Facility Location Layout for Convex Demand Point Optimization
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Solution Overview
Problem
Existing methods struggle to efficiently and accurately determine optimal facility locations for multiple facilities when demand locations satisfy a convex position condition, leading to slow operation speed and low accuracy.
Innovation Solution
An efficient optimal facility location determination method using dynamic programming and optimization algorithms to quickly calculate facility locations that minimize the maximum distance from demand locations to facilities, utilizing decision and optimization steps for different scenarios based on the number of facilities to be arranged.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If approximation algorithms are used for facility location determination, then computation speed is improved, but accuracy deteriorates (approximation error of at least 1.93 times minimum distance)
Solution Approach 1:
The algorithm segments the facility location problem into two distinct phases: a determination phase that checks feasibility and an optimization phase that refines the solution. This segmentation allows the system to first quickly assess whether a valid configuration exists, then systematically optimize for minimal maximum distance, thereby achieving both speed and accuracy that neither approximation nor brute-force methods alone can provide.
2Measurement precision
If exact algorithms are used for facility location determination, then accuracy is improved, but computation speed deteriorates (NP-hard problem)
Solution Approach 1:
The determination phase serves as a preliminary action that quickly evaluates whether a feasible facility configuration exists before committing to full optimization. By performing this preliminary check first, the algorithm avoids wasting computational resources on infeasible cases and can terminate early when solutions are found, significantly improving overall computation speed while maintaining exactness.
Solution Approach 2:
The algorithm dynamically adapts its approach based on problem characteristics, switching between the determination phase (for quick feasibility checks) and the optimization phase (for precise solution refinement). This dynamic structure allows the system to allocate computational resources efficiently, performing exact calculations only when necessary and using faster checks for routine evaluations.
3Adaptability or versatility
If existing facility location methods are applied to convex position demand points, then general applicability is maintained, but operation speed deteriorates (slow operation speed in existing methods)
Solution Approach 1:
The algorithm applies local quality by detecting whether demand points form a convex position configuration and then applying specialized optimization techniques tailored to this geometric property. When convex position is detected, the algorithm uses geometric properties specific to convex polygons to accelerate computation, while maintaining the ability to handle non-convex cases through general-purpose methods, thus achieving both speed and versatility.
Data Source
AI summary
The present invention relates to an efficient optimal facility location determination method for convex demand position demand points implemented to arrange a plurality of facilities as close as possible to given demand locations when positions of the demand locations satisfy a convex position condition. According to the efficient optimal facility location determination method for convex position demand points of the present invention, when demand locations satisfy a convex position condition, it is possible to quickly calculate a method of efficiently arranging a plurality of facilities in a very short time. In addition, according to the present invention, even if positions of demand locations do not satisfy a convex position condition, it is possible to approximate arrangement of facilities, and to be applied to various fields such as a location selection of a warehouse or data clustering.