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# Intelligent monetary denomination dispensing

IP.com Disclosure Number: IPCOM000125958D
Original Publication Date: 2005-Jun-24
Included in the Prior Art Database: 2005-Jun-24
Document File: 2 page(s) / 28K

IBM

## Abstract

One of the major costs associated with running an ATM machine is refilling the machine with money. Extending this service interval can help make banks more profitable. The problem of choosing denomination of bills can be modeled such that it can be solved using integer linear programming, a specialized branch of mathematics.

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Intelligent monetary denomination dispensing

One of the major costs associated with running an ATM machine is sending a guarded/armored vehicle and team to refill the machine with money. Extending this interval will make banks more profitable. Likewise automated change machines at cash registers save the cashier's time, but they could save even more time if they needed to be refilled less often. The same thing applies to vending machines which give change.

The problem of choosing denomination of bills can be modeled such that it can be solved using integer linear programming, a specialized branch of mathematics. The definition ends up looking like:

Minimize z = ta/aa * a + tb/ab * b + tc/ac * c + td/ad * d + te/ae * e subject to a + 5b + 10c + 20d + 50e=x a >= 0 and integer b >= 0 and integer c >= 0 and integer d >= 0 and integer e >= 0 and integer where x is the amount requested, the variables a,b,c,d, and e are the number of respective denomination of bills to give out. aa, ab, ac, ad, ae are the avilable quantity of each denomination of bills currently in the ATM, and ta,tb,tc,td, and te are the total quantity of each denomination of bills the machine is capable of holding, and z is the goodness value we are optimizing for.

These equations can be solved quickly using standard techniques such as branch and bound or cutting plane, which are not described here as they are standard practice.

As a simple example, consider a theoretical ATM machine which holds 200 o...