فصلنامه مدل سازی در مهندسی
پیاپی 51 (زمستان 1396)

Increasing the complexity of physical assets, mostly causes increasing in their price. On the other hand, financial limitation of companies do not let them to invest high amount of their capital in physical assets. Hence, equipment providers offer variety of financial ways for users to provide ability to fulfill their needed functions of an asset and efficient operation. Additionally, maintenance strategy of the equipment affect their life cycle cost and service level. Hence, companies are required to choose the optimum physical asset management strategy, in order to avoid inefficiency. The proposed mathematical model in this research determines the optimum strategy by interconnecting procurement parameters, maintenance scheduling variables and equipment working historical data based on the project time horizon. The output of the model consists of the procurement way (Buy, Lease &Upgrade), Maintenance Strategy (PM degree, PM Interval &Upgrade level) and cost. The model has been applied for a specific equipment in a copper mine for 10 years using to illustrate variables relationship.

The first order reliability method (FORM) is widely used to estimate the failure probability of structures. Appropriate evaluation of the reliability index is more important to estimate the failure probability in FORM. Generally, the iterative mathematical formula of FORM (i.e. Hasofer and Lind- Rackwitz and Fiessler (HL-RF)) was shown the instable solution of reliability index in highly nonlinear problems. The harmony search algorithm can be estimated the reliability index for concave and convex reliability problems due to capability and not need the gradient vector of random variables. In this paper, a global-best harmony search (GHS) algorithm with small harmony memory was proposed. In proposed GHS, a dynamical bandwidth, which is computed based on number of random variables, is proposed to adjust the harmony memory by a random generation with Normal distribution function. Accuracy and robustness of the proposed GHS have been compared with the HL-RF and stability transformation method (STM) through several limit state functions to that have been taken from. The results indicate that the HL-RF formula of FORM was not converged in several nonlinear examples. The proposed GHS was converged as similar as the STM results but it is more efficient )there is required less iterations to converge than STM). The GHS algorithm has top performance both of accuracy fast convergence rate.

One of the least cost methods to reduce drag on under-water projectiles is to create ventilated cavitation. So, many of researchers have focused on this subject during recent decade. In this research, ventilated cavitating flow around 30o cavitator is studied numerically and experimentally. The main objective of this research is studying the effects of some important parameters such as the air ventilation rate and flow velocity on the drag coefficient and the dimensions of cavities developed around the body. The experiments were done in a semi open-loop water tunnel. The fluid flow velocity in the test section was between 14 to 22 m/s. Also the 3D multiphase fluid flow over the cavitators within the test section are modeled and analyzed numerically by solving the corresponding governing equations using finite element method and mixture model and is coupled with the Rayleigh-Plesset equation to capture the cavity development. A comparison between numerical results and experiments shows that the numerical method using CFX accurately simulates the physics of ventilated cavitation phenomena such as the cavity length, cavity diameter and cavity shape. In final, after comparison result, effect of gas ventilation on drag coefficient and shape of cavity is presented. The results show that increasing air ventilated rate causes the amount of drag force and drag coefficient to be reduced to 36%. Also at constant air ventilated rate, with reducing cavitation number, length and diameter of the cavity are increased to 77 percent and 20 percent respectively.

The economic order quantity (EOQ) problem is one of the most common used models for the production planning and inventory control problems. A common and unrealistic assumption in these problems is considering prefect quality for all units. In this study, a multi-product EOQ model with imperfect items is proposed. In this system, all received products are not perfect, and imperfect items are scraped. Moreover, in this model the warehouse construction cost is considered as a part of inventory system costs. The objective of this study is to determine the optimal order quantity and reorder point of each product such that the total inventory cost is minimized. The proposed model is a development of a convex nonlinear programming problem therefore an exact algorithm is developed to solve this problem. Finally, to demonstrate the applicability of proposed procedure, a numerical problem is represented.

