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‎It is a well-known fact that finding a minimum dominating set and consequently the domination number of a general graph is an NP-complete problem‎. ‎In this paper‎, ‎we first model it as a nonlinear binary optimization problem and then extract two closely related semidefinite relaxations‎. ‎For each of these relaxations‎, ‎different rounding algorithm is exploited to produce a near-optimal dominating set‎. ‎Feasibility of the generated solutions and efficiency of the algorithms are analyzed as well‎.

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 We are concerned with solving Fuzzy Flexible Linear Programming (FFLP) problems. Even though, this model is very practical and is useful for many applications, but there are only a few methods for its situation. In most approaches proposed in the literature, the solution process needs at least, two phases where each phase needs to solve a linear programming problem. Here, we propose a method to solve the given problem in just one phase using only one problem. Furthermore, using our approach, sensitivity analysis of Fuzzy Flexible Linear Programming (FFLP) problem is simpler. For an illustration of our method, some numerical examples given. In particular, a practical problem is formulated and is solved by our method and several other methods and the obtained results are compared.

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One important step to achieve a sustainable transportation system is to control the impact and evaluate the effect of various influencing factors toward three dimensions of sustainability. Within this context, diverse analytical approaches have been developed to assess the sustainability level of various transportation systems, however, sustainability evaluation based on fuzzy multiple criteria decision-making approaches are still limited. In current research activity, an integrated quantitative evaluation technique is proposed to narrow the identified gap. The developed decision-making approach is consisted of two main phases. Firstly, fuzzy analytic hierarchy process is utilized to weigh the sustainability dimensions resulting in the incorporation of the experts’ knowledge along with the evaluation process. Then, a proposed fuzzy inference mechanism is proposed to provide an indication on the performance of an evaluated road transportation system. The developed approach is applied on a real-world case study. Finally, future works are presented together with some concluding remarks.

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New concepts of -feasibility and -efficiency of solutions for fuzzy mathematical programming problems are used, where  is a vector of distinct satisfaction degrees. Recently, a special kind of fuzzy mathematical programming entitled Fuzzy Flexible Linear programming (FFLP) is attracted many interests. Using the mentioned concepts, we propose a two-phase approach to solve FFLP. In the first phase, the original FFLP problem converts it to a Multi-Parametric Linear Programing (MPLP) problem, and then in phase II using the convenient optimal solution with the higher feasibility degree is concluded. Using this concept, we have solved the problem of the animal diet. In the process of milk production, the highest cost relates to animal feed. Based on reports provided by the experts, around seventy percent of dairy livestock costs included feed costs. In order to minimize the total price of livestock feed, according to the limits of feed sources in each region or season, and also the transportation and maintenance costs and ultimately milk price reduction, optimization of the livestock nutrition program is an essential issue. Because of the uncertainty and lack of precision in the optimal food ration done with existing methods based on linear programming, there is a need to use appropriate methods to meet this purpose. Therefore, in this study formulation of completely mixed nutrient diets of dairy cows is done by using a fuzzy linear programming in early lactation. Application of fuzzy optimization method and floating price make it possible to formulate and change the completely mixed diets with adequate safety margins. Therefore, applications of fuzzy methods in feed rations of dairy cattle are recommended to optimize the diets. Obviously, it would be useful to design suitable software, which provides the possibility of using floating prices to set feed rations by the use of fuzzy optimization method.

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Competing in today's marketplaces necessitates mobilizing resources and improving critical capabilities, one of which is agile marketing, or the capacity to quickly and cost-effectively react to changing international markets. The goal of this research is to create a model of agile marketing capability in the health tourism business so that it can progress. The agile marketing capacity model in health tourism was built and presented utilizing the data theory of the foundation using a qualitative research method and interviews with experts in the field. The research findings led to the identification of 38 secondary codes and finally 14 main concepts that in the form of paradigm model, the central category of agile marketing capabilities (specialized and structural capabilities), causal conditions (human capital, technology and understanding customer needs, existing structures and competition), Strategies (cost leadership and differentiation leadership strategies) are underlying factors (appropriate advertising and communication channels), interveners (environmental factors) and outcomes (improving marketing performance and sustainable development).
 

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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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One of the most useful tools in Operations Research (OR) which is essentially applied to evaluate the performance of treated Decision-Making Units (DMUs) is Data Envelopment Analysis (DEA). Because of in the current decades, DEA models have been used and extended in many disciplines and hence attracted much interests. The traditional DEA treats DMUs as black boxes and calculates their efficiencies by considering their initial inputs and their final outputs. Since, in the real situations, input data are included some uncertainties, hence in this study we consider a DEA with fuzzy stochastic data and suggest a three-stage DEA model by taking into account undesirable output. To achieve this aim, an extended probability approach is applied to the reform of three-stage DEA models. Finally, we give an illustrative example by considering a case study on the banking industry.

