Bergantiños, Gustavo and ValenciaToledo, Alfredo and VidalPuga, Juan (2016): Consistency in PERT problems.

PDF
MPRA_paper_68973.pdf Download (413kB)  Preview 
Abstract
The program evaluation review technique (PERT) is a tool used to schedule and coordinate activities in a complex project. In assigning the cost of a potential delay, we characterize the Shapley rule as the only rule that satisfies consistency and other desirable properties.
Item Type:  MPRA Paper 

Original Title:  Consistency in PERT problems 
English Title:  Consistency in PERT problems 
Language:  English 
Keywords:  PERT problem; consistency; delay 
Subjects:  B  History of Economic Thought, Methodology, and Heterodox Approaches > B4  Economic Methodology C  Mathematical and Quantitative Methods > C0  General C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory 
Item ID:  68973 
Depositing User:  Alfredo ValenciaToledo 
Date Deposited:  25 Jan 2016 12:03 
Last Modified:  26 Sep 2019 17:59 
References:  Bergantiños, G. and Sánchez, E. (2002). How to distribute costs associated with a delayed project. Annals of Operations Research, 109(14):159–174. Bergantiños, G. and VidalPuga, J. (2009). A value for PERT problems. International Game Theory Review, 11(04):419–436. Brânzei, R., Ferrari, G., Fragnelli, V., and Tijs, S. (2002). Two approaches to the problem of sharing delay costs in joint projects. Annals of Operations Research, 109(14):359–374. Friedman, E. and Moulin, H. (1999). Three methods to share joint costs or surplus. Journal of Economic Theory, 87(2):275 – 312. Friedman, E. J. (2004). Paths and consistency in additive cost sharing. International Journal of Game Theory, 32(4):501–518. Hart, S. and MasColell, A. (1989). Potential, value, and consistency. Econometrica, 57(3):pp. 589–614. Littlechild, S. and Owen, G. (1973). A simple expression for the Shapley value in a special case. Management Science, 20(3):370–372. Moulin, H. (2002). Axiomatic cost and surplus sharing. In Arrow, K., Sen, A., and Suzumura, K., editors, Handbook of Social Choice and Welfare, volume I, chapter 6, pages 289–357. NorthHolland, Amsterdam. Moulin, H. and Shenker, S. (1992). Serial cost sharing. Econometrica, 60(5):pp. 1009–1037. Moulin, H. and Shenker, S. (1994). Average cost pricing versus serial cost sharing: An axiomatic comparison. Journal of Economic Theory, 64(1):178–201. Shapley, L. (1953). A value for nperson games. In Kuhn, H. and Tucker, A., editors, Contributions to the theory of games, volume II of Annals of Mathematics Studies, pages 307–317. Princeton University Press, Princeton NJ. Shapley, L. and Shubik, M. (1954). A method for evaluating the distribution of power in a committee system. American Political Science Review, 48(3):787–792. Shubik, M. (1962). Incentives, decentralized control, the assignment of joint costs and internal pricing. Management Science, 8(3):325–343. Sprumont, Y. (1998). Ordinal cost sharing. Journal of Economic Theory, 81(1):126 – 162. Thomson, W. (2009). Consistent allocation rules. Mimeo, University of Rochester. Winter, E. (2002). The Shapley value. In Aumann, R. and Hart, S., editors, Handbook of game theory with economic applications, volume III of Handbooks in Economics. Elsevier Science, Amsterdam. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/68973 