Universities have long struggled with a deceptively simple question: how do you split a limited pot of money between departments, teaching programs, research initiatives, and administrative support without leaving critical operations underfunded? For public higher education institutions, which depend heavily on government appropriations that arrive late, arrive unevenly, or sometimes do not arrive at all, the question is anything but simple. Now a team of Iranian operations researchers has turned that question into a formal mathematical problem, and their answer—a mixed-integer nonlinear optimization model built around a concept they call Budget Shortfall Risk—suggests that the way most universities allocate money may be quietly exposing them to far more financial risk than they realize.
The study, published in the open-access journal Heliyon, was conducted by Ensie Sarpanahi, Bakhtiar Ostadi, and Seyed Hessameddin Zegordi, who tested their framework on real financial data from Yazd University in Iran. Their central insight is that budgeting failures at universities are usually not the product of deliberate manipulation—the well-studied phenomenon of “budgetary slack,” in which units inflate cost estimates or lowball revenue projections to build themselves a cushion. Instead, the authors argue, the more pervasive and less examined danger is structural: the gap between what a unit actually needs and what it is actually allocated. They formalize this gap as Budget Shortfall Risk, a quantitative measure that can be computed, optimized, and traded off against other institutional goals, rather than merely lamented in committee meetings.
What makes the new framework technically distinctive is its two-tier architecture. Most budget optimization models in the literature treat the institution as a flat set of recipients. The Iranian team’s model instead operates simultaneously at two interconnected levels: cost centers, such as academic departments and administrative units, and institutional activities, such as teaching, research, and strategic initiatives. This mirrors how universities actually function—money flows first from the central administration to departments, and then from departments to specific operational programs. The model introduces two complementary indicators: Activity-Level Budget Shortfall Risk, which captures funding gaps at the program level, and Cost-Center-Level Budget Shortfall Risk, which captures them at the departmental level. Because shortfalls at one level propagate to the other, tracking both simultaneously gives decision-makers a much sharper picture of where financial stress is actually accumulating.
The mathematics behind the framework is formidable. The researchers formulate the problem as a multi-objective mixed-integer nonlinear programming (MINLP) model with three competing objectives: maximizing institutional program benefits (PB), minimizing Budget Shortfall Risk, and maximizing a Level of Satisfaction (LoS) metric for each cost center. Solving such problems is notoriously difficult, because the objectives cannot generally be optimized at the same time. The team’s solution is a hybrid methodology that combines lexicographic optimization, in which objectives are ranked by strict priority, with the ε-constraint method, in which the lower-priority objectives are converted into constraints bounded by aspiration levels. The program-benefit objective is optimized first, while risk and satisfaction are handled as ε-constraints whose feasible ranges are mapped out through a payoff table.
To make the approach tractable, the researchers implemented the model in GAMS 25.1 and solved it with the BARON solver, running everything on an ordinary desktop computer with an Intel Core i5 processor and 16 gigabytes of RAM. The computational efficiency is one of the study’s quiet triumphs: all twenty-five scenario combinations, generated by crossing five aspiration levels for the risk objective with five for the satisfaction objective, solved to global optimality in less than one minute of total computing time. For finance offices accustomed to weeks of spreadsheet wrangling, the idea that a full institutional budget allocation, tested against two dozen policy scenarios, can be computed over a coffee break is likely to be the study’s most immediately viral takeaway.
The case study itself reveals how the timing of money matters as much as its total amount. Yazd University’s cost centers receive no government appropriations during the first three periods of the fiscal year, forcing them to run exclusively on the university’s own revenues and generating temporary shortfalls that must be compensated once state funds begin flowing in periods seven through nine. The optimization model tracks these shortfalls dynamically, calculating the amount of budget shortfall in the period in which it occurs and following its evolution through subsequent periods. In the selected Pareto-optimal solution, the model achieved a program benefit value of 67,642,247 monetary units with an overall Budget Shortfall Risk of 22.65 percent, while satisfaction levels for individual cost centers ranged from 96.97 percent to a perfect 100 percent. Only one cost center, the seventh, ended the planning horizon with an unresolved shortfall of 19,928 monetary units—signaling to administrators that this unit would need an alternative financing source to fully cover its demand.