One of the methods for assessing the potential of progressive collapse occurrence is the APM method. This method done by direct removing of one or several columns. However, in this method the damage of adjacent elements of removed columns under blast conditions was ignored and this issue can lead to an incorrect prediction of progressive collapse. Therefore in this study to evaluate the potential of progressive collapse due to blast loading a 4st steel moment frame building with Abaqus/CAE 6.11 software is simulated, and two methods '' alternative load path and applied of blast load directly'' were evaluated in this study. The results indicate that in assessment of the potential of progressive collapse occurrence by considering the blast loading as the initial reason of failure, the structure response will be different compared with the common methods that used for evaluation of progressive collapse occurrence and in those methods the initial reason of progressive collapse was ignored.

Recently, Quality Function Deployment (QFD) is used as a systematic approach to establish an appropriate connection between customers’ needs and technical requirements of provided services by many companies. In this paper a hybrid model composed of QFD, Analytic Hierarchy Process (AHP) and knapsack problem using fuzzy approach is proposed to create this connection. Afterwards, a case study on police services is presented. Accordingly, customers’ needs from police services are detected and after determination of their importance level with fuzzy group AHP approach, they are positioned in rows of House Of Quality (HOQ) matrix. Also, the main police processes are placed in columns of HOQ matrix. Finally, a model based on knapsack problem model is proposed to determine the priory of executive activities for quality enhancement in police services, regarding budget constraint.

Assembly flow shop production system includes two stages. In the first stage that is usually assumed one station with some parallel machines, the parts are processed. The second stage is an assembly station (or line) to assemble the parts and complete the products. Suppose that a number of products of different kinds are ordered to be produced and each product needs a set of several parts to complete. Some of the parts are common and some others are unique for each product. Therefore it is important to study the setup times and batch production. The aim is to schedule the parts for process and the products for assembly with the minimum complete time objective. Literature review shows that the considered problem is a NP-Hard problem, so the problem characteristics and its parameters are defined and then a branch and bound algorithm is introduced to solve the small and mediocre problems. Some lower bounds and upper bounds are improved to increase the algorithm efficiency. Finally, a variety of problem is designed and performance of the proposed algorithm is evaluated in solving this problems.

Any concurrent transaction should be taken in database could lead to conflict. The conflict occurs due to incorrect values for the data which lead to interference in executed transaction which has been taken. The concurrency control algorithms, to insure the concurrent action many transactions has been designed to work concurrently with a common data. In this paper, Wound-Wait and Wait-Die concurrency control algorithms which are the part of preventing Deadlock techniques, has been modeled. Since the Colored Petri Net is one of the best methods in analyzing the concurrency control mechanism, modeling are shown using Colored Petri. Ater modeling the evaluation is carried out using parameters such as the number of transactions entering the system, the number of commands, and the number of relevant and irrelevant data between transactions, and the number of relevant data in transactions without irrelevant data, has been taken place. After evaluation, according to mentioned parameters, this result has been obtained, that Wound-Wait algorithm has much better time performance in comparison with the Wait-Die algorithm.

Artificial Bee Colony Algorithm(ABC) is one of the swarm intelligence optimization algorithms that is extensively used for the goals and applications static. Many practical, real-world applications, nevertheless, are dynamic. Thus we need to get used optimization algorithms that could be solved problems in dynamic environments as well. Dynamic optimization problems where change(s) may occur through the time. In this paper we proposed one approach based on chaotic ABC combined with explicit memory method, for solving dynamic optimization problems. In this proposed algorithm, we used the explicit memory for store the aging best solution for the maintaining diversity in the population. Use the aging best solution and diversity in environments helps the speed convergence in algorithm. The proposed approaches have been tested on Moving Peaks Benchmark. The Moving Peaks Benchmark is the suitable function for testing optimization algorithms in dynamic environments. The experimental study on a Moving Peaks Benchmark show that proposed approach has a superior performance in comparison with several other algorithms in dynamic environments.

