Hierarchical Linear Programming Re-Solves Using Stored Optimal Bases
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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, using the primal and dual simplex methods to maintain optimal solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the supply chain planning problem is re-solved from scratch after minor changes, then the solution is complete and accurate, but the runtime is as long as the initial solution
Solution Approach 1:
The system performs preliminary actions by solving the supply chain planning problem once to obtain the optimal basis, then stores this basis for use in subsequent re-solves. When changes occur, the pre-computed optimal basis serves as a starting point, eliminating the need to restart from scratch and significantly reducing runtime while maintaining solution accuracy.
Solution Approach 2:
The system changes the parameter of using an optimal basis from previous runs as the starting point for re-solving. Instead of starting from a default basis, the system loads the stored optimal basis and adjusts it according to the changes, which transforms the solving process from a complete re-computation to an efficient update operation.
2Loss of time
If the supply chain planning problem is re-solved using the optimal basis from previous runs, then the runtime is significantly reduced, but the system must handle changes in supply chain data
Solution Approach 1:
The system dynamically adapts the optimal basis from previous runs to accommodate changes in supply chain data. When changes occur, the system modifies the stored optimal basis accordingly, allowing it to serve as an effective starting point for re-solves while adapting to the new conditions. This dynamic adjustment maintains both speed and accuracy.
Solution Approach 2:
The system uses feedback from comparing the current supply chain data with historical data to determine what changes have occurred. This feedback mechanism allows the system to identify which parts of the optimal basis need adjustment and applies targeted modifications, ensuring the basis remains valid and effective despite changes in supply chain conditions.
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.