Linear solution schemes for Mean-SemiVariance Project portfolio selection problems: An application in the oil and gas industry. (April 2017)

• Record Type: Journal Article
• Authors: Sefair, Jorge A.; Méndez, Carlos Y.; Babat, Onur; Medaglia, Andrés L.; Zuluaga, Luis F.
• Is Part Of: Omega. Volume 68(2017:Apr.)
• Page Start: 39
• Page End: 48
• Publication Date: 2017-04
• Subjects: Semivariance -- Project selection -- Project portfolio optimization -- Benders decomposition -- Mean-SemiVariance -- Risk -- Petroleum industry; Management -- Periodicals; 658.4005
• DOI: 10.1016/j.omega.2016.05.007
• Languages: English
• ISSNs: 0305-0483

Abstract

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. Abstract : Highlights: MIQP solvers may be unable to solve efficiently large-scale MSVP problem instances. Two proposed linear solution schemes solve the MSVP problem more efficiently than MIQP. A single MILP accurately approximates instances with positively correlated returns. Benders solves large-scale instances with arbitrary correlated returns. The linear schemes are tested on instances from an oil and gas company and PSPLIB.