Skip to main content
Log in

Combinatorial auction algorithm for project portfolio selection and scheduling to maximize the net present value

  • Published:
Journal of Zhejiang University SCIENCE C Aims and scope Submit manuscript

Abstract

Scheduling projects at the activity level increases the complexity of decision making of project portfolio selection but also expands the search space to include better project portfolios. An integer programming model is formulated for the project portfolio selection and scheduling problem. An iterative multi-unit combinatorial auction algorithm is proposed to select and schedule project portfolios through a distributed bidding mechanism. Two price update schemes are designed to adopt either a standard or an adaptive Walrasian tâtonnement process. Computational tests show that the proposed auction algorithm with the adaptive price update scheme selects and schedules project portfolios effectively and maximizes the total net present value. The price profile generated by the algorithm also provides managerial insights for project managers and helps to manage the scarce resources efficiently.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Abrache, J., Crainic, T.G., Gendreau, M., Rekik, M., 2007. Combinatorial auctions. Ann. Oper. Res., 153(1):131–164. [doi:10.1007/s10479-007-0179-z]

    Article  MATH  MathSciNet  Google Scholar 

  • Arrow, K., Debreu, G., 1954. Existence of equilibrium for a competitive economy. Econometrica, 22(3):265–290. [doi:10.2307/1907353]

    Article  MATH  MathSciNet  Google Scholar 

  • Badri, M.A., Davis, D., Davis, D., 2001. A comprehensive 0–1 goal programming model for project selection. Int. J. Proj. Manag., 19(4):243–252. [doi:10.1016/S0263-786399)00078-2]

    Article  Google Scholar 

  • Bikhchandani, S., Mamer, J., 1997. Competitive equilibrium in an exchange economy with indivisibilities. J. Econ. Theory, 74(2):385–413. [doi:10.1006/jeth.1996.2269]

    Article  MATH  MathSciNet  Google Scholar 

  • Brucker, P., Drexl, A., Mohring, R., Neumann, K., Pesch, E., 1999. Resource-constrained project scheduling: notation, classification, models, and methods. Eur. J. Oper. Res., 112(1):3–41. [doi:10.1016/S0377-2217(98)00204-5]

    Article  MATH  Google Scholar 

  • Carazo, A.F., Gomez, T., Molina, J., Hernandez-Diaz, A.G., Guerero, F.M., Caballero, R., 2010. Solving a comprehensive model for multiobjective project portfolio selection. Comput. Oper. Res., 37(4):630–639. [doi:10.1016/j.cor.2009.06.012]

    Article  MATH  MathSciNet  Google Scholar 

  • Chen, J., Askin, R.G., 2009. Project selection, scheduling and resource allocation with time dependent returns. Eur. J. Oper. Res., 193(1):23–34. [doi:10.1016/j.ejor.2007.10.040]

    Article  MATH  Google Scholar 

  • Cherkassky, B.V., Goldberg, A.V., 1997. On implementing the push-relabel method for the maximum flow problem. Algorithmica, 19(4):390–410. [doi:10.1007/PL00009180]

    Article  MATH  MathSciNet  Google Scholar 

  • Chien, C.F., 2002. A portfolio-evaluation framework for selecting R&D projects. R&D Manag., 32(4):359–368. [doi:10.1111/1467-9310.00266]

    Article  MathSciNet  Google Scholar 

  • Coffin, M.A., Taylor, B.W., 1996. Multiple criteria R&D project selection and scheduling using fuzzy logic. Comput. Operat. Res., 23(3):207–220. [doi:10.1016/0305-0548(96) 81768-0]

    Article  Google Scholar 

  • Demeulemeester, E., Herroelen, W., 2002. Project Scheduling: a Research Handbook. Kluwer Academic Publishers, New York, p.203–206.

