multi-objective modeling

Nowadays, one of the major concerns of investors is choosing a realistic stock portfolio and making proper decisions according to an individual's utility level. It is essential to consider two conflicting goals of return and risk for profitability; as a result, balancing the above goals has been identified as an investment concern. This paper modifies and optimizes a multi-objective and multi-period stock portfolio considering cone constraints and uncertain and stochastic discrete decisions. Non-dominated Sorting Genetic Algorithm-II (NSGA-II) was used to solve the model due to the issue's complexity. Two objective functions in the model could be explained by maximizing expected returns and minimizing investment risk. The Pareto chart of the problem was drawn, which allows investors to make decisions based on various levels of risk. Another result obtained in this study is calculating the percentage of optimal amounts assigned to each asset, providing a base for investors to avert investing in unsuitable assets and incurring losses. Finally, a sensitivity analysis of essential parameters was performed, which is critical in this issue. According to the results, increasing the number of problem constraints provides a base for the model reaction, and the optimal percentage allocated to each asset varies. Therefore, this prioritizes restrictions in different situations and according to the investors' choice.

This paper addresses a situation in which a firm is willing to locate several new multi-server facilities in a geographical area to provide a service to his customers within the M/M/m/K queue system. As a new assumption, it is also considered that there is already operating competitors in such system. This paper is going to find the location of facilities in a way that the market share of entering firm is maximized. For this purpose, simultaneous minimization of total cost and maximum idle time in each facility is considered as two objective functions in the model. The total cost consists of two parts: (1) the fixed cost for opening a new facility, and (2) the operational costs regarding to the customers, which depends on travel time to the facility and the waiting time at the facility. In addition, in order to make the problem more adapted to real-world situations, two new constraints on budget and number of the servers in each facility are added to the model. Eventually, to tackle the suggested problem, a non-dominated sorting genetic algorithm (NSGA-II) and a non-dominated ranked genetic algorithm (NRGA) are utilized. Finally, the performance of algorithms are investigated via analyzing a set of test problems.