Markowitz's model which determines the weight of each stock in the portfolio is based on the optimal choice of stocks in order to maximize the expected returns. However, this theory through paying special attention to the concept of total risk reaches to an efficient frontier which undoubtedly the portion of unsystematic risk that the market doesn't reward will not stand in the minimum level.Besides, Sharpe's theory presents a model using some simplifying assumptions which attains a new efficient frontier in which although the concept of systematic risk governs it, its fundamental defect will absolutely be applying market portfolio in the case of investing. This article aims to combine the theories of Markowitz and Sharpe to introduce a new model. This new model is much better and more efficient in comparison to Markowitz's efficient frontier. Moreover, it reforms the exiting defect in Sharpe's model The superiority of proposed model over Markowitz and Sharpe's traditional models from the view point of theory is definitely proven through paying attention to unsystematic risk, eliminating some assumptions of the traditional models and finally through finding the optimal portfolio of stocks for large cement corporations in Tehran stock exchange market.

The main goal In this paper is to merge fuzzy DEA with Markowitz model to construct optimized portfolio of efficient companies in Tehran bourse. So, first using of DEA we choose efficient companies as efficient group, although we choose two type of efficient companies with adding controlling relative weight constraints for two type of investors ( risk aversive & risk taker ), Then, using of Markowitz model with regarding of the level of risk aversion, we construct efficient portfolio from efficient group.The large number of criteria is one of the MCDM model's problems for solving this problem we can use of factor analysis to reduce a complex data set to a lower dimension. In this paper with respect to experts's opinions,firstly the main variables corresponding to company's efficiency were assigned ( 15 financial ratio ) and then using of factor analysis we reduse the number of these variables to eight, after that with adding controlling relative weight constraints to DEA model, we construct efficient groap for two type of investors ( risk aversive & risk taker ). due to relativeness of risk and return in terms of investors, whit imputing investors to type( risk aversive & risk taker), efficient groaps were constituted. Finaly investor can, with regarding of the level of his risk aversion, using of Markowitz model, construct optimal portfolio from efficient groaps. Though in final step optimal portfolios were choosed from efficient groaps, thus one of the main problem of Markowitz model that is nonregarding other criterion except risk and return, will be soleved.

In portfolio theory, it is well-known that the distributions of stock returns often have non-Gaussian characteristics. Therefore, we need non-symmetric distributions for modeling and accurate analysis of actuarial data. For this purpose and optimal portfolio selection, we use the Tail Mean-Variance (TMV) model, which focuses on the rare risks but high losses and usually happens in the tail of return distribution. The proposed TMV model is based on two risk measures the Tail Condition Expectation (TCE) and Tail Variance (TV) under Generalized Skew-Elliptical (GSE) distribution. We first apply a convex optimization approach and obtain an explicit and easy solution for the TMV optimization problem, and then derive the TMV efficient frontier. Finally, we provide a practical example of implementing a TMV optimal portfolio selection in the Tehran Stock Exchange and show TCE-TV efficient frontier.

In this paper, we introduce a new continuous quantum evolutionary optimization algorithm designed for optimizing nonlinear convex functions, non-convex functions, and efficiency evaluation problems using quantum computing principles. ‎ Traditional quantum evolutionary algorithms have primarily been implemented for discrete and binary decision variables‎. ‎The proposed method has been designed as a novel continuous quantum evolutionary optimization algorithm tailored to problems with continuous decision variables‎. ‎ To assess the algorithm’s performance, several numerical experiments are conducted‎, ‎and the simulated results are compared with the Grey Wolf Optimizer and Magnet Fish Optimization search algorithm‎. ‎The simulation results indicate that the proposed algorithm can approximate the optimal solution more accurately than the two compared algorithms.

Data Envelopment Analysis (DEA) models which evaluate the efficiency of a set of decision making units (DMUs) are unable to discriminate between efficient DMUs. The problem of discriminating between these efficient DMUs is an interesting subject. A large number of methods for fully ranking both efficient and inefficient DMUs have been proposed.Through real world applications, analysis may encounter data that are not deterministic or on have a stochastic essence but whose distribution can be defined by collecting data in successive periods and by statistical methods. In this paper, a method for ranking stochastic efficient DMUs is suggested which is based on the full inefficient frontier method. Using a numerical example, we will demonstrate how to use the result.

Product quality for plastic injection molding process is highly related with the settings for its process parameters. Additionally, the product quality is not simply based on a single quality index, but multiple interrelated quality indices. To find the settings for the process parameters such that the multiple quality indices can be simultaneously optimized is becoming a research issue and is now known as finding the efficient frontier of the process parameters. This study considers three quality indices in the plastic injection molding: war page, shrinkage, and volumetric shrinkage at ejection. A digital camera thin cover is taken as an investigation example to show the method of finding the efficient frontier. Solidworks and Moldflow are utilized to create the part’s geometry and to simulate the injection molding process, respectively. Nine process parameters are considered in this research: injection time, injection pressure, packing time, packing pressure, cooling time, cooling temperature, mold open time, melt temperature, and mold temperature. Taguchi's orthogonal array L27 is applied to run the experiments, and analysis of variance is then used to find the significant process factors with the significant level 0.05. In the example case, four process factors are found significant. The four significant factors are further used to generate 34 experiments by complete experimental design. Each of the experiments is run in Moldflow. The collected experimental data with three quality indices and four process factors are further used to generate three multiple regression equations for the three quality indices, respectively. Then, the three multiple regression equations are applied to generate 1,225 theoretical datasets. Finally, data envelopment analysis is adopted to find the efficient frontier of the 1,225 theoretical datasets. The found datasets on the efficient frontier are with the optimal quality. The process parameters of the efficient frontier are further validated by Moldflow. This study demonstrates that the developed procedure has proved a useful optimization procedure that can be applied in practice to the injection molding process.

The focus of this paper is on standard Markowitz mean-variance model and its traditional approach to solve portfolio selection problem (Quadratic Planning). For this goal we have applied a meta-heuristic method based on genetic algorithms (GA) in order to trace out the efficient frontier associated with the portfolio selection problem under cardinality and bounding constraints. These constraints ensure the investment in a given number of different assets and limit the amount of capital to be invested in each asset.We have presented some experimental results in two samples from Iranian stock market and overseas ones and compare the GA result with unconstrained quadratic results. Finally, we have found out which proposed GA can optimize portfolio selection problem under cardinality and bounded constrains.