Domain-Aware Decomposition for Supply Chain Master Planning
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Solution Overview
Problem
Monolithic linear programming (LP) problems in supply chain planning are not amenable to standard decomposition techniques, leading to overly time-consuming and resource-intensive solution processes, which complicates supply chain planning and often requires simplifying constraints or objectives to meet batch solve windows.
Innovation Solution
The approach involves identifying common resource and material constraints (complicating constraints) in supply chain networks, replicating these across subproblems, calculating an effective dual, and allocating resources using masterless iteration with subgradient descent to solve decomposed subproblems sequentially or in parallel, allowing for hierarchical optimization and reduced-cost calculations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If monolithic linear programming is used to solve supply chain planning problems, then optimal solutions can be generated, but the solution process becomes overly time-consuming and resource-intensive
Solution Approach 1:
The patent divides the monolithic supply chain planning problem into multiple domain-specific subproblems (e.g., production planning, inventory management, distribution planning). Each subproblem is solved independently using domain-aware decomposition, reducing computational complexity and time while maintaining solution quality through coordinated optimization across domains.
2Reliability
If monolithic linear programming is used to solve supply chain planning problems, then optimal solutions can be generated, but resource requirements increase significantly
Solution Approach 1:
The patent segments the computational workload across multiple domain-specific solvers that can operate in parallel or sequentially with reduced resource requirements. Each domain solver processes only its specific subset of variables and constraints, significantly reducing memory and computational resource demands compared to a single monolithic solver.
Solution Approach 2:
The patent introduces domain-specific interface layers and coordination mechanisms that act as intermediaries between subproblems. These intermediaries manage resource allocation and information exchange between domains, enabling efficient resource utilization while maintaining global optimality through coordinated decision-making.
3Productivity
If standard decomposition techniques are applied to monolithic LP problems, then solving speed may improve, but monolithic LP problems are generally not amenable to standard decomposition techniques
Solution Approach 1:
The patent applies domain-aware decomposition that recognizes the heterogeneous structure of supply chain problems. Different domains (production, inventory, distribution) have distinct characteristics, variables, and constraints that are optimized using domain-specific decomposition strategies tailored to each local problem structure, making decomposition applicable and effective.
Solution Approach 2:
The patent employs dynamic decomposition strategies that adapt to the specific structure and characteristics of the supply chain problem at hand. The decomposition approach can dynamically adjust the granularity and organization of subproblems based on problem features, enabling effective application to monolithic LP problems that were previously intractable with static decomposition methods.
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 include receiving an LP problem representing a supply chain planning problem for a supply chain network comprising material buffers and resource buffers, partitioning the supply chain network at a complicating node into at least two supply chains sharing the complicating node, formulating a decomposed subproblem for each of the supply chains, calculating an effective dual based, at least in part, on a mathematical difference of at least two dual values calculated by solving the functional-based decomposed subproblems, and generating a globally-optimal LP solution to the LP problem using subgradient descent with the effective dual.