One of the major concerns of engineers in power networks is out-of-step protection applied to the synchronous generators. Conventional out-of-step protection methods utilize a distance relay with blinders in the R–X plane and a timer. Many problems about the setting and incorrect operation of these relays has been reported in literature. Therefore, in order to overcome, some of the difficulties associated with the previous techniques, a new out-of-step detection algorithm, based on the local measurements of the generator in multi-machine power network, has been introduced in this paper. The measured angular velocity and acceleration data from active power of the machine are used to detect out-of-step conditions. The results of the simulation studies show that the application of the proposed technique is straightforward and can be directly applied to a multi-machine power network without any need to cumbersome methods of network reduction. Furthermore, the results verify the effectiveness, speed and sensitivity of the proposed method.

The Anti-Hazard Wrist Strap is a Wrist strap that can measure the flux of the current in which cross through the hand of a victim, and it will trigger an EMR (Electromagnetic Relay) or SSR (Solid State Relay) to keep the victim safe from electrocution. The material which has been used in this project as a core is a ferromagnetic material and a Hall-Effect Sensor. These Parts will place in the gap of the core. For directing flux to cross the Hall-Effect sensor, a non-magnetic material has been used in magnetic parallel ways of the core. The Anti-Hazard Wrist Strap uses a novel way to protect the person who is in danger of electrocution and this protection is based on direct protection of a person and is not depend on electrical ground. Phase to phase electrocution is an incident that any of available protection equipment cannot be efficient to sense it. The time of operation and the required current for operation of this Wrist Strap is as low as milliseconds and mill amperes.

Loss of excitation (LOE) event is among the most frequent failures in electric generators. However, LOE detection studies heretofore were usually confined to synchronous generators. Common LOE detection methods are based on impedance trajectory what makes the system slow and also prone to misoperation in the case of stable power swing (SPS). This paper presents a new method to detect the LOE based on the measured variables from the DFIG terminal. In this combined method for LOE detecting, rate of change of terminal voltage and output reactive power and for SPS detecting, DC-link voltage of DFIG have been used. The performance of the proposed method has been confirmed by Matlab/Simulink simulations for various power capacities and operating conditions. The results prove the method's velocity, simplicity and security.

In this paper, new approach for designing of TMD is presented. This method is categorized in passive control mechanism which is formulated based on structural dynamics theories. The proposed method tries to design the TMD's specifications based on studying the dynamic magnification factor. This formulation leads to complex stiffness which shows that the TMD has damping. Analytical and numerical verification are performed for verifying the proposed approach. These studies show that the proposed formulation has suitable efficiency in structural control so that structural vibrations are damped in few period of time.

Conical form is one of the standard and efficient fabric structure forms which is a suitable choice to cover small and intermediate spans. Since weight of fabric structures is not significant, wind pressure is the governing load in their design process. However, building codes do not suggest design wind loads for irregular shaped structures such as fabric structures. In this paper, effective parameters of wind pressure on conical fabric structures are investigated by using computational fluid dynamics. 48 cases of wind flow around conical formed fabric structures are modeled and analyzed in Fluent computer program. The effects of geometric characteristics of models, namely principal slope angel of form, proportional diameter of top circle of conical form, and lowest start angel of main curve, on wind pressure distribution is investigated. Among considered parameters, principal slope angel of conical form is recognized to be the most impressive parameter on wind pressure distribution.

Equal channel angular rolling (ECAR) is a severe plastic deformation (SPD) process in order to achieve ultrafine-grained (UFG) structure. In this paper, the mechanical properties of ECAR process using artificial neural network (ANN) and nonlinear regression have been illustrated. For this purpose, a multilayer perceptron (MLP) based feed-forward ANN has been used to predict the mechanical properties of ECARed Al6061 alloy sheets. Channel oblique angle, number of passes and the route of feeding are considered as ANN inputs and tensile strength, elongation and hardness are considered as the outputs of ANN. In addition, the relationship between input parameters and mechanical properties were extracted separately using nonlinear regression method. Comparing the outputs of models and experimental results shows that models used in this study can estimate the mechanical properties appropriately. Where, the performance of ANN model is better than the correlations to predict mechanical properties. Finally, the developed outputs of trained neural network model are used to analyze the effects of input parameters on tensile strength, elongation and hardness of ECARed Al6061 alloy sheets. The results showed that the ANN model, without highly expensive tests and experiments, is an efficient tool to predict the mechanical properties of ECARed Al6061 sheets.

