Time-Based Decomposition for Supply Chain Optimization
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Solution Overview
Problem
Multi-period supply chain planning problems are not efficiently solvable due to their monolithic nature, which prevents standard decomposition techniques from improving solving speed, leading to increased complexity and solve time.
Innovation Solution
The method involves time-based decomposition of supply chain planning problems into subproblems by dividing the planning horizon into time buckets, allowing for the identification of complicating constraints and using masterless iteration with subgradient descent to generate globally-optimal solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multi-period supply chain planning problems are modeled using time buckets to improve efficiency and accuracy, then modeling accuracy and efficiency are improved, but solve time and complexity increase
Solution Approach 1:
The patent applies segmentation by dividing the multi-period supply chain planning problem into separate single-period subproblems, each corresponding to a specific time bucket. This allows each subproblem to be solved independently and in parallel, significantly reducing the overall solve time while maintaining the modeling accuracy benefits of time-bucketed formulations.
2Productivity
If multi-period supply chain planning problems are modeled using time buckets to improve efficiency and accuracy, then modeling efficiency is improved, but problem complexity increases
Solution Approach 1:
The patent segments the complex multi-period problem into simpler single-period subproblems that can be solved independently. This segmentation reduces the computational complexity of each individual problem while maintaining the overall modeling efficiency through parallel processing of multiple time buckets.
3Speed
If standard decomposition techniques are applied to monolithic LP problems, then solving speed should improve, but monolithic LP problems are not amenable to standard decomposition techniques
Solution Approach 1:
The patent transforms the monolithic multi-period LP problem into multiple independent single-period LP subproblems through time-based segmentation. This segmentation makes the problems amenable to decomposition and enables parallel solving, thereby improving solving speed while maintaining adaptability to standard optimization techniques.
Data Source
AI summary
A system and method are disclosed for solving a supply chain planning problem modeled as a linear programming (LP) problem. Embodiments further include receiving a multi-period matrix formulation of a least a portion of an LP supply chain master planning problem representing a supply chain planning problem for a supply chain network and having a planning horizon divided into time buckets separated by time-bucket boundaries, mapping constraints of the LP supply chain master planning problem and variables of the LP supply chain master planning problem to the time buckets, calculating a quantity of cross-over variables for the constraints and the time buckets, selecting one or more decomposition boundaries from the time-bucket boundaries, and formulating at least two time-based decomposed subproblems by decomposing the LP supply chain master planning problem at the one or more decomposition boundaries.