Linear solution schemes for Mean-SemiVariance Project portfolio selection problems: An application in the oil and gas industry |
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| Institution: | 1. School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA;2. Centro para la Optimización y Probabilidad Aplicada (COPA), Departamento de Ingeniería Industrial, Universidad de los Andes, Bogotá, Colombia;3. Industrial and Systems Engineering Department, Lehigh University, Bethlehem, PA, USA;1. School of Engineering and Sciences, Tecnológico de Monterrey, Campus Monterrey, Eugenio Garza Sada Av. 2501 Sur, 64848 Monterrey, Mexico;2. SUTD-MIT International Design Centre, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore;1. Research Base of Beijing Modern Manufacturing Development, College of Economics and Management, Beijing University of Technology, Beijing, 100124, China;2. Environmental Systems Engineering Program, Faculty of Engineering, University of Regina, Regina, Sask, S4S 0A2, Canada;3. School of Mechanical Engineering, University of Science & Technology, Beijing, 100083, China;4. School of Economics and Management, North China Electric Power University, Beijing, 102206, China;5. Electric Power Research Institute, CSG, Guangzhou, 510080, Guangdong Province, China;1. Faculty of Civil Engineering, Autonomous University of Sinaloa, 80040 Sinaloa, Mexico;2. Postgraduate & Research Division, National Mexican Institute of Technology/Madero Institute of Technology, 89440 Tamaulipas, Mexico;3. Computer Science in the Graduate Division, National Mexican Institute of Technology/Tijuana Institute of Technology, 22500 Baja California, Mexico;1. Faculty of Industrial & Systems Engineering, Tarbiat Modares University, P.O. Box 14115 143, Tehran, Iran;2. Project & Construction Management Group, Faculty of Arts & Architecture, Tarbiat Modares University (TMU), P.O. Box 14155 4838, Tehran, Iran |
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| 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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| Keywords: | Semivariance Project selection Project portfolio optimization Benders decomposition Mean-SemiVariance Risk Petroleum industry |
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