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Top1. Introduction
Project Portfolio Management (PPM) is a set of procedures. These procedures are used to assist an organization in handling a combination of projects, which best fit the organization’s various needs (Archer et al., 1999). The set of processes consists of the project selection, established from the organization activities, and portfolio project management. PPM also considers a regular evaluation, to verify that the mix of the processes could benefit the organization (Ross et al., 2006).
To obtain efficient portfolios, investors are faced with a trade-off between a higher risk and a higher expected return by taking on more risk. Financial return, risk, or credibility are the most important criteria for investors to make a financial decision on investments under uncertainty. The financial problem related to project portfolio selection is how to maximize profits when distributing the available investment capital to the selected combination of projects. Several heuristic methods were proposed to deduce the financial feasibility of projects. For instance, Brigham (1975) used Discounted Cash Flow (DCF) analysis to establish the Net Present Value (NPV) and Rate of Return (IRR), and the Present Value Index (PVI) was reviewed by Boer (1999). In the DCF method, investment criteria, like cash inflows and outflows and available investment capital are regarded as definite real numbers. Nevertheless, these variables are perceived to be fuzzy and imprecise in reality.
A study by Beaujon et al. (2001) identified risk as a major problem underlying the choice of methodology for evaluating the value of a project (or a portfolio of projects). In the most basic case, if the value of each project is independent of the value of any other project, the major issue is to correctly identify the risk of each project, according to the selection of a portfolio. Furthermore, there are a number of proposed methodologies for valuing projects including some that explicitly account for risk. In this study, the risk is evaluated by the credibilistic risk index to evaluate the deviation of the result from the expected most-likely outcome as in the study by Zhang et al. (2011), and the credibility index that is evaluated by the possibility to occur that was introduced by Huang (2007).
This study also presents the optimal choice of portfolio investment under uncertain environments that satisfies all financial and risk constraints. The main contribution is to propose the portfolio investment optimization algorithm with uncertain parameters under a specified confidence level. The decision-makers decide what projects and when to invest under a limited budget by considering the credibility index and credibilistic risk index and the optimal logical relationships among invested projects. To our knowledge, judging the optimal portfolio by considering both the credibility index and credibilistic risk index has not been considered. Considering both risk terms is of importance as both results can contribute to each other, in terms of determining the acceptable amount of risk. This would help decision-makers to evaluate the financial return and inherent risk, simultaneously.
The rest of this paper is organized as follows. Section 2 is a literature review that includes relevant research in the field of portfolio optimization and optimization under uncertainty. Section 3 explains the problem formulation of integrating the objective functions by minimizing the credibilistic risk index of the project portfolio and maximizing the expected direct benefits. Moreover, this section also presents a numerical example of project portfolio optimization. Section 4 shows and compares the results. Finally, Section 5 concludes the findings and describes the limitations and suggestions for future research.