Resource Allocation with Sigmoidal Demands : Mobile Healthcare Units and Service Adoption

Achieving broad access to health services (a target within the sustainable development goals) requires reaching rural populations. Mobile healthcare units (MHUs) visit remote sites to offer health services to these populations. However, limited exposure, health literacy, and trust can lead to sigmoidal (S-shaped) adoption dynamics, presenting a difficult obstacle in allocating limited MHU resources. It is tempting to allocate resources in line with current demand, as seen in practice. However, to maximize access in the long term, this may be far from optimal, and insights into allocation decisions are limited.We present a formal model of the allocation of MHU resources, i.e., the frequency of visits to each site, to maximize long-term uptake of preventative health services. We formulate the problem as the optimization of a sum of sigmoidal functions. While the problem is NP-hard, we provide closed-form solutions to particular cases of the model that elucidate insights into the optimal allocation. For example, more visits should generally be allocated to sites where the cumulative demand potential is higher and, counterintuitively, often those where demand is currently lower. To apply our insights in practice, we propose a practical method for estimating our model's parameters from pre-existing data. Our estimation approach achieves better predictions than standard methods. Finally, we demonstrate the potential of our approach by applying our methods to family planning MHUs in Uganda. In particular, we show that operationalizable heuristic allocations, grounded in our insights, outperform allocations based on current demand