Quadratic model for allocating operational budget in public and nonprofit organizations

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4 Scopus citations


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.

Original languageEnglish
Pages (from-to)357-376
Number of pages20
JournalAnnals of Operations Research
Issue number1
StatePublished - 1 Sep 2014


  • Budgeting
  • Decision analysis
  • Fairness
  • Planning
  • Public sector
  • Quadratic programming
  • Resource allocation

ASJC Scopus subject areas

  • General Decision Sciences
  • Management Science and Operations Research


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