A polynomial rule for the problem of sharing delay costs in PERT networks

Castro Cantalejo, JavierGómez González, DanielTejada Cazorla, Juan Antonio2023-06-202023-06-202008Bergantiños G, Sánchez E. How to distribute costs associated with a delayed project. Annals of Operations Research 2002;109:159–74. Brânzei R, Ferrari G, FragnelliV, Tijs S. Two approaches to the problem of sharing delay costs in joint projects. Annals of Operations Research 2002;109:359–74. Moulin H, Shenker S. Serial cost sharing. Econometrica 1992;60:1009–37. Shapley LS. A value for n-person games. In: Kuhn HW, Tucker AW, editors, Contributions to the theory of games II. Annals of mathematics studies, vol. 28. Princeton, NJ: Princeton University Press; 1957. p. 307–17. Tijs S, Koster M. General aggregation of demand and cost sharing methods. Annals of Operations Research 1998;84:137–64. Potters J, Sudhölter P. Airport problems and consistent allocation rules. Mathematical Social Sciences 1999;38:83–102. Moulin H. On additive methods to share joint costs. Japanese Economic Review 1995;46:303–32. Albizuri MJ, Santos JC, Zarzuelo JM. On the serial cost sharing rule. International Journal of Game Theory 2002;31:437–46. Estévez-Fernandez A, Born P, Hamers H. Project games. Center discussion paper series, Tilburg University; 2005. De Frutos MA. Coalitional manipulation in a bankruptcy problem. Review of Economic Design 1999;4:255–72. Castro J, Gómez D, Tejada J. The use of proportional rule applied to durations for slack distribution in a PERT network. Technical Report,2005.0305-054810.1016/j.cor.2006.11.003https://hdl.handle.net/20.500.14352/50061In this paper we define the weighted serial cost sharing rule for the cost allocation problem.We apply this new rule to the problem of sharing delay costs in a PERT network. This rule belongs to the Core and is the Weighted Shapley Value for a particular game. Furthermore, we present a characterization of this rule and a polynomial algorithm for its calculation.engA polynomial rule for the problem of sharing delay costs in PERT networksjournal articlehttp://www.sciencedirect.com/science/article/pii/S0305054806002954http://www.sciencedirect.comrestricted access519.8PERTSerial cost sharingDelay costWeighted Shapley ValueInvestigación operativa (Matemáticas)1207 Investigación Operativa