Note--On Optimal Resource Allocation in Community Hypertension Programs

In Management Science (Vol. 24, No. 14, October, 1978), Nichols and Weinstein describe a model of a hypertension detection and treatment program, in which individuals proceed through a series of stages with transition probabilities that depend on expenditures at each stage. We generalize the model to include the case where the number of persons in the first stage is a decision variable. Surprisingly, this more general model is simpler to solve since it is shown that optimal transition probabilities and expenditures at any stage do not depend on probabilities and expenditures at later stages. The result is applied to simple cost functions fitted to data from the numerical example of Nichols and Weinstein. We also consider a more general form of the objective function, and present an algorithm for solving the resulting optimality conditions.