Patient-based pharmaceutical inventory management: a two-stage inventory and production model for perishable products with Markovian demand

Drug shortages have increased over the past decade, tripling since 2006. Pharmacy material managers are challenged with developing inventory policies given changing demand, limited suppliers, and regulations affecting supply. Pharmaceutical inventory management and patient care are inextricably linked; suboptimal control impacts both patient treatment and the cost of care. We study a perishable inventory problem motivated by challenges in pharmaceutical management. Inpatient hospital pharmacies stock medications in two stages, raw material and finished good (e.g. intravenous). While both stages of material are perishable, the finished form is highly perishable. Pharmacy demand depends on the population and patient conditions. We use a stochastic ‘demand state’ as a surrogate for patient condition and develop a Markov decision process to determine optimal, state-dependent two-stage inventory and production policies. We define two ordering and production scenarios, prove the existence of optimal solutions for both scenarios, and apply this framework to the management of Meropenem.