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Quadratic model for allocating operational budget in public and nonprofit organizations

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  • Zilla Sinuany-Stern

Abstract

We develop a quadratic model for allocating operational budgets in public and nonprofit organizations. The allocations for each organizational unit have lower and upper bounds. The objective function is to minimize the weighted sum of the quadratic deviations of each allocation from its bounds. The optimal allocations are mostly around the midpoint between the bounds. A simple algorithm is presented to derive the solution. The new quadratic model is compared to the familiar linear model for budget allocation, which almost always, provides extreme allocations on the bounds: for some units on the upper bound, while for others, on the lower bound. We perform sensitivity analyses, and resolve special cases of the model with closed form solution. Moreover, we show various properties of the quadratic budget allocation model and prove that its fairness index is higher than that of the linear model. The model, with its variants, was actually used for allocating budgets in various university setups; some examples are presented here. Copyright Springer Science+Business Media New York 2014

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  • Zilla Sinuany-Stern, 2014. "Quadratic model for allocating operational budget in public and nonprofit organizations," Annals of Operations Research, Springer, vol. 221(1), pages 357-376, October.
    • Handle: RePEc:spr:annopr:v:221:y:2014:i:1:p:357-376:10.1007/s10479-013-1392-6
    DOI: 10.1007/s10479-013-1392-6
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    1. Aditya U. Kulkarni & Christian Wernz, 2020. "Optimal incentives for teams: a multiscale decision theory approach," Annals of Operations Research, Springer, vol. 288(1), pages 307-329, May.

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