Adaptive Lagrangian Policies for a Multiwarehouse, Multistore Inventory System with Lost Sales

Adaptive Lagrangian Policies for Inventory Control Consider the problem of managing inventory in a multiwarehouse, multistore setting where each store can be periodically replenished from potentially a set of nearby warehouses. This is a practically relevant problem, and its optimal policy is not easy to compute because of the curse of dimensionality. Existing works in the literature have proposed a policy based on Lagrangian relaxation of the original stochastic problem. This vanilla policy applies the control parameters derived from the Lagrangian model and has been shown to perform well in some cases. In “Adaptive Lagrangian Policies for a Multiwarehouse, Multistore Inventory System with Lost Sales,” we go one step farther and develop adaptive Lagrangian policies that update (at certain update times) the control parameters of the vanilla policy based on the historical demand realizations. We analytically show that our proposed adjustment significantly improves the performance of the vanilla policy.