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A graphical approach to solve an investment optimization problem

Journal of Mathematical Modelling and Algorithms in Operations Research 2014年第4期13卷 597-614页

作者： Gafarov, Evgeny R. Dolgui, Alexandre Lazarev, Alexander A. Werner, Frank Ecole Nationale Superieure des Mines FAYOL-EMSE CNRS:UMR6158 LIMOS Saint-Etienne 42023 France Institute of Control Sciences of the Russian Academy of Sciences Profsoyuznaya st. 65 Moscow 117997 Russian Federation Higher School of Economics (National Research University) Moscow Russian Federation Lomonosov Moscow State University Moscow Russian Federation Moscow Institute of Physics and Technology (State University) Moscow Russian Federation Fakultät für Mathematik Otto-von-Guericke-Universität Magdeburg PSF 4120 Magdeburg 39016 Germany

We consider a project investment problem, where a set of projects and an overall budget are given. For each project, a piecewise linear profit function is known which describes the profit obtained if a specific amount is invested into this project. The objective is to determine the amount invested into each project such that the overall budget is not exceeded and the total profit is maximized. For this problem, a graphical algorithm (GrA) is presented which is based on the same Bellman equations as the best known dynamic programming algorithm (DPA) but the GrA has several advantages in comparison with the DPA. Based on this GrA, a fully-polynomial time approximation scheme is proposed having the best known running time. The idea of the GrA presented can also be used to solve somesimilar scheduling or lot-sizing problems in a more effective way, e.g., the related problem of finding lot-sizes and sequencing several products on a single imperfect machine. © Springer Science+Business Media Dordrecht 2014.

关键词： FPTAS Graphical algorithm Project investment pseudo-polynomial time complexity

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