### Abstract

We study the Mean-SemiVariance Project (MSVP) portfolio selection problem, where the objective is to obtain the optimal risk-reward portfolio of . non-divisible projects when the risk is measured by the semivariance of the portfolio's Net-Present Value (NPV) and the reward is measured by the portfolio's expected NPV. Similar to the well-known Mean-Variance portfolio selection problem, when integer variables are present (e.g., due to transaction costs, cardinality constraints, or asset illiquidity), the MSVP problem can be solved using Mixed-Integer Quadratic Programming (MIQP) techniques. However, conventional MIQP solvers may be unable to solve large-scale MSVP problem instances in a reasonable amount of time. In this paper, we propose two . linear solution schemes to solve the MSVP problem; that is, the proposed schemes avoid the use of MIQP solvers and only require the use of Mixed-Integer Linear Programming (MILP) techniques. In particular, we show that the solution of a class of real-world MSVP problems, in which project returns are positively correlated, can be accurately approximated by solving a single MILP problem. In general, we show that the MSVP problem can be effectively solved by a sequence of MILP problems, which allow us to solve large-scale MSVP problem instances faster than using MIQP solvers. We illustrate our solution schemes by solving a real MSVP problem arising in a Latin American oil and gas company. Also, we solve instances of the MSVP problem that are constructed using data from the PSPLIB library of project scheduling problems.

Original language | English (US) |
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Journal | Omega (United Kingdom) |

DOIs | |

State | Accepted/In press - Aug 18 2014 |

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### Keywords

- Benders decomposition
- Mean-SemiVariance
- Petroleum industry
- Project portfolio optimization
- Project selection
- Risk
- Semivariance

### ASJC Scopus subject areas

- Strategy and Management
- Management Science and Operations Research
- Information Systems and Management

### Cite this

*Omega (United Kingdom)*. https://doi.org/10.1016/j.omega.2016.05.007