SciELO - Scientific Electronic Library Online

vol.12 issue2Special Issue on Multicriteria Decision Support SystemsMulti-criteria Decision Model for Assessing Health Service Information Technology Network Support Using the Analytic Hierarchy Process author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand




Related links

  • Have no similar articlesSimilars in SciELO


Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.12 n.2 México Oct./Dec. 2008


Using MILP Tools to Study R & D Portfolio Selection Model for Large Instances in Public and Social Sector


Usando Herramientas de MILP para Estudiar el Modelo de Selección de Portafolios R&D para Casos de Grandes Carteras de Proyectos en el Sector Social


Igor Litvinchev, Fernando López Irarragorri, Miguel Mata Pérez and Elisa Schaeffer


Postgraduate Program in Systems Engineering Faculty of Mechanical and Electrical Engineering, UANL San Nicolás de los Garza, Nuevo León, Mexico e–mails:,,,


Article received on March 10, 2008
Accepted on August 12, 2008



In this paper a mixed–integer linear programming (MILP) model is studied for the bi–objective public R & D projects portfolio problem. The proposed approach provides an acceptable compromise between the impact and the number of supported projects. Lagrangian relaxation techniques are considered to get easy computable bounds for the objectives. The experiments show that a solution can be obtained in less than a minute for instances comprising of up to 25,000 project proposals. This brings significant improvement to the previous approaches that efficiently manage instances of a few hundred projects.

Keywords: R & D projects portfolios, mixed integer programming, multi–objective optimization.



En este trabajo se presenta un modelo de programación lineal entera mixta (MILP) para el problema del portafolio de proyectos públicos R & D bi–objetivo. El enfoque propuesto provee un punto medio entre el impacto y el número de los proyectos. Se consideran técnicas de relajación Lagrangiana para obtener cotas fácilmente calculables para los valores objetivos. La experimentación muestra que puede obtenerse una solución en menos de un minuto incluso para casos de carteras de más de 25,000 proyectos propuestos. Esto implica una mejora significativa a los enfoques previos que resuelven eficientemente casos con sólo algunos cientos de proyectos.

Palabras clave: Portafolios de proyectos, programación entera mixta, optimización multiobjetivo.





The work of the first author was partially funded by CONACyT (grant number 61343) while F. López and E. Schaeffer were supported by PROMEP (grant number 103,5/07/2523).



1. Alves, M. and J. Clímaco, "A review of interactive methods for multiobjective integer and mixed–integer programming", European Journal of Operations Research, 180: 99–115 (2007).        [ Links ]

2. Castro, M., "Diseño de un sistema de soporte a la decision para la optimización de carteras en organizaciones públicas", Master's Thesis, Universidad Autónoma de Nuevo León, San Nicolás de los Garza, Mexico, 2007.        [ Links ]

3. Fernández, E., F. López and J. Navarro, "Decision support tools for R & D project selection in public organizations", IAMOT 2004, Washington, DC, USA, 2004. Available online at        [ Links ]

4. Fernández, E., F. López, J. Navarro and A. Duarte, "Intelligent techniques for R & D projects selection in large social organizations", Computación y Sistemas, 10(1): 28–56 (2006).        [ Links ]

5. Fisher, M. L., "An aplication oriented guide to lagrangian relaxation", Interfaces, 15: 10–21 (1985).        [ Links ]

6. Frangioni, A., "About lagrangian methods in integer optimization", Annals of Operations Research, 139: 163– 169 (2005).        [ Links ]

7. Guignard, M., "Lagrangean relaxation", TOP, 11(2): 151–228 (2003).        [ Links ]

8. Hooker, J., Integrated Methods for Optimization. International Series in Operations Research & Management Science, Vol. 100. Springer, 2007.        [ Links ]

9. Hsu, Y–G., G–H. Tzeng and J.Z. Shyu, "Fuzzy multiple criteria selection of government–sponsored frontier technology R & D projects", R & D Management, (33)5: 539–551, 2003.        [ Links ]

10. Jain, V. and I. Grossmann, "Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems", INFORMS Journal on Computing, 13(4): 258–276, 2001.        [ Links ]

11. Klapka, J. and P. Pinos, "Decision support system for multicriterial R & D and information systems projects selection", European Journal of Operation Research, 140(2): 434–446, 2002.        [ Links ]

12. Lemaréchal, C., "Lagrangian relaxation". In Computational Combinatorial Optimization, edited by M., Junger and D. Naddef, pp.115–160. Springer Verlag, 2001.        [ Links ]

13. Litvinchev, I., and F. López, "An interactive algorithm for portfolio bi–criteria optimization of R & D projects in public organizations", Journal of Computer and Systems Sciences International, (47)1: 25–32, 2008.        [ Links ]

14. Litvinchev, I., F. López, A. Alvarez and E. Fernández, "Large scale public R & D portfolio selection by maximizing a biobjective impact measure", Technical Report PISIS–2008, Graduate Program in Systems Engineering, UANL, San Nicolás de los Garza, Mexico, 2008. Submitted for publication.        [ Links ]

15. Navarro, J., "Modelo difuso de preferencias para resolver problemas de cartera en organizaciones públicas", Master's. Thesis, Universidad Autónoma de Sinaloa, Sinaloa, Mexico, 2001.        [ Links ]

16. Navarro, J., "Herramientas inteligentes para la evaluación y selección de proyectos de investigación–desarrollo en el sector público", Doctoral Thesis, Universidad Autónoma de Sinaloa, Sinaloa, Mexico, 2005.        [ Links ]

17. Ringuest, J.L., S.B. Graves and R.H. Caseb, "Mean––Gini analysis in R & D portfolio selection", European Journal of Operational Research, (154)1: 157–169, 2004.        [ Links ]

18. Soland, R.M., "Multicriteria optimization: A general characterization of efficient solutions", Decision Sciences, (10)1: 26––38, 1979.        [ Links ]

19. Stummer, C. and K. Heidenberger, "Interactive R/ & D portfolio analysis with project interdependencies and time profiles of multiple objectives", IEEE Transactions on Engineering Management, (50)2: 175–183, 2003.        [ Links ]

20. Tian, Q., J. Ma, J. Liang, R. Kwok and O. Liu, "An organizational decision support system for effective R & D project selection", Decision Support Systems, 39(3): 403–413, 2005.        [ Links ]

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License