Partial Contribution Computation in ABC/M Cost Flow Models
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Solution Overview
Problem
Traditional cost flow models, such as activity-based costing and management systems, face challenges in accurately calculating costs due to self-contributions and double-counting issues, especially in cyclic graphs, leading to inflated and meaningless results.
Innovation Solution
A computer-implemented system and method that generates a system of linear equations based on cost flow model data, excluding relationships that satisfy a removal criteria, and solves for contribution values by removing out-edges from target nodes to prevent double-counting and self-contribution, thereby providing accurate partial contribution computations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional cost flow models include all relationships in the graph, then complete cost flow coverage is achieved, but self-contributions and double-counting occur leading to inflated results
Solution Approach 1:
The patent extracts and removes specific relationships (out-edges from target nodes) from the cost flow graph that cause self-contribution and double-counting problems. By selectively removing these problematic edges while retaining necessary cost flow relationships, the system eliminates harmful self-loops and redundant paths, thereby preventing inflated cost calculations while maintaining accurate cost allocation.
Solution Approach 2:
The patent segments the cost flow calculation process into distinct phases: identifying target nodes, removing their out-edges, solving the linear system, and allocating costs. This segmentation allows the system to handle complex reciprocal relationships by breaking them into manageable steps, where each phase addresses specific aspects of the cost flow problem without interference from self-contribution issues.
2Reliability
If all relationships are included in the system of equations, then complete cost allocation is achieved, but calculation complexity and computational burden increase
Solution Approach 1:
The patent extracts and removes unnecessary relationships (out-edges from target nodes) from the system of equations before solving. This extraction reduces the number of variables and equations in the linear system, thereby decreasing computational complexity and solving time while still achieving complete and accurate cost allocation for all entities in the cost flow graph.
3Ease of operation
If traditional methods are used for reciprocal relationships, then simple calculation procedures are maintained, but cost calculations appear abnormally large due to self-contributions
Solution Approach 1:
The patent removes out-edges from target nodes before solving the cost allocation problem, which eliminates self-contribution paths while maintaining a relatively simple linear system solution approach. This extraction modifies the graph structure to prevent harmful cycles and self-loops, allowing the use of straightforward linear algebra methods while achieving accurate cost calculations without abnormal inflation.
Solution Approach 2:
The patent performs preliminary modification of the cost flow graph by removing problematic out-edges from target nodes before initiating the cost allocation calculation. This preliminary action prevents self-contribution and double-counting issues from occurring during the calculation process, thereby ensuring accurate results while maintaining operational simplicity through a pre-conditioned graph structure.
Data Source
AI summary
Computer-implemented systems and methods for analyzing costs associated with a cost flow model having components of relationships and entities. A system and method can be configured to receive a data associated with the cost flow model as well as source-entity definitions, via-entity sets, and target-entity definitions. A set of linear equations is created that is representative of the costs and entity relationships, wherein data about certain relationships satisfying a removal criteria are not included in the matrices. The system of linear equations is solved to determine contribution values from the source entities to the target entities through the via-sets.