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Linear solution schemes for Mean-SemiVariance Project portfolio selection problems: An application in the oil and gas industry

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  • Sefair, Jorge A.
  • Méndez, Carlos Y.
  • Babat, Onur
  • Medaglia, Andrés L.
  • Zuluaga, Luis F.

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.

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  • Sefair, Jorge A. & Méndez, Carlos Y. & Babat, Onur & Medaglia, Andrés L. & Zuluaga, Luis F., 2017. "Linear solution schemes for Mean-SemiVariance Project portfolio selection problems: An application in the oil and gas industry," Omega, Elsevier, vol. 68(C), pages 39-48.
    • Handle: RePEc:eee:jomega:v:68:y:2017:i:c:p:39-48
    DOI: 10.1016/j.omega.2016.05.007
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    2. Jorge A. Sefair & Oscar Guaje & Andrés L. Medaglia, 2021. "A column-oriented optimization approach for the generation of correlated random vectors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 777-808, September.
    3. Korotkov, Vladimir & Wu, Desheng, 2021. "Benchmarking project portfolios using optimality thresholds," Omega, Elsevier, vol. 99(C).
    4. Quezada, Luis E. & López-Ospina, Héctor A. & Ortiz, César & Oddershede, Astrid M. & Palominos, Pedro I. & Jofré, Paulina A., 2022. "A DEMATEL-based method for prioritizing strategic projects using the perspectives of the Balanced Scorecard," International Journal of Production Economics, Elsevier, vol. 249(C).
    5. Korotkov, Vladimir & Wu, Desheng, 2020. "Evaluating the quality of solutions in project portfolio selection," Omega, Elsevier, vol. 91(C).
    6. Hassan Zohali & Bahman Naderi & Vahid Roshanaei, 2022. "Solving the Type-2 Assembly Line Balancing with Setups Using Logic-Based Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 315-332, January.

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