Linear Optimization
Younes Nozarpour; Sayyed Mohammad Reza Davoodi; Mahdi Fadaee
Abstract
Purpose: The multi-period portfolio after closing, can be reviewed and modified at regular intervals. The philosophy behind using multi-period stock portfolio models is that investors often have a multi-period view of future asset changes that can be derived from technical, fundamental, or statistical ...
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Purpose: The multi-period portfolio after closing, can be reviewed and modified at regular intervals. The philosophy behind using multi-period stock portfolio models is that investors often have a multi-period view of future asset changes that can be derived from technical, fundamental, or statistical models. In conventional multi-period portfolio models, it is assumed that the forecast and correction horizons are the same for all assets. However, one asset may be predicted for the one-month horizon and another for the two-month horizon, and may be revised in the future in these periods. The purpose of this study is to present a multi-period stock portfolio model in which assets have different time horizons for correction or an asset can not be traded for the first few periods and then enter the correction cycle.Methodology: In this model, uncertainty variables defined on an uncertainty space are used to describe the returns. The objective function of the model is to maximize the ultimate wealth of the portfolio, and to limit portfolio risk, a constraint is used in which the uncertainty of the ultimate wealth below a threshold is controlled at a confidence level. To find the optimal solution, the model is converted into a form of linear programming by a change of variable method.Findings: After explaining how to model the research portfolio, using a numerical example the model is implemented on two portfolios with 6 and 10 stocks and 4 monthly time steps on the Tehran Stock Exchange.Originality/Value: The present study extends the uncertain multi-period portfolio to a multi-period portfolio with different time horizons and offers an optimal solution through linear programming. In the research stock portfolio, transaction costs are also considered to be more in line with the real conditions.
Linear Optimization
Sajad Moradi; Gholamreza Karamali
Abstract
Shortest path problem is one of the practical issues in optimization, and there are many efficient algorithms in this area. In this issue, a network of some nodes and arcs is considered in which, each arc has a specific parameter such as distance or cost. The main objective is to find the shortest or ...
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Shortest path problem is one of the practical issues in optimization, and there are many efficient algorithms in this area. In this issue, a network of some nodes and arcs is considered in which, each arc has a specific parameter such as distance or cost. The main objective is to find the shortest or least costly route between two distinct points. By considering an additional parameter and adding a new limitation, as a capacity constraint, the problem will be closer to the real world condition. This extended issue is known as the constrained shortest path problem and has a higher complexity order and practical algorithms are needed to solve it. In this study, an effective algorithm is presented that obtains the optimal solution within a short time. In this method, a repetitive pattern is used so that, in each iteration, the relaxed model, after adding a logical cut, is solved. The results of the implementation of the proposed algorithm on different networks show its efficiency.
Linear Optimization
Mehdi Allahdadi; Hasan Mishmast Nehi
Abstract
In this paper, solution space of interval linear programming (ILP) models that is a NP-hard problem, has been considered. In all of the solving methods of the ILP, feasibility condition has been only considered. Best-worst case (BWC) is one of the methods for solving the ILP models. Some of the solutions ...
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In this paper, solution space of interval linear programming (ILP) models that is a NP-hard problem, has been considered. In all of the solving methods of the ILP, feasibility condition has been only considered. Best-worst case (BWC) is one of the methods for solving the ILP models. Some of the solutions obtained by the BWC may result in an infeasible space. To guarantee that solution is completely feasible, improved two-step method (ITSM) is proposed. By using a new approach, we introduce a space for solving ILP models in which by two tests, feasibility and optimality of the obtained space has been guaranteed.