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

Abstract

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 cross shipping, the near-simultaneous deposit of used cash to—and withdrawal of fit cash from—the Fed; and (ii) offering a custodial inventory 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 Value of Local Reuse 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.

A Review of Operational Issues in Managing Physical Currency Supply Chains

“…Section 4.2 considers the problems faced by large US banks (Geismar et al 2007). Zhu et al (2011), discussed in section 4.3, studies the operations of medium-sized US banks. (Small commercial banks are exempted from the US Federal Reserve 2007 Cash Recirculation Policy because of their low transaction volume.)…”

“…Moreover, medium-size banks have a significantly different cost structure: there is only a fixed-cost for ordering transportation, but there are both a setup cost and a perbundle cost for fit-sorting. Zhu et al (2011)'s Basic Model (BM) captures the bank's mode of operations if it chooses not to locally reuse banknotes and, instead, incurs the cross-shipping penalty (see Figure 6a). An optimal solution to BM has two important structural properties regarding fit-banknote withdrawal and usedbanknote deposit: (i) the withdrawal of fit banknotes only occurs when the fit-banknote inventory becomes 0 (an analog of Wagner and Whitin 1958) and (ii) the bank deposits either none or all of its used-banknote inventory.…”

“… Appendix S1: Devising Optimal Security Policies for a Banknote Supply Chain while Considering Transportation, Insurance, and Inventory Holding Costs. Appendix S2: A Multiple Denomination Extension of Zhu et al (). Appendix S3: A Stochastic Extension of Zhu et al ().…”

“…Appendix S2: A Multiple Denomination Extension of Zhu et al (). Appendix S3: A Stochastic Extension of Zhu et al (). Appendix S4: A Route‐First/Cluster‐Second Heuristic for Risk‐Constrained Cash‐In‐Transit Vehicle Routing Problem.…”

Managing Logistics in Regional Banknote Supply Chain Under Security Concerns

“…For exam-ple, Rajamani et al (2006) describe the Fed's currency recirculation guidelines and model the US Cash Supply Chain as a closed-loop supply chain. Next, the impact of the Fed's recirculation policy on the currency supply operations has been studied by Geismar et al (2007), Dawande et al (2010), Mehrotra et al (2010Mehrotra et al ( , 2012, and Zhu et al (2011). Hatzakis et al (2010) provide an excellent review of the recent work on operations in the financial services.…”