A Multiechelon Inventory Problem with Secondary Market Sales

Abstract

We consider a finite-horizon, multiechelon inventory system in which the surplus of stock can be sold (i.e., disposed) in the secondary markets at each stage in the system. What are called nested echelon order-up-to policies are shown to be optimal for jointly managing inventory replenishments and secondary market sales. Under a general restriction on model parameters, we establish that it is optimal not to both sell off excess stock and replenish inventory. Secondary market sales complicate the structure of the system, so that the classical Clark and Scarf echelon reformulation no longer allows for the decomposition of the objective function under the optimal policy. We introduce a novel class of policies, referred to as the disposal saturation policies, and show that there exists a disposal saturation policy, determined recursively by a single base-stock level at each echelon, that achieves the decomposition of this problem. The resulting optimal replenishment policy is shown to be the echelon base-stock policy. We demonstrate the heuristic performance of this disposal saturation policy through a series of numerical studies: except at extreme ranges of model parameters, the policy provides a very good approximation to the optimal policy while avoiding the curse of dimensionality. We also conduct numerical studies to determine the value of the secondary markets for multistage supply chains and assess its sensitivity to model parameters. The results provide potentially useful insights for companies seeking to enter or develop secondary markets for supply chains. This paper was accepted by Martin Lariviere, operations management.

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