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Two Approaches to the Problem of Sharing Delay Costs in Joint Projects

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  • Brânzei, R.

    (Tilburg University, Center For Economic Research)

  • Ferrari, G.
  • Fragnelli, V.
  • Tijs, S.H.

    (Tilburg University, Center For Economic Research)

Abstract

This paper concentrates on cost sharing situations which arise when delayed joint projects involve joint delay costs. The problem here is to determine “fair” shares for each of the agents who contribute to the delay of the project such that the total delay cost is cleared. We focus on the evaluation of the responsibility of each agent in delaying the project based on the activity graph representation of the project and then on solving the important problem of the delay cost sharing among the agents involved. Two approaches, both rooted in cooperative game theory methods are presented as possible solutions. In the first approach delay cost sharing rules are introduced which are based on the delay of the project and on the individual delays of the agents who perform activities. This approach is inspired by the bankruptcy and taxation literature and leads to five rules: the (truncated) proportional rule, the (truncated) constrained equal reduction rule and the constrained equal contribution rule. By introducing two coalitional games related to delay cost sharing problems, which we call the pessimistic delay game and the optimistic delay game, also game theoretical solutions as the Shapley value, the nucleolus and the τ-value generate delay cost sharing rules. In the second approach the delays of the relevant paths in the activity graph together with the delay of the project play a role. A two-stage solution is proposed. The first stage can be seen as a game between paths, where the delay cost of the project has to be allocated to the paths. Here serial cost sharing methods play a role. In the second stage the allocated costs of each path are divided proportionally to the individual delays among the activities in the path. Copyright Kluwer Academic Publishers 2002
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Brânzei, R. & Ferrari, G. & Fragnelli, V. & Tijs, S.H., 2001. "Two Approaches to the Problem of Sharing Delay Costs in Joint Projects," Discussion Paper 2001-22, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:0c51f267-e6c5-4d4e-a05f-d649c66b6115
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    Cited by:

    1. Estévez-Fernández, Arantza, 2012. "A game theoretical approach to sharing penalties and rewards in projects," European Journal of Operational Research, Elsevier, vol. 216(3), pages 647-657.
    2. Arantza Estévez-Fernández & Peter Borm & Herbert Hamers, 2007. "Project games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 149-176, October.
      • Estevez Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2005. "Project Games," Discussion Paper 2005-91, Tilburg University, Center for Economic Research.
      • Estevez Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2007. "Project games," Other publications TiSEM 809ba203-2bd2-48ce-ae6d-b, Tilburg University, School of Economics and Management.
      • Estevez Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2005. "Project Games," Other publications TiSEM 21fd9b62-93b6-4a8b-9bf4-4, Tilburg University, School of Economics and Management.
    3. Rodica Branzei & Giulio Ferrari & Vito Fragnelli & Stef Tijs, 2011. "A bonus-malus approach to project management," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(4), pages 495-512, December.
    4. Nima Zoraghi & Aria Shahsavar & Babak Abbasi & Vincent Peteghem, 2017. "Multi-mode resource-constrained project scheduling problem with material ordering under bonus–penalty policies," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 49-79, April.
    5. Bergantiños, Gustavo & Lorenzo, Leticia, 2019. "How to apply penalties to avoid delays in projects," European Journal of Operational Research, Elsevier, vol. 275(2), pages 608-620.
    6. Brânzei, R. & Dimitrov, D.A. & Pickl, S. & Tijs, S.H., 2002. "How to Cope with Division Problems under Interval Uncertainty of Claims?," Discussion Paper 2002-96, Tilburg University, Center for Economic Research.
    7. Javier Castro & Daniel Gómez & Juan Tejada, 2014. "Allocating slacks in stochastic PERT network," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(1), pages 37-52, March.
    8. van Beek, Andries & Borm, Peter & Quant, Marieke, 2021. "Axiomatic Characterizations of a Proportional Influence Measure for Sequential Projects with Imperfect Reliability," Other publications TiSEM 223195b0-d201-458d-8402-7, Tilburg University, School of Economics and Management.
    9. repec:ebl:ecbull:v:3:y:2008:i:56:p:1-10 is not listed on IDEAS
    10. J. C. Gonçalves-Dosantos & I. García-Jurado & J. Costa, 2020. "Sharing delay costs in stochastic scheduling problems with delays," 4OR, Springer, vol. 18(4), pages 457-476, December.
    11. Xiaowei Lin & Jing Zhou & Lianmin Zhang & Yinlian Zeng, 2021. "Revenue sharing for resource reallocation among project activity contractors," Annals of Operations Research, Springer, vol. 301(1), pages 121-141, June.
    12. van Beek, Andries, 2023. "Solutions in multi-actor projects with collaboration and strategic incentives," Other publications TiSEM 3739c498-5edb-442f-87d8-c, Tilburg University, School of Economics and Management.
    13. Rodica Branzei & Sirma Zeynep Alparslan Gok, 2008. "Bankruptcy problems with interval uncertainty," Economics Bulletin, AccessEcon, vol. 3(56), pages 1-10.
    14. Hartmann, Sönke & Briskorn, Dirk, 2008. "A survey of variants and extensions of the resource-constrained project scheduling problem," Working Paper Series 02/2008, Hamburg School of Business Administration (HSBA).
    15. Šůcha, Přemysl & Agnetis, Alessandro & Šidlovský, Marko & Briand, Cyril, 2021. "Nash equilibrium solutions in multi-agent project scheduling with milestones," European Journal of Operational Research, Elsevier, vol. 294(1), pages 29-41.
    16. Bergantiños, Gustavo & Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2016. "Consistency in PERT problems," MPRA Paper 68973, University Library of Munich, Germany.
    17. Hartmann, Sönke & Briskorn, Dirk, 2010. "A survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 207(1), pages 1-14, November.
    18. Mahendra Piraveenan, 2019. "Applications of Game Theory in Project Management: A Structured Review and Analysis," Mathematics, MDPI, vol. 7(9), pages 1-31, September.
    19. Rodica Branzei & Marco Dall'Aglio & Stef H. Tijs, 2013. "On Bankruptcy Game Theoretic Interval Rules," Papers 1301.3096, arXiv.org.
    20. Estevez Fernandez, M.A., 2008. "A Game Theoretical Approach to Sharing Penalties and Rewards in Projects," Other publications TiSEM e7bb0378-03bf-43ce-9cab-c, Tilburg University, School of Economics and Management.

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