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.

In this paper, a multi- objective quadratic programming (Poss- MOQP) problem with possibilistic variables coefficients matrix in the objective functions is studied. Through the use of b-level sets the Poss- MOQP problem is converted into the corresponding deterministic multi- objective quadratic programming (b-MOQP) problem and hence into the single parametric quadratic programming problem using the weighting method. An extended b-possibly efficient solution is specified. A necessary and sufficient condition for finding such a solution is established. A relationship between the solutions of possibilistic levels is constructed. Numerical example is given to clarify the obtained results.

Disaster relief logistics is one of the major activities in disaster management. The significance of accounting for uncertainty in such context stimulates an interest to develop appropriate decision making tools to cope with uncertain and imprecise parameters in relief logistics system design problems. This paper proposes a multi-objective possibilistic non-linear programming model (MOPNLP) to deal with such issues. Our multi-objective model contains: (i) the minimization of the sum of setup cost, transportation costs and shortage costs of commodity in affected area, (ii) the maximization customer satisfaction. The model includes the imprecise nature of some critical parameters such as demands for various types of relief commodities, cost coefficients and capacity levels. To solve the proposed model, a two-phase interactive fuzzy solution approach is developed. Numerical experiments demonstrate the significance and applicability of the developed possibilistic model as well as the usefulness of the proposed solution approach for actual decision making problem.

The purpose of this study is to develop a dairy global supply chain planning model in which operational and financial dimensions are appropriately integrated in order to adjust the credit sale strategy. In order to evaluate the financial performance of the dairy supply chain, economic value-added index and some financial ratios are used. The proposed model is compared to traditional approaches, which usually use the profit maximization as an objective function. Also, the amount of credit sales is considered as a decision variable for the first time in this research. The developed model utilized a new risk measure, i. e., the fuzzy CVaR, to cope with the uncertainty of the exchange rate and the quality and quantity of returned products. The effectiveness and efficiency of the proposed model are analyzed and assessed using the data of a real dairy supply chain. The analysis of results obtained from the developed fuzzy mathematical model shows an increase in profit and a reduction in semi-variance compared to previously developed models. Also, some numerical experiments analyses index and the impact of credit sales strategy.

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.

Portfolio selection problem is one of the most important issues in the area of financial management in which is attempted to allocate wealth to different assets with controlling the return and risk. The aim of this paper is to obtain the optimum portfolio with regard to the cardinality and threshold constraints. In this paper, a novel multi-objective possibilistic programming model is developed for considering the fuzzy return of the portfolio that can maximize mean return and upside risk and minimize the downside risk. Two different approaches are applied for converting the model to a single objective one. The performance of the proposed model was evaluated by using historical data introduced by Markowitz and data of Tehran Stock Exchange. The results show that the model is able to propose an appropriate portfolio for investors with optimizing the return and risk, simultaneously.

In the case of a metro disruption, the planned timetable cannot be operated and a large number of passengers are left stranded in the stations. When the disruption is over, some stations may be skipped in the recovery period, which speeds up the circulation of trains and makes the number of stranded passengers reduce faster. Considering an over- crowded and time-dependent passenger flow, this paper proposes an optimization model to reschedule a metro line. To achieve a balance between theoretical validity and compu- tational convenience, the optimization model is decomposed, and an iterative algorithm is proposed to solve the model. Numerical experiments based on the Beijing Metro are carried out, the results of which verify the effectiveness and efficiency of our method. We used different types of robust possibilistic programming (RPP) approaches for coping with uncertain parameters and multi-choice goal programming for solving multi-objective problem. Robust possibilistic approaches can be classified into three groups: hard worst case robust programming, soft worst case robust programming and realistic robust programming. By solving numerical example the value of goal programming objective function is compared in different approaches. Evalution results illustrate the performance and applicability of the RPP models.

The design of closed-loop supply chain networks has attracted increasing attention in recent decades with environmental concerns and commercial factors. Due to the rapid growth of knowledge and technology, the complexity of the supply chain operations is increasing daily and organizations are faced with numerous challenges and risks in their management. Most organizations with limited resources, capabilities, and knowledge outsource their logistics services to reduce costs and increase customer satisfaction. The Third-Party Logistics (3PL) Providers have been set up to outsource various supply chain activities to specialized companies. This paper proposes a bi-objective possibilistic mixed-integer nonlinear programming model for designing a closed-loop supply chain network from the perspective of 3PL. To solve the proposed multi-objective model, a two-stage solving approach was applied first to converting the possibilistic model into its equivalent crisp counterpart and second, to converting the crisp multi-objective model into a single-objective one. Using this approach, a single-objective equivalent auxiliary crisp model was obtained and solved optimally by IBM ILOG CPLEX software. Solving numerical examples proved the effectiveness of the proposed bi-objective, possibilistic framework. Several sensitivity analyses were performed to gain managerial insights.