage is extremely unaffordable. Therefore demonstration of near-exact heuristic method such as Genetic Algorithm (GA) appears. In this paper sufficient discussion around solving this kind of problems and their algorithms analysis and a combination between Dynamic Programming (DP) and genetic algorithm as a newly born method is proposed that stand on DP performance and genetic algorithm search power, and finally comparison on the recent developed method has been held. Then this method can deal with real-world problem easily. Thus, decision makers actually can use this modification of dynamic programming for coping with un-crisp problem.

In this study, we show that ranking fuzzy numbers with the area method using circumcenter of centroids presented by Rao and Shankar failed to rank effectively the generalized fuzzy numbers. By proving a theorem and using some numerical examples, we demonstrate that their proposed method cannot rank consistently some fuzzy numbers or is not consistent with human intuition.

In this paper, we generalize a linear programming problem with symmetric trapezoidal ‎fuzzy number which is introduced by Ganesan and et al. in [3] to a general kind of trapezoidal fuzzy number. In this way, we first establish a new ‏arithmetic operation for multiplication of two ‏trapezoidal fuzzy numbers. Then in order to ‎preparing a method for solving the fuzzy linear programming as well as the primal simplex ‎algorithm, we use a general linear ranking function as a convenient approach in the literature. In fact, our main contribution in this work is based on 3 items: 1) Extending the current fuzzy linear program to a general kind which is not essentially including the symmetric trapezoidal fuzzy number‎s ‎‏,‏ 2) Defining a new multiplication role of two trapezoidal fuzzy number‎s‎, 3) Establishing a fuzzy primal simplex algorithm for solving the generalized model. We in particular emphasize that this study can be used for establishing fuzzy dual simplex algorithm, fuzzy primal-dual simplex algorithm, fuzzy multi objective linear programming and the other similar methods which are appeared in the literature.

The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP) in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.