Back Projection Constraints for Chemical Production Scheduling
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Solution Overview
Problem
Chemical production scheduling using mixed integer programming is computationally intensive, leading to slow processing times that hinder practical application in factory environments due to the complexity of NP-hard problems.
Innovation Solution
The implementation of a 'back projection' method that analyzes chemical processing quantities from output to input, providing constraints for mixed integer programming models to increase processing speed by eliminating unrealizable schedules and tightening the search space, thereby improving computational efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If mixed integer programming is used to solve chemical production scheduling problems, then scheduling optimization is achieved, but computational processing time becomes excessively long
Solution Approach 1:
The patent performs back projection analysis before running the full MIP solver to pre-calculate minimum production requirements and establish tight bounds on material flows. This preliminary action constrains the search space of the MIP problem, allowing the optimizer to find optimal schedules faster without sacrificing solution quality
Solution Approach 2:
The patent transforms the scheduling problem by changing parameters through back projection - calculating minimum production levels and material flow constraints that convert the original complex MIP problem into a more tractable form with tighter bounds, reducing computational complexity while maintaining optimization accuracy
2Productivity
If the search space of linear programming is constrained using back projection, then computational speed increases, but model complexity increases
Solution Approach 1:
The patent segments the scheduling problem into two parts: (1) back projection analysis that calculates minimum production requirements and material flow constraints, and (2) the constrained MIP optimization. This segmentation allows the complex problem to be solved in stages, improving computational speed while managing model complexity through structured decomposition
Data Source
AI summary
A scheduling system for chemical processing provides an electronic computer that models the process as a set of tasks with known production ranges. A desired output from the process is back projected through the process to determine production quantities of each task of the process within the production ranges. These values are used to constrain a mixed integer programming evaluation of the schedule which may be used to control operation of the equipment.