  Most solutions to the inventory management problem assume a centralization of
information that is incompatible with organisational constraints in real supply
chain networks. The inventory management problem is a well-known planning
problem in operations research, concerned with finding the optimal re-order
policy for nodes in a supply chain. While many centralized solutions to the
problem exist, they are not applicable to real-world supply chains made up of
independent entities. The problem can however be naturally decomposed into
sub-problems, each associated with an independent entity, turning it into a
multi-agent system. Therefore, a decentralized data-driven solution to
inventory management problems using multi-agent reinforcement learning is
proposed where each entity is controlled by an agent. Three multi-agent
variations of the proximal policy optimization algorithm are investigated
through simulations of different supply chain networks and levels of
uncertainty. The centralized training decentralized execution framework is
deployed, which relies on offline centralization during simulation-based policy
identification, but enables decentralization when the policies are deployed
online to the real system. Results show that using multi-agent proximal policy
optimization with a centralized critic leads to performance very close to that
of a centralized data-driven solution and outperforms a distributed model-based
solution in most cases while respecting the information constraints of the
system.
