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عنوان فارسی مقاله:
طرح های راه حل خطی برای مشکلات انتخاب مجموعه پروژه Mid-SemiVariance: کاربرد در صنعت نفت و گاز
عنوان انگلیسی مقاله:
Linear solution schemes for mean-semivariance project portfolio selection problems: An application in the oil and gas industry
سال انتشار : 2016
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بخشی از مقاله انگلیسی:
3. Linear solution schemes
In this section we show that the MSVP problem in (4) can be efficiently solved without using QP solvers; that is, it can be solved using branch-and-bound in conjunction with linear programming techniques. We refer to these solution methodologies as linear solution schemes. Besides substantially enlarging the number of optimization solvers that can be used to solve the MSVP problem, these linear solution schemes allow us to solve large-scale instances of the MSVP problem much faster than with a MIQP approach. Note that the MIQP problem in (4) can easily become a large-scale problem when either the number of projects, n, or the number of samples used to estimate the distribution of the projects’ NPVs, m, is large. Clearly, this behavior results from n and m being the dimension of the x- and y-variables in (4), respectively. In this regard, we emphasize the difference in the project portfolio selection problem when the variance is used as a measure of risk. As opposed to semivariance, using the variance implies the solution of a single MIQP problem whose size depends on the number of candidate projects, but not on the number of samples used to estimate the mean and the variancecovariance matrix of project’s NPVs. Further, in order to solve a single MIQP problem, it is necessary (loosely speaking) to solve a large number of (potentially large) QP problems (relaxed MIQP problems), obtained by branching on the corresponding binary variables. For the reasons discussed above, in Section 3.1 we first introduce a MILP formulation that accurately approximates the solution of the MSVP problem when the project’s NPVs are positively 5 correlated and the total number of projects is moderate. Next, in Section 3.2 we show that a general class of the MSVP problem, and in particular instances of the problem with a large number of projects and samples, can be solved efficiently by solving a sequence of MILP problems using a Benders decomposition approach in which the Benders cuts (cf. Nemhauser and Wolsey [27, Sections II.3.7 and II.5.4], and Freund [14]) are computed in closed-form.
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