An optimization model for the allocation of resources in family planning programs

In this paper we present a quadratic programming model for the allocation of resources in a family planning program. A quadratic cost function is minimized subject to three sets of linear constraints: one for a diffusion model of the acceptance, switching and dropout behavior of the target population; one for manpower limitations; and one for incorporating government policies on desired levels of birth rate. There are two important features to be noted. First, a recruitment cost parameter is introduced to account for the effects of market saturation on new acceptance. Second, by treating the problem as one of cost minimization rather than one of birth rate minimization, the model can be utilized to evaluate the feasibility and the minimum cost requirement of government policies on desired reductions in the birth rate. Computational considerations are also discussed.