Atomic force microscopy is a powerful tool in imaging and detection of nanoscale materials. The performance of this device in liquid environment has a great advantage such as ability of imaging biological samples, reducing the van der Waals forces and elimination of capillary forces. Understanding of dynamic behavior of the device in liquid environment under various conditions is essential. Therefore in this paper the atomic force microscopy is modeled as a cantilever beam and its dynamic behavior is investigated using the analytical method of multiple scales. For this purpose the equation of motion of microcantilever is obtained using the continuous beam model. Subsequently the hydrodynamic force due of fluid incorporates into the equation using additional mass and damping. Then using the method of separation of variables and use of the Galerkin approximation method, partial differential equation of motion of the beam is turned to an ordinary differential equation. Finally, using the method of multiple scales, the frequency response of the micro-beam near its resonance frequencies is obtained. Moreover the effect of the fluid viscosity and beam dimensions on beam frequency response is studied. In addition, since in nonlinear systems, addition to the primary resonance, it is possible to there is another resonant frequencies, so in this paper the resonant frequencies other than the natural frequency of the linear system is studied and the existence of two resonant frequencies lower than the natural frequency is shown.

This study is aimed to increase the effectiveness of film cooling in rotating blades by performing forward diffused shaped hole. For both cylindrical and forward diffused holes three different rotational speed of zero, 300 and 500 rpm have been investigated. Three-dimensional numerical simulation of turbulent flow and heat transfer in rotating reference frame are performed using modified low Reynolds k-ε model. Comparison show that low Reynolds models have acceptable ability to predict the effectiveness of film cooling of the rotating blade. The results show that by increasing the rotational speed the Coriolis acceleration consequences the deviation of the cooling air from the central line. In rotating blade, the effectiveness of the central line, especially downstream of the injection holes is reduced. Also injection of cooling air through the forward diffused hole lead to reduce the mixing of cooling air with main stream flow. Comparison of the results shows that the effectiveness of the forward diffused hole is considerably higher than the cylindrical hole.

In the roll forming process, control of input parameters is essential in order to maintain the quality of the final profile. In this investigation, a new hybrid approach is used for optimization of the roll forming process. That is based on the finite element simulation. Firstly, the process was modeled using the finite element method and then verified with the experimental results. Then necessary experiments have been designed using the central composite design method. In this design roll diameter, distance and number of stands and linear velocity of the sheet are considered as input variables and maximum plastic longitudinal strain and angle precession (reverse of spring back) are considered as response functions. Then the response surface model of the objective functions was obtained using the response surface method based on the finite element outputs of the runs. Finally, optimum point of the input parameters has been obtained using the desirability function approach. Results show that the response surface method can model the effect of the input parameters on the objective functions precisely. According to this model, increasing of distance of the stands and roll diameter, lead to decreasing of maximum plastic longitudinal strain. Increasing the linear velocity of the sheet leads to decreasing the maximum plastic longitudinal strain. Decreasing distance and increasing number of stands cause to increase the angle precession and increasing the linear velocity of the blank leads to decreasing of the angle precession. Also optimization results represent increasing of the angle precession and decreasing of the maximum plastic longitudinal strain in comparison to conventional results.

