Humanitarian Logistics; Diffusion of Innovations; Sigmoidal Programming; Gradient Boosting
Problem definition: 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.Academic/practical relevance: the authors present a formal model of the long-term allocation of MHU resources as the optimization of a sum of sigmoidal functions. The authors develop insights into optimal allocation decisions and propose pragmatic methods for estimating their model’s parameters from data available in practice.The authors demonstrate the potential of their approach by applying their methods to family planning MHUs in Uganda.Methodology: nonlinear optimization of sigmoidal functions and machine learning, especially gradient boosting, are used.Results: although the problem is NP-hard, the authors provide closed form solutions to particular cases of the model that elucidate insights into the optimal allocation. Operationalizable heuristic allocations, grounded in these insights, outperform allocations based on current demand. The authors' estimation approach, designed for interpretability, achieves better predictions than standard methods in the application.Managerial implications: incorporating the future evolution of demand, driven by community interaction and saturation effects, is key to maximizing access with limited resources. Instead of proportionally assigning more visits to sites with high current demand, a group of sites should be prioritized.Optimal allocation among prioritized sites aims at equalizing demand at the end of the planning horizon. Therefore, more visits should generally be allocated to sites where the cumulative demand potential is higher and counterintuitively, often those where demand is currently lower.