Application of Mathematical Programming to Budget Allocation in State Universities in Adamawa State

This study applies mathematical programming techniques to the challenge of optimal budget allocation in state universities in Adamawa State, North East Nigeria, where severe fiscal constraints have intensified competition for limited institutional resources among academic and administrative units. The efficient allocation of budgetary resources across competing departmental, research, and infrastructure needs is a complex multi-objective decision problem, and the application of quantitative programming methods offers a more rigorous and transparent basis for allocation than informal negotiation processes. Working with budget and expenditure data from a state university in Adamawa for the five-year period 2019 to 2023, the study formulates a multi-objective linear programming model that seeks simultaneously to maximise academic output indicators and minimise unit-level expenditure variances, subject to revenue constraints, accreditation minimum spending requirements, and equity constraints across faculties. Goal programming is applied to handle the multiple, potentially conflicting objectives, with weights elicited from university management through an analytic hierarchy process exercise. The resulting optimal allocation is compared against actual historical allocations, and efficiency gains are quantified using data envelopment analysis. Results indicate that reallocation of approximately 12 percent of the current capital expenditure budget from administrative infrastructure to laboratory equipment and library resources would yield the most significant improvement in academic output indices under the multi-objective framework. Keywords: mathematical programming, budget allocation, goal programming, university management, Adamawa State