In today's modern turbines, temperature of the first row of blades, which are said the hot zone of turbine, has been boosted up to1000℃. These blades should be work for long periods. Since the main reason of fraction the pieces which are being used at high temperature and cyclic load are fatigue and creep, estimating the precise life time of these pieces is vital, whether by numerical methods or experiments. There are a couple of models for estimating the life time of work piece in interaction of creep and fatigue. In this paper, the creep and fatigue of first line of Tri60 turbofan blades has been investigated. In order to estimating the creep and fatigue life of motor turbine, initially, the analyses of blade's thermal stress and heat transfer have been conducted by Abaqus software Afterwards, the life time of blades has been done by Smith-Watson-Taper algorithm in fe-safe software. Fatigue analyze based on transient modal analysis has been also studied which leads to deriving destructive natural frequency. Finally, by using corrected Godman equations, Maro and Larson Miler the validity of blade's fatigue and creep have been investigated respectively.

Microcellular foams are a group of foams which have a lot of micro cells in the size of about 10 microns. In these foams, neutral gases (Nitrogen or Carbon dioxide) are used as a foaming material. Because of their small sizes, these foams have better mechanical and physical properties (such as fatigue strength, yield strength and de-electrical and thermal properties) than non-foamed plastics. In this study, the mechanical properties of polystyrene microcellular foams have been studied. The rate of relative density, the size of the cells, the structure of the foams and yield and fatigue strength have been studied and measured. To achieve an optimal structure, the results show that temperature and time of foaming should be controlled carefully. This condition is in the temperature of about 100° c and the time of 100 second. Also, the tensile strength of the foamed sample has been reduced and the rate of energy absorption has been significantly increased.

In this paper, a new method based on signal flow graph is proposed for modeling a Cuk converter. Furthermore, the original signal flow graph based method suggested in literature is also implemented on the Cuk converter. The proposed method is very simple in the process, compared to other methods of modeling and the old method of signal flow graph. By using signal flow graph approach the three models of small signal, large signal and steady state are extracted. Also, without adding any additional computation, the desired transfer function between any two state variables of the circuit is extractable. After modeling the converter, a controller design problem for the Cuk converter will be discussed. A robust control method is proposed for controlling the system. It will be shown that, although the switching converter has a nonlinear nature, but this does not affect the controller design problem. By using a linear controller with parameters tuned with a robust method of mixed sensitivity type, controlling the converter is possible.

Local scour of hydraulic structures has a great influence on the design of these structures. Therefore, investigation of the flow and bed profile changes, affected by the presence of different structures is inevitable. In this paper, a three-dimensional Eulerian-Eulerian model is used to estimate the maximum scour depth downstream of hydraulic structures. By using open source software OpenFOAM and make appropriate capabilities for modeling of scour, model built and efficiency and weaknesses of Eulerian-Eulerian method is evaluated. Finite volume method is used for solving differential equations of sediment transport and flow field. the model has been developed by considering the parameters affecting the amount of scour and the use of two-phase flow equations. For construction of numerical model of fluid flow, a context of repeated speed-pressure is used. To verify the final results of the numerical results of laboratory research and researchers like Chatterjee, Liu and Van Rijn is used. The results showed that the method is appropriate to estimate the maximum scour depth.

One of the most important issues in the supply chain is supplier selection with the aim of optimizing expenditures on uncertain demand. On the other hand, due to today's competitive environment, rising customer expectations for high quality and affordable products purchased, lead to development the long-term relationship of supply chain members including buyer and supplier. Therefore, selection of an appropriate set of efficient supplier and allocating orders to theirs, is one of the most important strategic decisions to create effective and efficient supply chain system in competitive environment that characterized by uncertainty. This study, at first, is attempted to select a set of efficient suppliers in a non-competitive environment with uncertain demand through the presenting an integrated model of multi objective programming including data envelopment analysis (DEA) and single buyer-multi vendor (supplier) coordination. Afterwards, by presenting a DEA model based on Nash bargaining game, the competitive environment among suppliers is simulated. The results of the two models shows that competitive environment has led to improved efficiency.

