| A significant portion of physical cash is recirculated and reused in an economy. In addition to its various regulatory functions, the Federal Reserve System of the U.S. (Fed) also provides currency services (e.g., separating cash into notes that are fit and unfit for recirculation) to Depository Institutions (DIs; e.g., banks) who, in turn, satisfy the public's demand for cash. In July 2007, the Fed introduced its new recirculation policy for physical cash. The primary aim of this policy is to encourage DIs to reuse the cash deposited (by customers) to meet subsequent demand of cash (from customers). This research addresses novel coordination and optimization problems in the supply chain of physical cash that result from the implementation of the Fed's policy. We first evaluate the efficacy of the Fed's policy to lower the societal cost of providing currency to the public. We show that the policy may not induce DIs' to behave in a manner that the Fed is seeking to engender. Instead, we propose a novel scheme that not only encourages DIs to become more self-reliant, but also rewards those institutions that do more than their fair share of recirculating physical cash. Next, we address the problem of obtaining an efficient operating policy for a DI for managing cash under the Fed's policy. In addition to a set of "good" operating policies, along with their respective domains of optimality, we quantify the monetary impact of recirculation on a DI and assess the extent to which the Fed will achieve its goal of reducing the overuse of its cash processing operations. The Fed's policy has resulted in a new business opportunity, namely fit-sorting cash, for private secure-logistics providers (SLPs). For an SLP, we study the joint pricing of the new fit-sorting service and its traditional service of transporting cash between DIs and the Fed, in the presence of a realistic logistics network of DIs and processing centers that provide these two services. Using a combination of theoretical analysis and computational experiments, we develop several insights into the behavior of the optimal prices and quantify the impact of the logistics network. |
