Parallel Hierarchical Linear Programming With Auxiliary Warm Starts
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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 increases significantly
Solution Approach 1:
The patent performs preliminary actions by solving objectives in parallel before the previous objective is fully solved, using the current bounds as placeholders. This allows subsequent objectives to be prepared in advance, reducing the overall processing time while maintaining correctness through iterative refinement once dependencies are resolved
Solution Approach 2:
The system dynamically adjusts the solving process by allowing objectives to be solved in parallel when possible, and sequentially when dependencies require it. The bounds and solutions are dynamically updated and refined through multiple iterations, transitioning between parallel and sequential processing based on the current state of objective dependencies
2Manufacturing precision
If multi-objective hierarchical LPPs are solved in sequence, then the solution quality is maintained, but the cost of cloud-based infrastructure increases
Solution Approach 1:
By performing preliminary parallel solves of subsequent objectives using current bounds as placeholders, the system reduces the total computational workload that needs to be performed sequentially. This preliminary action allows for more efficient use of cloud infrastructure resources while maintaining solution quality through iterative refinement
Solution Approach 2:
The system changes parameters by allowing bounds to be provisional and subject to update. Instead of requiring fixed, final bounds before solving each objective, the system accepts approximate bounds and refines them through multiple iterations, enabling parallel processing that reduces computational costs
3Productivity
If objectives are solved in parallel, then processing time is reduced, but the complexity of managing dependencies increases
Solution Approach 1:
The patent segments the solving process into independent parallel tasks that can be executed simultaneously. Each objective is treated as a separate task that can be solved in parallel with others, with dependency management handled through structured bound propagation and iterative refinement rather than complex inter-task coordination
Solution Approach 2:
The bounds serve as intermediaries that carry information between objectives. Instead of direct complex dependencies between objective solutions, the bounds act as a mediator that transmits constraints and information, simplifying the management of inter-objective relationships while enabling parallel processing
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.