This paper present a gas turbine cycle combined with a solid oxide fuel cell with hydrogen fuel’s is exergy and energy modeled. In this way all components of the system are separately modeled. Fuel cell model presented, as well as show its behavior in different condition performance. Then, the effects of various parameters on efficiency, exergy was evaluated. And for accuracy, the results were compared with results of references and shows a good match. Increasing the turbine inlet temperature results in decreasing the thermal and exergy efficiency of hybrid system, whereas it improves the net power output. Moreover, an increase in the turbine inlet temperature leads to increases irreversibility and compression ratio leads to decreases irreversibility of the hybrid system. The results in the design point showed that 81% of irreversibility takes place in the fuel cell and combustion chamber(41% in the SOFC and 40% in combustion chamber). Hybrid system efficiency is 58.4%, while the system without SOFC efficiency is 31%, that is a combination of superior performance system.

One approach to improve the aerodynamic performance of airfoils and hydrofoils is inject a small amount of energy to the system (such as fluid injection or suction on the surface), to change the lift and drag. In fact, surface suction and blowing of the fluid can improve the pressure distribution and velocity gradient on the airfoil/hydrofoil surfaces and modify the flow separation point. Therefore, in this study the hydrodynamic behavior of turbulent flows over an airfoil exposed to the injection and suction of fluid in a part of its upper surface is discussed. Firstly, the behavior of the airfoil under one position of the injection or suction and then under two positions of injection or suction are investigated. In this simulation, the FLUENT software is used. The aim of this study is to investigate the effect of the power, the number, the position and the angle of blowing or suction on the hydrodynamic performance of the airfoil. The most important results are the reduction of 10 to 50 percent of the drag and the increase of 5 to 10 percent of the lift (for the blowing) and the reduction of 5 to 30 percent of the drag and the increase of 5 to 10 percent of the lift (for the suction) by considering two positions of injection in comparison to one position.

In power system, dynamic voltage stability margin corresponding with hopf bifurcation (HB) and reactive power limit of generators, As the two basic concepts in power system operation are defined in terms of voltage stability. Occurrence of HB, leads to oscillatory problem with constant or incremental amplitude in power system. Moreover, occurrence reactive power limit of generators, have a significant effect on power system stability and therefore reduce voltage stability margin or some times leads to voltage collapse occurrence. Therefore, knowledge of relation between operational point of power system and defined margins is very important for network operators to provide corrective and preventive strategies. Accordingly, the use of forecasting tools for the determination and prediction of the operating condition of the power system based on the defined margins is essential. In this paper, to prediction of operating condition of power system, a new classification based on the defined limits is proposed. The proposed algorithm is examined on the IEEE 39 and 68 buses test systems.

In this paper, design and optimization of a biosensor based on the nano resonator using two-dimensional photonic crystal (2D-PhC) is presented. The biosensor is consisted of two waveguides and a nano resonator. In order to increase the light confinement and well optical coupling between waveguides and nano resonator, one-end waveguide is selected as the input/output waveguides. Also, the size of three holes of structure has been changed. Due to the biomolecule bio-materials binding to the sensing hole, the refractive index of the hole is changed and consequently the resonant wavelength is shifted. The results show that the quality factor is about 2530. The sensitivity of biosensor for bio-materials sensing with effective refractive index about 1.45 (DNA molecule) is also obtained 9.48 nm/fg.

Continuous increase in fuel prices and its variations together with the emerged environmental pollutions cause to tendency to the renewable energy sources. However, the variable and uncertain natures of these generations as well as the market pressure due to the electricity market background threat the network security. Therefore, the recognition of the security index states in different operation conditions and considering the preventive and corrective actions are vital. Employment of the expected value of the uncertain variables for the power system security analysis would result in unrealistic outcomes and threatening of the power system security. Conventional approaches relying on the analysis of the large sum of scenarios such as Monte Carlo method are not efficient in the realistic large scale power systems due to the high computational burden and required time. This paper, in order to analysis the power system security, uses a point estimation method which consider the uncertainty while still has the satisfactory computational burden and time. The proposed method is examined on several power system test cases and its ability to effective uncertainty modeling in acceptable time is shown.