When the researchers compared their optimized allocation against the university’s actual 2019 fiscal year budget, the contrast was striking. The real-world allocation, the analysis showed, had primarily emphasized financing cost centers rather than achieving institutional program objectives, and carried an estimated Budget Shortfall Risk of roughly 24 percent. The optimization framework, by redistributing part of the available budget from lower-priority cost centers toward higher-priority activities, achieved a lower estimated risk while still respecting the university’s stated priority structure. In other words, the same total pot of money, allocated differently, could deliver more institutional value with less financial exposure. An expert panel that had helped estimate the model’s parameters reviewed the resulting allocation patterns and judged them consistent with the university’s budgeting practices and operational requirements.
Perhaps the most counterintuitive finding comes from the study’s sensitivity analysis, in which the researchers systematically varied the university’s total available budget from 1 percent to 200 percent of its baseline value across 200 computational runs, holding all other parameters fixed. The naive expectation is that more money means less risk. The model shows this is often—but not always—true. In several computational cases, increasing the total available budget actually produced higher Budget Shortfall Risk values, because the final allocation depends simultaneously on the institutional priority structure and the model’s constraints. Simply pouring more money into a university does not guarantee reduced shortfall risk; how the money is routed through the priority structure matters just as much. For policymakers debating funding increases for public universities, that result deserves particular attention.
The framework also functions as a policy stress-tester. In one alternative scenario, the researchers simulated a cost center experiencing a complete budget shortfall in period seven that remained unresolved through year’s end; overall Budget Shortfall Risk jumped by approximately 18 percent. In another, the governing board quadrupled the priority weight of the research program, and in a third, one cost center was restricted to a single funding source, which cut the allocations of two cost centers by more than 20 percent relative to baseline. Because each scenario can be solved in seconds, administrators could, in principle, evaluate the financial consequences of board decisions, funding restrictions, or appropriations delays before those decisions are implemented—rather than discovering the damage mid-fiscal-year.
The researchers are careful about the boundaries of their claims. Every model parameter in the case study was drawn either from institutional records, explicit modeling rules, structured expert elicitation, or analytical formulation, and the team notes that each scenario represents a point on the Pareto frontier rather than an independent statistical observation. The model also treats government funding as a fixed, inflexible parameter—an assumption that captures the reality of public universities but means the framework does not model political volatility in appropriations directly. Still, by giving universities a formal, quantitative way to see where the next funding gap will open, the study transforms a perennial administrative headache into an optimizable engineering problem. As public universities worldwide face tightening budgets and unpredictable state support, the message from Yazd is clear: the risk is not in the money you do not have, but in the gap between what you need and what you get—and that gap can now be measured, anticipated, and managed.
Subject of Research: Budget allocation and Budget Shortfall Risk mitigation in public higher education institutions using multi-objective optimization
Subject of Research: Biology
Article Title: Mitigating budget shortfall risk in higher education: A multi-objective optimization approach
Article References: Sarpanahi, E., Ostadi, B., & Zegordi, S. H. (2026). Mitigating budget shortfall risk in higher education: A multi-objective optimization approach. Heliyon, 12(14), Article e45392. https://doi.org/10.1016/j.heliyon.2026.e45392
Image Credits: AI Generated
DOI: 10.1016/j.heliyon.2026.e45392
Keywords: Budget Shortfall Risk, higher education budgeting, multi-objective optimization, mixed-integer nonlinear programming, MINLP, lexicographic optimization, ε-constraint method, cost centers, public universities, Pareto frontier, resource allocation, Yazd University
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Drew Townsend. (September 7, 2026). Multi-objective optimization helps universities manage budget shortfall risk. Scienmag. https://scienmag.com/multi-objective-optimization-helps-universities-manage-budget-shortfall-risk/
Drew Townsend. “Multi-objective optimization helps universities manage budget shortfall risk.” Scienmag, 7 September 2026, https://scienmag.com/multi-objective-optimization-helps-universities-manage-budget-shortfall-risk/. Accessed 7 September 2026.
Drew Townsend. “Multi-objective optimization helps universities manage budget shortfall risk.” Scienmag. September 7, 2026. https://scienmag.com/multi-objective-optimization-helps-universities-manage-budget-shortfall-risk/
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