A Dynamic Inventory Rationing Model for Last-Mile Delivery of Medication in Liberia's Community Health Program

Baris Ata, Yufan Chen, Robert Montgomery

We study the dynamic allocation of scarce medications in Liberia's community health program. A central warehouse supplies a health facility and the Community Health Assistants (CHAs) it supervises. When a CHA runs out of medication, patients are referred to the facility, incurring travel costs if they complete the referral and remain untreated otherwise. Allocating inventory to CHAs allows more patients to receive treatment without traveling, while retaining inventory centrally preserves flexibility to respond to uncertain demand. The allocation problem must balance these considerations while accounting for fairness across locations. We formulate this problem as a finite-horizon stochastic control problem whose objective combines the costs of referrals and untreated patients with a demand-weighted fairness utility. Because standard dynamic programming methods are computationally intractable in this setting, we develop a continuous-time approximation that involves controlling the drift rate of a reflected Brownian motion. We then adapt the deep splitting method, using deep neural networks to approximate the value function and its gradient and compute a dynamic allocation policy.…