  A key challenge in inventory management is to identify policies that
optimally replenish inventory from multiple suppliers. To solve such
optimization problems, inventory managers need to decide what quantities to
order from each supplier, given the net inventory and outstanding orders, so
that the expected backlogging, holding, and sourcing costs are jointly
minimized. Inventory management problems have been studied extensively for over
60 years, and yet even basic dual-sourcing problems, in which orders from an
expensive supplier arrive faster than orders from a regular supplier, remain
intractable in their general form. In addition, there is an emerging need to
develop proactive, scalable optimization algorithms that can adjust their
recommendations to dynamic demand shifts in a timely fashion. In this work, we
approach dual sourcing from a neural network--based optimization lens and
incorporate information on inventory dynamics and its replenishment (i.e.,
control) policies into the design of recurrent neural networks. We show that
the proposed neural network controllers (NNCs) are able to learn near-optimal
policies of commonly used instances within a few minutes of CPU time on a
regular personal computer. To demonstrate the versatility of NNCs, we also show
that they can control inventory dynamics with empirical, non-stationary demand
distributions that are challenging to tackle effectively using alternative,
state-of-the-art approaches. Our work shows that high-quality solutions of
complex inventory management problems with non-stationary demand can be
obtained with deep neural-network optimization approaches that directly account
for inventory dynamics in their optimization process. As such, our research
opens up new ways of efficiently managing complex, high-dimensional inventory
dynamics.
