In this paper, we study the single-item dynamic lot-sizing problem in an environment characterized by stochastic demand and lead times. A recent heuristic called Demand Driven MRP, widely implemented using modern ERP systems, proposes an algorithm that is will effectively tackle this problem. Our primary goal is to propose a theoretical foundation for such a heuristic approach. To this aim, we develop an optimization model inspired by the main principles behind the heuristic algorithm. Specifically, controls are of the type (s(t), S(t)) with time varying thresholds that react to short-run real orders; in this respect, control is risk-based and data-driven. We also consider service levels derived as tail risk measures to ensure fulfillment of realized demand with a predetermined probability; in this respect, our approach is prudential. Finally, we use our model as a benchmark to theoretically validate and contextualize the aforementioned heuristic