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The most convenient models of Solid Transportation (ST) problems have been justly considered a kind of uncertainty in their parameters such as fuzzy, grey, stochastic, etc. and usually, they suggest solving the main problems by solving some crisp equivalent model/models based on their proposed approach such as using ranking functions, embedding problems etc. Furthermore, there exist some shortcomings in formulating the main model for the realistic situations, since it omitted the flexibility conditions in their studies. Hence, to overcome these shortages, we formulate these conditions for the mentioned these problems with fuzzy flexible constraints, where there are no exact predictions for the values of the resources. In particluar, numerical investigation shows that each increasing for the values of the supply and demand is not effective for improving the objective function.  The value of the objective function is sensitive when supply and demand change, so we conduct a new study to diversify the value of the objective function, due to changes in resource and demand levels simultaneously.

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One of the most important and widely used problems in the logistics part ‎of ‎any supply chain is the location-routing problem (LRP) of vehicles. The ‎‎purpose is to select distribution centers to supply goods for ‎‎customers and create suitable travel routes for vehicles to serve ‎customers.‎ Studies conducted in the field of supply chain logistics systems have shown that if vehicle travel routing is neglected when locating supply centers, the costs of the logistics system may increase dramatically. Therefore, in the LRP problem, the location of supply centers and the routing of vehicles are considered simultaneously. In this paper, we will present a multi-objective model for vehicle location-routing problems with a flexible fuzzy ‎approach. Its' goals are to make strategic decisions to deploy ‎candidate supply centers at the beginning of the planning horizon, as well as ‎form the vehicle travel at the tactical level to serve the customers in ‎short-term periods of time. Therefore, in ‎order to adapt the mathematical model to the real conditions, the ‎constraints related to the capacity of the vehicles have been considered in a ‎flexible fuzzy state, and also the problem has been modeled in a multi-period state along with the presence of the distance limit and the ‎accessibility factor for each vehicle. The evaluation criterion is to minimize costs related to the establishment of candidate supply centers, the fixed cost of using vehicles and transportation costs, as well as maximizing customer satisfaction by reducing shortage costs and reducing harmful environmental effects. To solve the model, it is first converted into a single-objective model using the weight method and then solved using the proposed algorithm. Finally, using a numerical example in the field of waste management, the effectiveness of the proposed solution method is shown. It should be mentioned that the model was solved using GAMS software and the results are shown.
 

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In this work, we consider a ‎multi-objective‎ ‎minimal ‎cost ‎flow (MMCF) ‎problem where there are several commodities to transport from‎ sources ‎to ‎destinations and there is more than one conveyance for those transporting. We also assume that in each conveyance, there are distinct capacities for each commodity. The obtained model is not necessary balanced, and we introduced a method to solve this model without converting it to a balanced model. Some advantages of the proposed method is discussed.
 

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Supplier selection is one of the main discussions in the Supply Chain. The issue of assigning purchase orders to suppliers that act differently in terms of quality, cast, services, etc. criteria is one of the significant concerns of purchase managers in the supply chain. To adopt an optimal decision in this regard is related to a multi-objective problem that the objectives are contradicting each other and have different importance and priority depending on the location. In practice, the existence of kind of ambiguity in explaining the information related to the problem constraints and complicated. In this regard, the emergence of Fuzzy set theory as a tool to describe such conditions besides presenting question model realistically can help to solve such problems well. Despite the importance of the model with the mentioned structure, unfortunately, few original works have been done in this field. As a result, in this paper, in addition to presenting a new multi-objective Fuzzy model being modelled based on assigning purchase order to suppliers in a supply chain a solution method is introduced based on using Fuzzy linear programming. To clarify solution process modelling and description, a case study is included related to selecting flour supplier for providing industrial bread of Khoshkar factory. The proposed model includes four objective functions:

1. Aggregate costs of minimizing type,
2. Services of maximizing type (such as packing, being faithful to promise, factory heath, discount, correct transportation, good relationships, honestly, etc.),
3. Flour useful survival of maximizing type (regarding monthly flour buying by the factory),
4. The purchased flour quality of maximizing type (concerning product type).

 Especially in the solution process, a method is determined based on setting weight for each of the objectives concerning the major factory stockholders.