Cash Replenishment Algorithm for ATMs Using Linear Equation Solutions
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Solution Overview
Problem
Existing banknote-dispensing methods in financial self-service equipment face inefficiencies due to long calculation times and low dispensing efficiency, especially with multiple denominations, as they rely on exhaustive search algorithms.
Innovation Solution
A method that calculates the general solution of a linear indeterminate equation with integer coefficients to quickly determine the number of banknotes to dispense for each denomination, using the greatest common divisor and specific banknote-dispensing principles to optimize the dispensing process, reducing the need for exhaustive searches.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If exhaustive search is performed to find all banknote-dispensing schemes, then completeness of dispensing schemes is improved, but dispensing time increases significantly
Solution Approach 1:
The patent transforms the banknote dispensing problem from an exhaustive search approach to a mathematical equation solving approach. By changing the parameter representation from discrete combination enumeration to continuous variable equations with integer constraints, the system achieves both completeness and efficiency. The linear indeterminate equation with integer coefficients captures all possible dispensing schemes while allowing mathematical solution methods to find them systematically without brute-force enumeration.
2Adaptability or versatility
If the number of denominations in the self-service equipment increases, then the versatility of the equipment is improved, but the calculating time increases
Solution Approach 1:
The patent segments the complex multi-denomination dispensing problem into a structured mathematical framework. By representing each denomination as a separate variable in a linear equation system, the problem is divided into manageable components that can be solved systematically. This segmentation allows the system to handle any number of denominations by simply adding more variables to the equation rather than exponentially increasing computational complexity.
Solution Approach 2:
The patent replaces the mechanical exhaustive search algorithm with a mathematical substitution approach. Instead of mechanically enumerating all possible combinations, the system uses algebraic substitution and elimination methods to solve for the unknown quantities of each denomination. This substitution of computational mechanics dramatically reduces calculating time while maintaining completeness.
3Measurement precision
If exhaustive search is used to ensure all practicable schemes are found, then accuracy of dispensing solution is improved, but dispensing efficiency decreases
Solution Approach 1:
The patent incorporates feedback mechanisms through the mathematical constraint system. The linear indeterminate equation with integer coefficients provides continuous feedback about valid dispensing combinations, allowing the system to verify accuracy through mathematical consistency rather than exhaustive verification. The constraints on variables (non-negative integers within available banknote limits) provide built-in validation that ensures accurate solutions without requiring complete enumeration of all possibilities.
Data Source
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AI summary
A cash replenishment method for financial self-service equipment. The method comprises: by using a general solution method for directly solving an integral solution of a linear equation with n unknowns, obtaining a general solution formula of the integral solution of the linear equation with n unknowns; then, in accordance with a principle that the cash replenishment amount of each denomination must be greater than zero and less than the number of remaining available banknotes of this denomination in self-service equipment, solving a limiting range of free factors in the general solution formula, so that all cash replenishment solutions are obtained; and lastly, in accordance with a cash replenishment principle of a self-service equipment system, obtaining an optimal cash replenishment solution. The cash replenishment method can find out all cash replenishment solutions without using an exhaustive attack method, and can achieve rapid and highly-efficient cash replenishment.