Value of Local Cash Reuse: Inventory Models for Medium-Size Depository Institutions Under the New Federal Reserve Policy

The effective local reuse of physical cash by depository institutions (DIs) is the primary goal of the new cash recirculation policy of the Federal Reserve System (Fed) of the United States. These guidelines, implemented since July 2007, encourage the reuse of cash by (i) penalizing a DI for the practice of <i>cross shipping</i>, the near-simultaneous deposit of used cash to--and withdrawal of fit cash from--the Fed; and (ii) offering a <i>custodial inventory</i> program that enables a DI to transfer fit cash to the Fed's books, but physically hold it within the DI's secured facility. The effective management of the inventory of cash under these new guidelines is both a challenging and important issue for DIs. We introduce two new multiperiod models--designed specifically to capture the operations of a medium-size DI--that emerge from the DI's objective to minimize the total cost incurred in managing the inventory of cash over a finite planning horizon. The Basic Model (BM) captures the DI's mode of operations if it chooses not to locally reuse cash and, instead, incur the cross-shipping penalty. Using two important structural properties, we provide a polynomial-time dynamic programming algorithm for BM. The Reuse Model (RM) represents the DI's actions when it locally recirculates cash. We first prove the hardness of RM and then develop an integer programming formulation. A comprehensive test bed--based on our interaction with a leading secure-logistics provider--helps us to develop several useful insights into the relative impacts of the DI-specific parameters and the Fed's cross-shipping fee on the effective management of cash. In particular, we show that the <i>Value of Local Reuse</i> for a DI, measured as the percentage cost saving between the optimal solutions of BM and RM, is substantial, and we analyze the forces that influence the volume of cross shipping. We also develop a rolling-horizon procedure to adapt the optimal solutions of BM and RM for obtaining near-optimal real-time solutions in the presence of a modest amount of uncertainty. Finally, we provide a comparative analysis of a DI's decisions under the Fed's mechanism and those under a socially optimal mechanism.