## Center for Applied Mathematics Colloquium

Inventory models encompass problems in stochastic control which arise in the optimization of supply chains and logistics networks and are of considerable interest to large companies, such as Amazon and Walmart. Many classical inventory models become notoriously challenging to optimize in the presence of positive lead times, since the state-space blows up and dynamic programming techniques become intractable. In this talk, we present a new algorithmic approach to such problems, which shows that as the lead time grows large, simple heuristics become asymptotically optimal. These results are quite surprising, as this setting had remained an open algorithmic challenge for over forty years. Our results provide a new algorithmic approach to these problems, as well as a solid theoretical foundation for the good performance of these heuristics observed numerically by previous researchers. Our approach combines ideas from the theory of random walks and convexity. The talk will be entirely self-contained, not requiring any specific background in the mathematics of inventories or operations research.