IJPAM: Volume 36, No. 4 (2007)


Eyüp Çetin$^1$, Seda Tolun Esen$^2$
$^{1,2}$Department of Quantitative Methods
School of Business Administration
Istanbul University
Istanbul, 34320, TURKEY
$^1$e-mail: eycetin@istanbul.edu.tr
$^2$e-mail: stolun@istanbul.edu.tr

Abstract.This effort derived a mathematical model for the allocation of rewards in project-based or teamwork cases. The model, considering multicriteria decision environment, allocates a constant monetary reward to team members in an optimal frame such that the balance of equity and equality is established using an inequality index Gini coefficient and hence Lorenz curves as post analyses of the Shapley values of $n$-person game theory. The model generates a convex combination of the Shapley vectors, which is better than its parents in inequality base. The recipe offers optimal weights of the convex combination and cumulative frequencies of team members. A hypothetical illustrative example is solved and computed by MS Excel's add-in Evolutionary Solver, which uses genetic algorithms as a powerful spreadsheet tool. The model is a good example of the synergistic area consisting of social psychology, operations research, organizational behavior and human resources management.

Received: November 15, 2006

AMS Subject Classification: 91A06, 90C99, 91E99, 91E45, 91C99, 90C59

Key Words and Phrases: $n$-person games, mathematical programming, mathematical psychology, measurement and performance, fairness mechanism, approximation methods and heuristics

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 4