A State-Dependent Riccati Equation Index Policy for Dynamic Production Sequencing in Compounding Pharmacies

Abstract

When patients require personalized medications or medications that are otherwise unavailable, e.g., due to patients’ allergies or drug shortages, retail pharmacies must rely on compounding pharmacies that produce medications to order. Inspired by discussions with the management team of a compounding pharmacy, this project aims to improve timely access to compounded medications through the development of a dynamic production control policy designed to minimize the time between the prescription request and when the medication is ready. We propose and evaluate a novel and theory-driven heuristic policy based on a fluid model of production dynamics paired with a State-Dependent Riccati Equation controller, lightly modified for use as a value function approximation technique, which serves as the basis of an easily implementable index policy. Numerical studies suggest that for large systems this heuristic is within 11% of a lower bound on waiting cost per unit time within a representative fluid setting demonstrating strong theoretical performance. Within a data-driven simulation with more than 1000 unique medications where arrival rates are dynamic and must be estimated, a hybrid policy combining an age-limit with the proposed heuristic can reduce the average cost of waiting time by 32.5% compared to the status-quo oldest request sequencing policy without increasing worst case delays. The proposed heuristic thus contributes a novel and easily implementable approach to production sequencing within compounding pharmacies and a generalizable approach to challenging multiproduct production management problems where optimal policies are intractable.