Fuzzy Chance-Constrained Project Portfolio Selection Model Based on Credibility Theory
This paper discusses a fuzzy chance-constrained project portfolio selection problem based on credibility theory. Risk of project portfolio is measured using conditional value at risk (CVaR) approach. The proposed model maximizes the expected fuzzy net pre
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Abstract This paper discusses a fuzzy chance-constrained project portfolio selection problem based on credibility theory. Risk of project portfolio is measured using conditional value at risk (CVaR) approach. The proposed model maximizes the expected fuzzy net present value (FNPV) subject to credibilistic chance constraint (CCC) of CVaR. We transform the chance-constrained model into deterministic model when the investment cost and return are characterized by triangular and trapezoidal fuzzy numbers. An improved genetic algorithm (GA) is designed to solve this problem. Two numerical examples with different types of membership function are also given to illustrate the modeling idea of the paper and to demonstrate the effectiveness of the proposed algorithm.
Keywords Conditional value at risk Credibility theory optimization Project portfolio Genetic algorithm
Chance-constrained
1 Introduction The problem of project portfolio selection is to allocate the limited resources to a right combination of projects. Selecting right project portfolios is crucial for organizations to survival in the intense competition environment. One of the important issues to select the right projects is balancing risk and reward [1, 2]. There are various attempts to measure the risk. Conditional value at risk (CVaR) L. Li J. Li Q. Qin (&) Department of Management Science, Shenzhen University, ShenZhen, China e-mail: [email protected] S. Cheng Division of Computer Science, The University of Nottingham Ningbo, Ningbo, China
Z. Wen and T. Li (eds.), Foundations of Intelligent Systems, Advances in Intelligent Systems and Computing 277, DOI: 10.1007/978-3-642-54924-3_69, Springer-Verlag Berlin Heidelberg 2014
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measure in many literatures has been widely used to define the risk in the project portfolio selection problems. Meng et al. [3] presented a smoothing sample average approximation method for stochastic optimization problems with CVaR risk measure. Szolgayová proposed a dynamic CVaR-portfolio approach using real options and put an application into energy investments [4]. Wang solved a mixed 0–1 LP for index tracking problem with CVaR risk constraints [5]. The traditional models under the CVaR measure were usually in the constrained form of CVaR R. Since each variable must absolutely meet the constraint, this constrained form is obviously so conservative that it is too costly or even impossible to apply in real portfolio selection problems [6]. In order to alleviate the problem, Charnes initially presented the randomized chance-constrained optimization (RCC) model in the form of pfcðx; nÞ\0g 1 a. The advantage of this constraint way is that the variables are just required to be satisfied with respect to certain probability level and constraints removal allows one to improve the cost function with permitting to keep control the feasibility of the obtained solution. Considerable literature studies were dedicated recently to further development of the RCC model [7–9]. These models were propos
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