Managing Coins for Depository Institutions in Coin Supply Chains for Improved Circulation

Abstract

We study the U.S. Coin Supply Chain from both the demand and supply side perspectives to improve coin circulation in the economy. More specifically, we provide an operating policy for Depository Institutions (DIs) to improve their efficiency in packaging, distributing, coordinating, and managing the inventory of coins. We further propose a new policy (via a Rewards Program) to increase coin circulation in the economy and optimally determine a reward price, which, if implemented by the Federal Reserve System (FRS), can incentivize DIs to process the coins themselves and/or frequently deposit excess coins at the FRS. We identify the structures of DIs’ best response to the reward price and FRS’s optimal pricing policy. The results and insights developed in this study can be beneficial to both the FRS and DIs in increasing the efficiency of the nation’s coin circulation and thereby reducing their operating costs. Additionally, to estimate the societal benefit from the Rewards Program, we formulate the coin flow for an entire FRS region as an optimization problem from the supply side perspective and quantify the societal costs (and benefits) with and without the reward. We show via numerical experiments that both the FRS and Dis reduce their operating costs as a result of the program and produce a surplus benefit for the society. The reward price that maximizes this surplus is determined optimally. We also propose a robust optimization framework to help DIs and the FRS to manage their inventory under uncertain demand while attaining their cost reduction goals.