Parallel Hierarchical Linear Programming for Supply Chain Replanning
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Solution Overview
Problem
Solving multi-objective hierarchical linear programming problems in supply chain planning sequentially results in significant processing times, making it difficult to quickly respond to changes and incurring high costs when using cloud-based infrastructure.
Innovation Solution
Solve the objectives of a multi-objective linear programming problem in parallel, using starting solutions derived from previous objectives to reduce processing time and maintain solution quality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multi-objective hierarchical linear programming problems are solved sequentially, then solution quality is maintained, but processing time increases significantly
Solution Approach 1:
The patent applies preliminary action by solving relaxed versions of subsequent objectives in advance before the main sequential solving process begins. These preliminary solutions serve as starting points that reduce the computational effort needed during the main solving process, thereby decreasing overall processing time while maintaining solution quality.
Solution Approach 2:
The patent implements dynamics by adaptively adjusting the solving strategy based on problem characteristics. The system dynamically determines whether to use parallel preprocessing for subsequent objectives based on the specific problem structure, allowing flexibility in balancing computation time and solution quality for different supply chain planning scenarios.
2Measurement precision
If multi-objective hierarchical linear programming problems are solved sequentially, then solution accuracy is preserved, but response time to supply chain changes decreases
Solution Approach 1:
The patent applies preliminary action by pre-solving relaxed versions of subsequent objectives to generate initial feasible solutions. These preliminary solutions are then used as starting points in the main sequential solving process, enabling faster convergence to accurate solutions and thereby improving response time to supply chain changes while preserving solution accuracy.
Solution Approach 2:
The patent uses copying by creating simplified copies (relaxed versions) of subsequent objectives that can be solved in advance. These copied problems have fewer constraints but preserve the essential structure, allowing rapid generation of starting solutions that accelerate the main solving process without compromising the accuracy of the final solution.
3Loss of energy
If multi-objective hierarchical linear programming problems are solved sequentially, then computational resources are used efficiently, but processing time increases
Solution Approach 1:
The patent applies segmentation by dividing the solving process into distinct phases: a preprocessing phase where relaxed versions of subsequent objectives are solved, and a main phase where the full sequential solving occurs. This segmentation allows computational resources to be distributed more effectively, with less intensive computations performed in advance and the main computational effort focused on refining solutions with guaranteed optimality.
Solution Approach 2:
The patent applies preliminary action by performing preliminary computations on relaxed versions of subsequent objectives before the main solving process. This preliminary action reduces the computational burden during the main phase by providing warm-start solutions, thereby decreasing total processing time while maintaining efficient resource utilization through strategic placement of computational efforts.
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.