Parallel Hierarchical Linear Programming for Supply Chain Re-Solving
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Solution Overview
Problem
Solving multi-objective hierarchical linear programming problems (LPPs) in sequence results in significant processing times, making it difficult to quickly respond to changes in the supply chain and incurring high costs when using cloud-based infrastructure.
Innovation Solution
Solving objectives of a multi-objective LPP in parallel while using previous solves as starting solutions, storing these solutions, and continuing the process until all objectives are solved, thereby reducing processing time without impairing the quality of the calculated plan.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If multi-objective hierarchical LPPs are solved in sequence, then the objectives are solved correctly with proper dependence handling, but the processing time becomes significant and response to supply chain changes is slow
Solution Approach 1:
The patent applies preliminary action by solving subsequent objectives in advance using relaxed bounds from the current objective, storing these preliminary solutions. When the current objective is solved, these pre-computed solutions can be quickly adjusted and used, eliminating the need to wait for sequential completion of each objective.
Solution Approach 2:
The patent introduces a new dimension of computation by solving objectives in parallel across different computational threads rather than sequentially in a single thread. This dimensional change from sequential to parallel processing allows multiple objectives to be solved simultaneously, dramatically reducing total processing time while maintaining correctness through proper bound propagation.
2Productivity
If multi-objective hierarchical LPPs are solved in sequence, then computational resources are used efficiently, but the ability to quickly respond to supply chain changes is impaired
Solution Approach 1:
The patent segments the multi-objective LPP solving process into independent parallel tasks. Each subsequent objective is solved as a separate computational task that can run in parallel with the current objective, using the bounds from the current objective as constraints. This segmentation enables parallel processing while maintaining the hierarchical dependence structure.
3Loss of time
If cloud-based infrastructure is used to solve LPPs sequentially, then computational power is sufficient, but costs become significant due to prolonged processing time
Solution Approach 1:
The patent ensures continuity of useful action by keeping multiple computational threads actively solving different objectives simultaneously rather than having them wait in sequence. Each thread continuously performs useful computation on its assigned objective using available bounds, maximizing resource utilization and reducing total cloud infrastructure time requirements.
Data Source
AI summary
A system and method are disclosed for solving a multi-objective linear programming supply chain problem. Embodiments include defining a hierarchy of objectives of a supply chain problem, executing a first thread as a mainline solve of a first objective and executing secondary threads as auxiliary solves of additional objectives and determining if a next objective has been solved by the auxiliary solves in response to the first objective being solved. Embodiments further include using the auxiliary solve of a next objective as a starting solution for a mainline solve of the next objective, using a solution from a previous solved mainline objective as a starting solution for a mainline solve of the next objective in response to the next objective of the hierarchy not being solved by the auxiliary solves, and repeating the determining and using steps to solve each objective in the hierarchy.