Coefficient Matrix Clustering for Production Slot Scheduling
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Solution Overview
Problem
Existing methods for assigning physical items to production slots using integer programming problems require excessive memory, exceeding the capacity of common computer hardware, necessitating more expensive and sophisticated equipment.
Innovation Solution
The method generates coefficient matrix clusters, reduces non-zero factors within these clusters, and solves programming problems to assign physical items to production slots, thereby reducing memory requirements and avoiding the need for advanced hardware.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If integer programming problems are solved using existing computer hardware, then scheduling optimization can be achieved, but memory requirements exceed the capacity of common hardware
Solution Approach 1:
The patent segments the coefficient matrix into multiple clusters, where each cluster represents a subset of constraints and variables. This segmentation allows the large-scale integer programming problem to be divided into smaller, more manageable clusters that can be processed within the memory limits of common hardware, thereby resolving the contradiction between achieving scheduling optimization and managing memory requirements.
Solution Approach 2:
The patent introduces a new dimension of clustering organization by grouping coefficients spatially into clusters rather than treating them as a flat matrix. This dimensional reorganization enables efficient memory management by allowing selective loading and processing of cluster subsets, reducing the peak memory footprint while maintaining the ability to solve the overall scheduling optimization problem.
2Quantity of substance
If more sophisticated and expensive hardware is used to solve IP problems, then memory capacity increases, but cost increases
Solution Approach 1:
By segmenting the coefficient matrix into clusters, the patent enables common hardware with limited memory capacity to handle large-scale IP problems. The segmentation allows the system to process clusters incrementally rather than requiring all coefficients to reside in memory simultaneously, thus avoiding the need for sophisticated high-capacity hardware.
Solution Approach 2:
The patent creates compressed representations of coefficient clusters that can be stored and processed efficiently. By working with clustered subsets rather than the complete matrix, the system effectively creates manageable copies of the problem data that fit within standard hardware memory, eliminating the need for expensive hardware upgrades.
3Measurement precision
If the complete coefficient matrix is processed, then optimal scheduling solution is achieved, but processing time and memory usage increase
Solution Approach 1:
The patent segments the coefficient matrix into clusters that can be processed in smaller batches. This segmentation maintains solution optimality by ensuring all constraints are ultimately considered, while reducing processing time through incremental cluster-by-cluster evaluation rather than requiring the entire matrix to be loaded and processed simultaneously.
Solution Approach 2:
The patent performs preliminary clustering and organization of coefficients before the main optimization process. By pre-grouping coefficients into meaningful clusters and identifying their relationships in advance, the system prepares the data structure to enable faster subsequent processing while maintaining the completeness needed for optimal solutions.
Data Source
AI summary
A schedule is generated by which physical items to be manufactured are assigned into production slots. The physical items have constraints governing manufacture of the physical items. The method generates coefficient matrix clusters from a mathematical programming problem based on an actual scheduling problem. Each coefficient matrix cluster defines a variable cluster-constraint cluster pair. A variable cluster of each coefficient matrix cluster defines production slot-physical item pairs. A constraint cluster of each coefficient matrix cluster defines a group of constraints. Each coefficient matrix cluster includes coefficient-binary variable pairs, each pair having a binary variable multiplied by a coefficient. For each coefficient matrix cluster, the method reduces non-zero factors within the cluster. Each non-zero factor within the coefficient matrix cluster is defined as a coefficient-binary variable pair such that the binary variable of the pair multiplied by the coefficient of the pair is non-zero. The schedule is then generated.