Accurate indiscrimination of CT saturation can be caused mal-operation of protection systems. Due to nonlinear and loss characteristic behavior of CTs, it is necessary to use a numerical method to detect CT saturation, accurately. In this paper a new method has been presented to determine the CT saturation. In proposed method, the core loss of CT and instantaneous inductance of magnetic core have been modeled by linear and nonlinear resistances and Jiles Atherton model, respectively. Then the instantaneous impedance of magnetic branches has been calculated by Fast Inverse Laplace Transform (FILT). This algorithm has been implemented to Matlab and PSCAD/EMTDC softwares. Also, impact of different parameters such as type of fault, residual flux, fault initial angle, DC offset and etc. have been evaluated. In comparison with previous researches, simulation results show this algorithm have the proper accuracy, speed and reliability.

The steel plate shear wall (SPSW) system has emerged as a promising lateral load resisting system in recent years. However, seismic code provisions for these systems are still based on elastic force- based design methodologies. Considering the ever increasing demands of efficient and reliable design procedures, a shift towards performance based plastic design (PBPD) procedure is proposed in this work. The proposed PBPD procedure for SPSW systems is based on a target inelastic drift and pre-selected yield mechanism. The proposed procedure is tested on a four-story building with rigid connections. Three different designs are considered: (1) the code design (2) the DBE design and (3) the MCE design. In addition, the displacement profiles and the selected yield mechanism are also compared at target drift.

Gate scheduling is a key activity at airports that is proposed as an optimization problem. The main purpose of this problem is to find an assignment for the flights arriving and departing while satisfying a set of practical constraints. Studies show that the gate assignment tables have been used to minimize the gate flights delay and maximize the gate efficiency and productivity. Depending on the situation, different objectives become important. If the load balancing with number of passengers in the gates becomes a bottleneck one has to make sure that the flights are equally spread over the different gates. This load balancing objective function has to be balanced with other objectives, especially minimization total delay time and maximization of the total gate assignment preference score. The related problem is formulated as a mixed-integer programming (MIP). We address this problem using real life data from Mehrabad International Airport for both small and medium size problem. To find the set of Pareto solutions, NSGA-II algorithm is proposed to demonstrate the effectiveness of the solutions which is obtained in small dimensions compared with the results obtained by the method of epsilon constraint. The results show that the percentage of error of objective function compared to epsilon constraint method is less than 1.5% for all problems. Indeed, this shows the efficiency of proposed algorithm which is recommended for solving the medium and large size problem.

Uncertainty involved in human judgments is an important cause of error and loss of credibility in outputs provided by performance appraisal (PA) processes. In few existing studies related to the errors and uncertainties in PA process, solutions mainly based on the use of fuzzy tools have been presented in this regard. These solutions have fundamental deficiencies such as inability to cope with epistemic uncertainty and also problems associated with their implementation. Considering these problems, in this paper, a new model based on evidence theory and fuzzy tools has been proposed to model uncertainty in PA process. The proposed model makes it possible for assessors to provide their ratings commensurate with their level of knowledge and also has the ability to deal with uncertainty caused by randomness and ignorance. In the proposed model which has been designed based on multi-source assessment framework, the uncertainty contained in the data obtained from two common evaluation scales, including Visual Analogue Scale and fuzzy linguistic scale, along with data related to the reliability of evaluator, have been modeled in evidence theory structure. These data then have been aggregated with evidence combination rules. The performance, benefits and improvements resulting from the proposed model, compared with other common aggregation methods in P.A models, have been investigated using simulated data and a numerical example. The results show that the proposed model in addition to improving the ability of dealing with uncertainty in P.A processes and facilitating announcing opinion by raters, provides more accurate results than traditional P.A models.