Item Transfer Control System Using Flow Network Rounding
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Computing devices face challenges in completing computational tasks related to transferring items between multiple source and destination sites in polynomial time due to exponentially increasing computations, which overwhelm available resources, especially when dealing with large numbers of items.
Innovation Solution
The system generates a fractional solution and then an approximate fractional solution, which is rounded to an integral approximate solution using a flow network, allowing for efficient computation and transfer of items in polynomial time by identifying non-zero transfers and rounding them to integral values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional techniques are used to compute accurate solutions for item transfer, then transfer accuracy is improved, but computational complexity increases exponentially
Solution Approach 1:
The patent changes the parameter of solution type from exact integer transfers to fractional transfers, allowing the linear programming problem to be solved in polynomial time. The fractional solution provides a relaxation that avoids exponential complexity while maintaining sufficient accuracy for practical purposes.
Solution Approach 2:
The patent uses a flow network as a temporary computational structure to convert the fractional solution into an approximate integral solution. This flow network is constructed and then discarded after generating the transfer plan, avoiding the need for complex persistent optimization structures.
2Manufacturing precision
If exact solutions are computed for large numbers of items, then transfer precision is improved, but computational resources are overwhelmed
Solution Approach 1:
The patent changes the solution space from integer constraints to fractional constraints, enabling the system to handle large quantities of items (millions daily) with polynomial time complexity. The fractional values are subsequently rounded to integers through the flow network approach.
Solution Approach 2:
The patent computes an approximate integral solution rather than an exact solution, accepting a small amount of excess or deficit in transfers. This partial precision approach allows handling of large-scale item transfers without overwhelming computational resources.
3Productivity
If fractional solutions are generated, then computational efficiency is improved, but transfer feasibility deteriorates due to non-transferable fractions
Solution Approach 1:
The patent introduces a flow network as an intermediary structure that bridges the fractional solution and the final integral transfer plan. The flow network takes fractional values as input and produces rounded integer transfers as output, making the solution both computationally efficient and practically feasible.
Solution Approach 2:
The patent creates an approximate copy of the fractional solution in the form of an integral solution through the flow network. This copied solution maintains the essential transfer patterns while converting fractional values to integers that can be actually executed.
Data Source
AI summary
In implementations of item transfer control systems, a computing device implements a transfer system to receive input data describing types of requested items and corresponding quantities of the types of requested items to receive at each of a plurality of destination sites and types of available items and corresponding quantities of the types of available items that are available at each of a plurality of source sites. The transfer system constructs a flow network having a source node for each of the plurality of the source sites and a destination node for each of the plurality of the destination sites. An integral approximate solution is generated that transfers the corresponding quantities of the types of requested items to each of the plurality of the destination sites using a maximum flow solver and the flow network. The transfer system causes transferences of the corresponding quantities of the types of requested items to each of the plurality of the destination sites based on the integral approximate solution.