Article Preview
TopIntroduction
The major banks in the United States own cash distribution centers called vaults. A vault is a large warehouse with no windows and lots of security. Deposits and withdrawals are made using armored vehicles carrying millions in cash. Vaults contain equipment that counts, sorts, and packages currency for redistribution. The fit currency can be distributed to their branch banks, can be used to supply ATMs, or can be returned to the Fed. Currency that is determined to be unfit for further circulation is returned to the Fed for destruction. Large national banks have created a network of cash warehouses (vaults) to manage their cash requirements.
Vaults may experience either a deficit or a surplus of currency of the various denominations. In the past, the Fed supplied deficits and accepted surplus cash from the various vaults at a nominal fee. Beginning in July 2007, the Fed imposed penalties on certain types of cash transfers called cross-shipping fees. Since counterfeit bills are usually 100s and 50s, these were excluded from cross-shipping fees. That is, the Fed wants to continue frequent checks of these denominations so that counterfeit bills could be quickly removed from circulation. For other denominations, cross-shipping fees apply when both an order and a deposit occur during the same week. That is, placing an order for 20s on Monday and making a deposit of 20s on Thursday results in a cross-shipping fee on the smaller of the two transactions.
In order to help the vaults avoid excessive cross-shipping fees, the Fed allows a vault to designate a certain area with a given capacity for what is known as custodial inventory. Any currency placed in custodial inventory belongs to the Fed but is physically located at the vaults. The advantage to the vault is that this currency has been taken off the books of the vault and essentially returned to the Fed. In addition, the Fed excuses a certain amount of cross-shipping without penalty during each quarter. This value is known as de minimus (Fedfocus, 2007). Suppose de minimus is 20 million for a given vault. Then no cross-shipping penalty is paid until the 20 million in cross-shipping transactions is exceeded during the current quarter.
Fiserv Corporation is a major player in banking software. One of their products, iCom, helps banks manage the logistics of cash with respect to vaults, branches, and ATMs. In 2005 they began to develop a new module that would optimize logistical operations at vaults under the new cross-shipping environment to be imposed in the summer of 2007. This manuscript presents the linear multi-commodity integer programming model developed to support the logistical operations of their clients. This model is written in OPL 5.0 (http://www.ilog.com/products/cplex/). solver. The optimization model was implemented as a new module within iCom and was used in a six month pilot study by one of their bank clients. Since computational time is a major issue for this project, we also developed a new heuristic that mitigates the computational time issue.
Due to the different possible combinations of cash transfers that can occur, certain assumptions were made in the model. Any cash transfer from the Fed on a particular day is available at the vault on the same day for distribution. A cash transfer between vaults on the same day implies the cash is available at the destination vault on that day. A one day cash transfer between vaults implies that the money is available on the very next day at the destination vault for distribution. The upper bound on the bundles of cash that can be transferred is infinity, i.e. there are always trucks available for cash transfers. The variable cost on cash transfers is linear.