one of the most important financial and investment issues is Portfolio selection, that seeks to allocate a predetermined capital (wealth) over one or multiple periods between assets and stocks in such a way that the wealth of investor (portfolio owner) is maximized and, Simultaneously, its risk minimized. In the paper, we first propose a mathematical programming model for Portfolio selection to maximize the minimum amount of Sharpe ratios of the portfolio in all periods (max-min problem). Then, due to the uncertain property of the input parameters of such a problem, a robust possibilistic programming model (based on necessity theory) has been developed, which is capable of adjusting the robust degree of output decisions to the uncertainty of the parameters. The proposed model was tested on 27 companies active in the Tehran stock market. In the end, the results of the model demonstrated the good performance of the robust possibilistic programming model.

Portfolio selection is one of the most important financial and investment issues. Portfolio selection seeks to allocate a predetermined capital (wealth) over one or multiple time periods between assets and stocks in a such way that the wealth of investor (portfolio owner) is maximized the risks are minimized. In the paper, we first propose a mathematical programming model for Portfolio selection to maximize the minimum amount Sharpe ratios of portfolio in all periods (max-min problem). Then, due to the uncertain property of the input parameters of such a problem, a robust possibilistic programming model (based on necessity theory) has been developed, which is capable of adjusting the robust degree of output decisions to the uncertainty of the parameters. The proposed model has been tested on 27 companies active in the Tehran stock market. At the end, the results of the model demonestrate the good performance of the robust possibilistic programming model.

This paper proposes a new robust optimization approach for solving multi-objective linear programming problems under uncertainty. The uncertainty is assumed to be in the objective function coefficients and the constraint parameters. The proposed approach is based on an alternative model for obtaining robust efficient solutions to the original problem. A numerical example is given to test and illustrate the effectiveness of the proposed approach, and a comparison with a method given in the literature is discussed based on certain performance metrics.

The provision of an efficient master plan which is able to integrate the procurement, production and distribution plans is a critical need in the way of achieving the competitive advantage in today’s marketplace. In this paper, a supply chain master planning problem of a drug supply chain is taken into account. The considered drug supply chain includes multiple suppliers, one manufacturer and multiple distribution centers. In this paper, a multi-objective possibilistic mixed integer linear programming model (MOPMILP) which minimizes the total logistics cost and maximizes the total value of supplier selection aggregate function is developed. It should be noted that both economic and environmental criteria are considered in the supplier selection objective function to support the green and sustainable purchasing approach. Then to cope with the input parameters tainted with high degree of uncertainty, a new effectual robust possibilistic programming (RPP) model is elaborated. The proposed robust possibilistic programming model is able to appropriately adjust the degree of feasibility and optimality robustness of output decisions against business-as-usual uncertainty. Also the proposed robust optimization model can be appropriately applied in the cases in which reliable and sufficient historical data is not available for imprecise parameters (i.e., most of the real-life problems). To show the usefulness and effectiveness of the proposed robust possibilistic programming model numerical and comparative experiments are provided. The numerical results endorse the validity and practicability of the rendered model as well as presenting the efficiency and felicity of the developed approach.

In portfolio selection models, uncertainty plays an important role. The parameter’ s uncertainty leads to getting away from optimal solution so it is needed to consider that in models. In this paper we presented a two-stage robust model that in first stage determines the desired percentage of investment in each industrial group by using return and risk measures from different industries. One reason of this work is that general conditions of various industries is different and according to the concepts of fundamental analysis should be chosen good groups before selection assets for investment. Another reason is that the identification of several good industries helps to diversify between several groups and reduce the risk of investment. In the second stage of the model, considering assets return, systematic risk, non-systematic risk and also first stage’ s result, amount of investment in each asset is determined. In both stages of the model there are uncertain parameters. To deal with uncertainty, a robust approach has been used. Since the model is a multi-objective problem, goal programming method used to solve it. The model was tested on actual data. The results showed that the portfolio formed by this model can be well-established in the conditions of high uncertainty and obtain higher returns.