Supply Chain Multi-Objective Hierarchical LP Re-solving With Basis Reuse
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Solution Overview
Problem
Re-solving supply chain planning problems after minor changes is inefficient, taking as much time as the initial solution, despite known changes.
Innovation Solution
Utilize the optimal basis and variable fixing from a previous solving run to efficiently solve subsequent runs of multi-objective hierarchical linear programming problems, reducing runtime by using the optimal basis and fixing variables to their bounds.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the supply chain planning problem is re-solved from scratch after changes, then the solution is guaranteed to be optimal, but the solving time increases significantly
Solution Approach 1:
The patent performs preliminary actions by solving the supply chain planning problem once to obtain the optimal basis, then reuses this pre-computed optimal basis for subsequent re-solves after changes. This preliminary solution preparation eliminates the need to start from scratch each time, significantly reducing solving time while maintaining optimality through the reuse of the pre-computed optimal basis.
2Adaptability or versatility
If the supply chain planning problem is re-solved after changes, then the solution reflects current conditions, but the computational efficiency decreases
Solution Approach 1:
The patent applies parameter changes by modifying the problem parameters (changes in supply chain conditions) and efficiently re-solving using the optimal basis from the previous solve. The method handles parameter changes systematically, updating only the necessary portions of the solution while maintaining the overall computational efficiency through the reuse of the optimal basis structure.
3Loss of time
If variables are fixed to their bounds using optimal basis information, then the solving time is reduced, but the problem complexity increases
Solution Approach 1:
The patent extracts the optimal basis information from the previous solution and uses it to fix variables to their bounds in subsequent solves. By taking out and reusing the optimal basis, the method reduces the computational complexity of re-solves while maintaining solution quality, as the optimal basis provides a starting point that eliminates the need to search the entire solution space again.
Data Source
AI summary
A system and method efficiently solve subsequent runs of a supply chain planning problem modeled as a multi-objective hierarchical linear programming problem. Embodiments include modeling a supply chain planning problem as a multi-objective hierarchal linear programming problem having first Run1 objectives and based, at least in part, on supply chain input data, receiving one or more changes to the supply chain input data, modeling a second supply chain planning problem based, at least in part, on the one or more changes to the supply chain input data, and modeled as a second multi-objective hierarchal linear programming problem having Run2 objectives, generating a superset matrix, and generating a supply chain plan comprising the one or more changes to the supply chain input data by converting a solution of the second supply chain planning problem.