    MATH  Google Scholar 

  • de Vries, S., Vohra, S., 2003. Combinatorial auctions: a survey. INFORMS J. Comput., 15(3):284–309. [doi:10.1287/ijoc.15.3.284.16077]

    Article  MathSciNet  Google Scholar 

  • Doerner, K.F., Gutjahr, W.J., Hartl, R.F., Strauss, C., Stummer, C., 2004. Pareto ant colony optimization: a metaheuristic approach to multiobjective portfolio selection. Ann. Oper. Res., 131(1–4):79–99. [doi:10.1023/B:ANOR.0000039513.99038.c6]

    Article  MATH  MathSciNet  Google Scholar 

  • Doerner, K.F., Gutjahr, W.J., Hartl, R.F., Strauss, C., Stummer, C., 2006. Pareto ant colony optimization with ILP preprocessing in multiobjective project portfolio selection. Eur. J. Oper. Res., 171(3):830–841. [doi:10.1016/j.ejor.2004.09.009]

    Article  MATH  MathSciNet  Google Scholar 

  • Dramitinos, M., Stamoulis, G.D., Courcoubetis, C., 2007. An auction mechanism for allocating the bandwidth of networks to their users. Comput. Networks, 51(18):4979–4996. [doi:10.1016/j.comnet.2007.08.007]

    Article  MATH  Google Scholar 

  • Dye, L.D., Pennypacker, J.S., 1999. Project Portfolio Management: Selecting and Prioritizing Projects for Competitive Advantage. Center for Business Practices, West Chester, PA, USA.

    Google Scholar 

  • Ertogral, K., Wu, S.D., 2000. Auction-theoretic coordination of production planning in the supply chain. IIE Trans., 32(10):931–940. [doi:10.1023/A:1007660530806]

    Google Scholar 

  • Fisher, M.L., 1981. The Lagrangian relaxation method for solving integer programming problems. Manag. Sci., 27(1):1–18. [doi:10.1287/mnsc.27.1.1]

    Article  MATH  Google Scholar 

  • Gabriel, S.A., Kumar, S., Ordonez, J., Nasserian, A., 2006. A multiobjective optimization model for project selection with probabilistic considerations. Soc.-Econ. Plan. Sci., 40(4):297–313. [doi:10.1016/j.seps.2005.02.002]

    Article  Google Scholar 

  • Ghasemzadeh, F., Archer, N., Iyogun, P., 1999. A zero-one model for project portfolio selection and scheduling. J. Oper. Res. Soc., 50(7):745–755. [10.1057/palgrave.jors.2600767]

    MATH  Google Scholar 

  • Graves, R.L., Schrage, L., Sankaran, J., 1993. An auction method for course registration. Interfaces, 23(5):81–92. [doi:10.1287/inte.23.5.81]

    Article  Google Scholar 

  • Gutjahr, W.J., Katzensteiner, S., Reiter, P., Stummer, C., Denk, M., 2008. Competence-driven project portfolio selection, scheduling and staff assignment. Cent. Eur. J. Oper. Res., 16(3):281–306. [doi:10.1007/s10100-008-0057-z]

    Article  MATH  MathSciNet  Google Scholar 

  • Henriksen, A.D., Traynor, A.J., 1999. A practical R&D project-selection scoring tool. IEEE Trans. Eng. Manag., 46(2):158–170. [doi:10.1109/17.759144]

    Article  Google Scholar 

  • Kolisch, R., 1996. Serial and parallel resource-constrained project scheduling methods revisited: theory and computation. Eur. J. Oper. Res., 90(2):320–333. [doi:10.1016/0377-2217(95)00357-6]

    Article  MATH  Google Scholar 

  • Kurtulus, I., Davis, E.W., 1982. Multi-project scheduling: categorization of heuristic rule performance. Manag. Sci., 28(2):161–172. [doi:10.1287/mnsc.28.2.161]

    Article  MATH  Google Scholar 

  • Kurtulus, I., Narula, S.C., 1985. Multi-project scheduling: analysis of project performance. IIE Trans., 17(1):58–66. [doi:10.1080/07408178508975272]

    Article  Google Scholar 

  • Kutanoglu, E., Wu, S.D., 1999. On combinatorial auction and Lagrangean relaxation for distributed resource scheduling. IIE Trans., 31(9):813–826. [doi:10.1023/A:1007666414678]

