On the Use of Linear Programming for Family Planning Resource Allocation

Implementable linear programming models have been developed for the allocation of family planning resources in developing countries. These models minimize births over a planning horizon subject to resource constraints. This choice of the objective function leads to nonpositive shadow prices, which are not intuitively appealing. Moreover, the dual problem underestimates the number of averted births resulting in an overestimate of the cost per averted birth. By viewing family planning as a production problem with averted births as output, this paper suggests that maximization of averted births is a more natural choice for an objective function. The primal problem then gives the number of averted births accurately while the dual problem gives nonnegatives shadow prices whose interpretation (e.g. averted births per money unit) is straightforward. Furthermore, this objective function dispenses with noncontraception variables and accounting identities thus reducing the size of the model.