Dynamic Allocation of Scarce Resources Under Supply Uncertainty

Abstract

We present a model of dynamic resource allocation in a setting where continuity of service is important and future resource availability is uncertain. The paper is inspired by the challenges faced by HIV clinics in resource-limited settings in the allocation of scarce HIV treatment among a large pool of eligible patients. Many clinics receive insufficient supply to treat all patients and the supply they do receive is highly uncertain. This supply uncertainty, combined with the clinical importance of an uninterrupted treatment throughout patients’ life, requires the clinics to make a trade-off between providing access to treatment for new patients and ensuring continuity of treatment for current patients. Setting aside other aspects of the treatment rationing problem, we model the decisions of a clinic facing this trade-off using stochastic dynamic programming. We derive sufficient conditions under which the optimal policy coincides with the clinically preferred policy of prioritizing previously enrolled patients. We use numerical examples to investigate the impact of supply uncertainty on the performance of enrollment policies used in practice. We also discuss how our model applies to other intertemporal resource allocation decisions such as that faced by non-profit organizations where continuity of service is crucial to meeting the organization’s social objective, or that faced by an entrepreneur who wants to attract new customers without reducing service quality to existing customers.

Keywords: inventory rationing, HIV, supply uncertainty