Reciprocal Distribution Calculation Using Transition Probability Matrix
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Solution Overview
Problem
The reciprocal distribution method for cost accounting is computationally intensive and requires high-performance computers, making it impractical for large enterprises due to the complexity and time required for calculating cost allocations between numerous departments.
Innovation Solution
The method employs the limit and convergence of a transition probability matrix to calculate reciprocal distribution costs, using a state-transition matrix approach that doubles the power of the distribution matrix until all elements representing subsidiary department relations converge to zero, significantly reducing calculation time and resource requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the traditional reciprocal distribution method is used for cost accounting, then calculation accuracy is improved, but calculation time and computational resources increase significantly
Solution Approach 1:
The patent transforms the cost accounting problem by changing the mathematical parameters from traditional iterative distribution ratios to transition probability matrix elements. This parameter transformation allows the use of matrix power operations instead of iterative calculations, significantly reducing computation time while maintaining accuracy in cost allocation among departments.
Solution Approach 2:
The patent replaces the mechanical iterative calculation process with a mathematical matrix operation system. By substituting the traditional step-by-step iterative distribution mechanism with matrix power operations and limit calculations, the system achieves the same cost allocation result much faster without requiring high-performance computing resources.
2Loss of information
If the traditional reciprocal distribution method is used for cost accounting, then comprehensive cost information is obtained, but device complexity and computational requirements increase
Solution Approach 1:
The patent changes the computational parameters from iterative distribution coefficients to transition probability matrix elements that converge to a stable limit. This parameter transformation enables the use of standard computers to handle the calculations, as matrix power operations and limit calculations are computationally more efficient than traditional iterative methods, thereby reducing device complexity requirements.
Solution Approach 2:
The patent creates a mathematical model copy of the cost distribution system using transition probability matrices. This abstract mathematical representation allows complex multi-department cost relationships to be calculated through simple matrix operations, avoiding the need for complex computational systems while preserving all cost information.
3Measurement precision
If the traditional reciprocal distribution method is used for cost accounting, then accurate inter-departmental cost allocation is achieved, but productivity decreases due to lengthy calculation processes
Solution Approach 1:
The patent performs preliminary transformation of the cost distribution problem into matrix form before actual calculation. By pre-defining the transition probability matrix and its properties, the system can directly compute the limit through power operations without iterative trials, significantly improving calculation speed while maintaining accurate cost allocation results.
Solution Approach 2:
The patent substitutes the slow mechanical iterative calculation process with fast matrix power operations. This substitution replaces time-consuming step-by-step iterations with efficient linear algebra computations that can be executed rapidly on standard computers, thereby大幅提高 calculation speed while preserving accuracy.
Data Source
AI summary
Provided are a reciprocal distribution calculating method and a reciprocal distribution calculating system for cost accounting, in which, when performing cost accounting using a computer, a reciprocal distribution method is used to effectively perform cost accounting of each department. In the reciprocal distribution calculating method and the reciprocal distribution calculating system for cost accounting, reciprocal distribution costs are calculated using the limit and convergence of a transition probability matrix. And, a reciprocal distribution calculation is performed in a completely different way from the method of calculating reciprocal distribution known for the last several tens of years and in an effective manner, thereby calculation of reciprocal distribution costs at a high speed.