Multi-period models of portfolio selection have been developed in the literature with respect to certain assumptions. In this study, for the first time, the portfolio selection problem has been modeled based on mean-semi variance with transaction cost and minimum transaction lots considering functional constraints and fuzzy parameters. Functional constraints such as transaction cost and minimum transaction lots were included. In addition, the returns on assets parameters were considered as trapezoidal fuzzy numbers. An efficient genetic algorithm (GA) was designed, results were analyzed using numerical instances and sensitivity analysis were executed. In the numerical study, the problem was solved based on the presence or absence of each mode of constraints including transaction costs and minimum transaction lots. In addition, with the use of sensitivity analysis, the results of the model were presented with the variations of minimum expected rate of programming periods.

Banking industry has significant contribution in development of economies of developing countries. Most banks execute their operations through different branches. Therefore it is important to measure the relative efficiencies of these branches. Data envelopment analysis (DEA) is one of the most useful tools in measuring banks’ performance. The present paper aims to extract ranking pattern of banks based on performance evaluation using DEA analysis. In the present research, 120 bank branches of Bank Shahr in city of Tehran were selected and their efficiencies were evaluated using DEA technique. The results are discussed and compared with similar studies.

The single machine scheduling problem aims at obtaining the best sequence for a set of jobs in a manufacturing system with a single machine. In this paper, we optimize rewards in single machine scheduling in rewards-driven systems such that total reward is maximized while the constraints contains of limitation in total rewards for earliness and learning, independent of earliness and learning and etc. are satisfied. In mentioned systems as for earliness and learning the bonus is awarded to operators, we consider only rewards in mentioned systems and it will not be penalized under any circumstances. Our objective is to optimize total rewards in mentioned system by taking the rewards in the form of quadratic for both learning and earliness. The recently-developed sequential quadratic programming (SQP), is used by solve the problem. Results show that SQP had satisfactory performance in terms of optimum solutions, number of iterations, infeasibility and optimality error. Finally, a sensitivity analysis is performed on the change rate of the objective function obtained based on the change rate of the “amount of earliness for jobs (Ei parameter)”.

In this paper, we study no-wait flow shop problem where setup times depend on sequence of operations. The proposed problem considers sequence-independent removal times, release date with an additional assumption that there are some preliminary setup times. There are two objectives of weighted mean tardiness and makespan associated with the proposed model of this paper. We formulate the resulted problem as a mixed integer programming, where a two-phase fuzzy programming is implemented to solve the model. To examine the performance of the proposed model, we generate several sample data, randomly and compare the results with other methods. The preliminary results indicate that the proposed two-phase model of this paper performed relatively better than Zimmerman & apos; s single-phase fuzzy method.