Coordination under Unknown Demand Distribution : Online Learning for Two-Echelon Supply Chains

In the literature on supply chain management (SCM), the multi-echelon stochastic inventory models with known demand distributions have played a fundamental role for developing firms’ collaborative strategies, including the optimal policy to maximize efficiency of the centralized supply chain (the ``first-best” policy) and contract design in the decentralized supply chain such that the self-interested parties are incentivized to adopt the first-best policy (supply chain is ``coordinated"). In this work, we extend the classic two-echelon inventory problem to an online setting with an unknown demand distribution and then re-examine the optimal inventory control and supply chain coordination problems. The new setting brings two novel challenges. (1) Since the upstream firm only observes orders from the downstream firm, it does not necessarily receive the true demand information, which is aggravated by the online setting as the downstream firm may experiment with different policies facing the unknown demand distribution. (2) The above issue is compounded by the complex inventory interactions due to the multi-echelon nature of the system, as the downstream firm’s inventory level can be impacted by the upstream firm’s shortages. For the centralized system, we design algorithms based on Online Newton Step with the low-switching (``lazy-update”) property to achieve convergence to the first-best policy. For the decentralized system, our algorithms, together with a protocol for learning the optimal contract parameter value, also achieve favorable guarantees for individual regret and convergence to the first-best decisions such that the supply chain is coordinated