A Non-Parametric Learning Algorithm for a Stochastic Multi-Echelon Inventory Problem

We consider a periodic-review single-product multi-echelon inventory problem with instantaneous replenishment. In each period, the decision-maker makes ordering decisions for all echelons. Any unsatisfied demand is backordered, and any excess inventory is carried to the next period. In contrast to the classic inventory literature, we assume that the information of the demand distribution is not known a priori, and the decision-maker observes demand realizations over the planning horizon. We propose a non-parametric algorithm that generates a sequence of adaptive ordering decisions based on the stochastic gradient descent method. We compare the T-period cost of our algorithm to the clairvoyant, who knows the underlying demand distribution in advance, and we prove that the expected T-period regret is at most O( √ T), matching a lower bound for this problem