Multi-Objective Hierarchical Linear Programming Solver Update
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Solution Overview
Problem
Re-solving supply chain planning problems modeled as multi-objective hierarchical linear programming problems can be inefficient, even with minor changes, as the process takes as long as the initial solution, despite only a few known changes.
Innovation Solution
The system uses the optimal basis and variable bounds from a previous solving run to efficiently update subsequent solving runs by iteratively solving each objective, using primal and dual simplex methods to maintain primal and dual feasibility, and categorizing changes as primal or dual feasibility changes to apply them efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the supply chain planning problem is re-solved from scratch when changes occur, then the solution accuracy is maintained, but the solving time increases significantly
Solution Approach 1:
The patent performs preliminary action by solving the supply chain planning problem once to obtain the optimal basis and variable bounds before changes occur. When changes happen, the pre-computed optimal basis is used as a starting point for updating, avoiding the need to solve from scratch. This preliminary solution structure is stored and reused to accelerate subsequent solving operations while maintaining solution accuracy.
Solution Approach 2:
The patent creates a copy of the optimal basis and variable bounds from the initial solution and uses this copied structure as the foundation for subsequent updating operations. Instead of discarding the initial solution structure, it is replicated and adapted to incorporate changes efficiently, preserving the computational work already performed while adapting to new conditions.
2Reliability
If the complete re-solving process is used for minor changes, then solution optimality is ensured, but computational efficiency deteriorates
Solution Approach 1:
The patent segments the solving process into two distinct phases: (1) a complete solve to establish the optimal basis and variable bounds, and (2) an efficient updating phase that only processes changes. The updating phase further segments changes into primal feasibility changes and dual feasibility changes, handling each type separately using appropriate methods. This segmentation allows the system to maintain optimality through structured updates while dramatically improving computational efficiency for minor changes.
Solution Approach 2:
The patent applies partial action by performing only the necessary updating operations rather than complete re-solving. When changes occur, the system applies partial updates to the optimal basis and variable bounds, processing only the affected portions of the problem. This partial action approach maintains solution optimality for the changed elements while avoiding the excessive computational effort of complete re-solving.
3Speed
If iterative updating with simplex methods is used, then solving speed improves, but algorithmic complexity increases
Solution Approach 1:
The patent utilizes parameter changes by modifying the optimal basis and variable bounds parameters iteratively using primal and dual simplex methods. Instead of changing the entire problem structure, the algorithm makes targeted parameter adjustments to the basis matrix and bound values based on the specific changes detected. This parameter-focused approach accelerates solving by working with existing solution parameters rather than rebuilding the entire solution from scratch.
Data Source
AI summary
A system and method are disclosed for solving subsequent runs of a supply chain planning problem modeled as a multi-objective hierarchical linear programming problem. Embodiments further include receiving supply chain input data for a supply chain planning problem, modeling the supply chain planning problem as a multi-objective hierarchal linear programming problem having a first objective and at least one additional objective, solving a base run of the multi-objective hierarchical linear programming problem for the first objective and the at least one additional objective, generating a base plan by converting a solution of the base run of the multi-objective hierarchical linear programming problem, receiving one or more changes to the supply chain input data, identifying primal feasibility change of the one or more changes that affect only primal feasibility, and identifying dual feasibility changes of the one or more changes that affect only dual feasibility.