Graph Partitioning for Manufacturing Scheduling Sub-problems
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Solution Overview
Problem
Large manufacturing scheduling problems with numerous stations and tasks are computationally intensive, making them difficult to solve directly due to the vast number of variables and factors involved, leading to inefficiencies in traditional scheduling systems.
Innovation Solution
A method and system that splits scheduling problems into sub-problems using a graph partitioning approach with a cut algorithm, identifying task exceptions and reducing computational resources required by converting the problem into smaller, manageable sub-graphs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional scheduling systems attempt to solve large scheduling problems directly, then comprehensive scheduling coverage is achieved, but computational time and resources increase significantly
Solution Approach 1:
The patent divides a large scheduling problem into multiple smaller sub-problems by partitioning the set of tasks and stations into disjoint subsets. Each sub-problem can be solved independently and more efficiently, then the solutions are integrated to form the complete schedule. This segmentation reduces computational complexity while maintaining comprehensive scheduling coverage.
2Productivity
If the size of scheduling problem increases, then more tasks and stations can be managed, but difficulty of solving grows very fast
Solution Approach 1:
The system segments the large scheduling problem into smaller sub-problems that can be solved independently. By partitioning tasks and stations into subsets, each sub-problem has reduced complexity that can be managed by existing scheduling algorithms, thereby enabling the system to handle larger overall problems without exponential growth in solving difficulty.
Solution Approach 2:
The patent transforms the original scheduling problem into a graph problem where tasks and stations become nodes and dependencies become edges. This dimensional transformation allows the application of graph partitioning algorithms to divide the problem, converting a complex combinatorial optimization problem into a more manageable graph theory problem that can be solved more efficiently.
3Reliability
If comprehensive scheduling of all tasks and stations is attempted, then complete schedule is produced, but computational resources are excessively consumed
Solution Approach 1:
The patent partitions the scheduling problem into multiple independent sub-problems that can be solved in parallel or sequentially with reduced computational resource requirements. Each sub-problem involves a smaller subset of tasks and stations, requiring fewer computational resources while the collection of all sub-problem solutions provides complete schedule coverage.
Data Source
AI summary
A computing system receives user input of scheduling problem data. The scheduling problem data relates to a scheduling problem and includes one or more stations and tasks to be performed by at least one station. The computing system constructs a graph problem using the scheduling problem data. The graph problem includes a graph. The computing system cuts the graph into sub-graphs using a cut algorithm to create a cut result that satisfies a threshold and identifies one or more task exceptions from the sub-graphs in the cut result. The one or more task exceptions are tasks that can be assigned to more than one sub-graph. The computing system creates scheduling sub-problems pertaining to the one or more task exceptions using the cut result.