Iterative Coefficient Determination for Production Planning Models
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Solution Overview
Problem
Conventional techniques for determining objective function coefficients in linear programming models for production planning are subjective and lack systematic, automated, and repeatable methods, leading to variability in solutions due to reliance on intuition and trial-and-error.
Innovation Solution
A method and system for determining objective function coefficients through iterative refinement, utilizing attribute and preference rules, and the Analytic Hierarchy Process to evaluate and rank solutions, ensuring systematic and repeatable optimization of production planning models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional techniques utilizing intuition and trial-and-error guesswork are used to determine objective function coefficients, then the process is simple to implement, but the solution varies widely and lacks reliability
Solution Approach 1:
The patent implements an iterative feedback mechanism where the system generates multiple candidate solutions, evaluates them against the model attributes, and uses the evaluation results to refine and update the objective function coefficients. This closed-loop feedback process continues until convergence criteria are met, ensuring reliable and consistent coefficient determination while eliminating subjective trial-and-error approaches.
Solution Approach 2:
The system systematically varies and adjusts the objective function coefficients based on model attributes and solution evaluations. By changing parameters in a controlled, automated manner rather than through subjective intuition, the system achieves reliable coefficient determination. The iterative process modifies coefficient values until optimal values are found that satisfy the mathematical programming model constraints.
2Extent of automation
If iterative refinement with multiple solution evaluations is employed, then the determination of objective function coefficients becomes systematic and automated, but the computational complexity and time increase
Solution Approach 1:
The patent performs preliminary actions by pre-identifying and ranking the attributes of the mathematical programming model before the iterative optimization begins. This preliminary structuring of the problem space allows the subsequent automated iteration to proceed more efficiently, as the evaluation criteria are already established and the search space is better organized from the outset.
Solution Approach 2:
The system generates and evaluates multiple candidate solutions beyond what might be strictly necessary, using a specified tolerance threshold to determine when to stop. By performing slightly excessive evaluations and then applying convergence criteria, the system ensures thorough automated determination while providing a practical stopping point that balances completeness with computational efficiency.
3Measurement precision
If multiple solutions are generated and evaluated to select the optimal solution, then the quality of the final solution improves, but the quantity of computations required increases
Solution Approach 1:
The patent segments the determination process into distinct phases: generating candidate solutions, evaluating each solution against model attributes, ranking solutions based on evaluation criteria, and selecting the best solution. This segmentation allows for systematic precision in each phase while managing computational load by focusing evaluations only on relevant model attributes rather than exhaustive analysis.
Solution Approach 2:
The system replaces manual, intuitive coefficient determination with an automated computational mechanism that systematically generates and evaluates multiple solutions. This substitution of mechanical/computational processes for human judgment enables higher precision in coefficient determination while the automated nature maintains productivity by eliminating manual iteration and evaluation steps.
Data Source
AI summary
A method and system for determining a plurality of coefficients of an objective function of a mathematical programming model. Attributes of the model are identified. A first set of coefficient values determining a first solution and initially representing the plurality of coefficients is determined by employing a specified ranking of the attributes. A prevailing solution is initialized to the first solution. Additional sets of coefficient values are generated, each set determining a corresponding additional solution of the model. The additional solutions are evaluated (e.g., by the Analytic Hierarchy Process) to provide a ranking of the solutions, where the ranking is dependent upon the attributes. The ranking of the additional solutions is used to select a second solution. The prevailing solution is set to the second solution if the second solution exceeds a sum of the prevailing solution and a specified tolerance.