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Ratios in Planning-Budgeting and Bounds on Resource Requirements

This paper formulates and solves a budgeting problem that originates from the use of ratios of two variables as performance criteria for an organization. There are two main features to the problem: the presence of two conflicting groups or subsystems that disagree on a desirable trend for the ratio over a planning horizon, and a lag factor, which means that if one group is in a relatively unfavorable position in a given period, then an extra weight is given to its demands, with respect to changes in the ratio, in the next period. The lag factor takes the form of constraints in the model. The two conflicting objectives in the system are translated into minimization and maximization of a real-valued function. The solution produces lower and upper bonds for the value of a decision variable; an actual budget allocation has to be within these bounds. An application of the model to the use of student-to-library-seat ratios is presented.