    Google Scholar 

  • Lim, A., Rodrigues, B., Xu, Z., 2008. Transportation procurement with seasonally varying shipper demand and volume guarantees. Oper. Res., 56(3):758–771. [doi:10.1287/opre.1070.0481]

    Article  MATH  MathSciNet  Google Scholar 

  • Linton, J.D., Walsh, S.T., Morabito, J., 2002. Analysis, ranking and selection of R&D projects in a portfolio. R&D Manag., 32(2):139–148. [doi:10.1111/1467-9310.00246]

    Article  Google Scholar 

  • McAfee, R.P., McMillan, J., 1987. Auctions and bidding. J. Econ. Lit., 25(2):699–738.

    Google Scholar 

  • Meade, L.M., Presley, A., 2002. R&D project selection using the analytic network process. IEEE Trans. Eng. Manag., 49(1):59–66. [doi:10.1109/17.985748]

    Article  Google Scholar 

  • Medaglia, A.L., Graves, S.B., Ringuest, J.L., 2007. A multiobjective evolutionary approach for linearly constrained project selection under uncertainty. Eur. J. Oper. Res., 179(3):869–894. [doi:10.1016/j.ejor.2005.03.068]

    Article  MATH  Google Scholar 

  • Mohring, R.H., Schulz, A.S., Stork, F., Uetz, M., 2003. Solving project scheduling problems by minimum cut computations. Manag. Sci., 49(3):330–350. [doi:10.1287/mnsc.49.3.330.12737]

    Article  Google Scholar 

  • Nakamura, Y., Tsuji, M., 2004. Study on the allocation of R&D investment: method of evaluating and selecting R&D projects for investment. Int. J. Innov. Technol. Manag., 1(1):55–74. [doi:10.1142/S0219877004000027]

    Article  Google Scholar 

  • Patterson, J.H., 1984. A comparison of exact approaches for solving the multiple constrained resource, project scheduling problem. Manag. Sci., 30(7):854–867. [doi:10.1287/mnsc.30.7.854]

    Article  Google Scholar 

  • Rassenti, S.J., Smith, V.L., Bulfin, R.L., 1982. A combinatorial auction mechanism for airport time slot allocation. The Bell J. Econ., 13(2):402–417. [doi:10.2307/3003463]

    Article  Google Scholar 

  • Schmidt, R.L., 1993. A model for R&D project selection with combined benefit, outcome and resource interactions. IEEE Trans. Eng. Manag., 40(4):403–410. [doi:10.1109/17.257733]

    Article  Google Scholar 

  • Stummer, C., Heidenberger, K., 2003. Interactive R&D portfolio analysis with project interdependencies and time profiles of multiple objectives. IEEE Trans. Eng. Manag., 50(2):175–183. [doi:10.1109/TEM.2003.810819]

    Article  Google Scholar 

  • Turner, J.R., 2008. The Handbook of Project-Based Management. McGraw-Hill, London, p.323–326.

    Google Scholar 

  • Yang, K.K., Sum, C.C., 1997. An evaluation of due date, resource allocation, project release, and activity scheduling rules in a multiproject environment. Eur. J. Oper. Res., 103(1):139–154. [doi:10.1016/S0377-2217(96)00266-4]

    Article  MATH  Google Scholar 

  • Yeo, K.T., 1993. Systems thinking and project management: time to reunite. Int. J. Proj. Manag., 11(2):111–117. [doi:10.1016/0263-7863(93)90019-J]

    Article  Google Scholar 

  • Zhao, X., Luh, P.B., Wang, J., 1999. Surrogate gradient algorithm for Lagrangian relaxation. J. Optim. Theory Appl., 100(3):699–712. [doi:10.1023/A:1022646725208]

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yong-yi Shou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shou, Yy., Huang, Yl. Combinatorial auction algorithm for project portfolio selection and scheduling to maximize the net present value. J. Zhejiang Univ. - Sci. C 11, 562–574 (2010). https://doi.org/10.1631/jzus.C0910479

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1631/jzus.C0910479

Key words

CLC number

Navigation