Pack Optimization System Using Heuristic Decomposition
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Solution Overview
Problem
Large-scale distribution networks, such as national apparel retailers, face challenges in optimizing pack distribution across multiple levels of their distribution networks due to the complexity of mixed-integer linear programming (MILP) methods, which are computationally intensive and impractical for quick solution generation.
Innovation Solution
The implementation of heuristics, such as the main rounding heuristic and separability heuristic, to decompose pack optimization problems into simpler sub-problems, allowing for the use of linear programming (LP) solvers to quickly generate optimal pack distributions while adhering to integer constraints, thereby reducing computational complexity and improving solution speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If mixed-integer linear programming (MILP) methods are used to solve pack optimization problems, then optimal pack distribution can be achieved, but computation time becomes excessively long and complexity increases
Solution Approach 1:
The patent segments the complex MILP optimization problem into multiple simpler linear programming (LP) sub-problems that can be solved independently and more quickly. By dividing the overall optimization task into smaller components, the system achieves near-optimal solutions without the excessive computation time required by complete MILP methods.
Solution Approach 2:
The patent changes the mathematical approach from integer constraints (MILP) to continuous relaxation (LP), allowing fractional pack assignments during intermediate calculations. This parameter change enables faster computation while maintaining practical optimality through subsequent rounding and adjustment steps that restore integer constraints.
2Reliability
If mixed-integer linear programming (MILP) methods are used to ensure integer pack constraints, then distribution feasibility is maintained, but device complexity and computational burden increase
Solution Approach 1:
The patent segments the complex MILP optimization problem into multiple simpler linear programming (LP) sub-problems that can be solved independently and more quickly. By dividing the overall optimization task into smaller components, the system achieves near-optimal solutions without the excessive computation time required by complete MILP methods.
Solution Approach 2:
The patent introduces an intermediary rounding step that converts fractional LP solutions into integer pack assignments. This intermediary process acts as a bridge between the computationally efficient LP relaxation and the practical requirement for integer pack constraints, maintaining feasibility while reducing complexity.
Data Source
AI summary
Computer-implemented systems and methods are provided for optimizing the distribution of packs of an item across an entity's distribution network. Constraint values may be specified to limit the values that may be included in a planned distribution of packs. Also, heuristics may be used to reduce the computation time required to determine optimal values for a planned distribution of packs. Modeling of the planned distribution of packs and optimization of the number of packs to be distributed can be accomplished using a mixed-integer linear programming solver.