Marketing Optimization System Using Lagrange Relaxation
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Solution Overview
Problem
Marketing campaign optimization becomes complex due to the need to maximize or minimize quantitative measures like expected response probability or profit while adhering to various aggregate and contact policy constraints, especially when dealing with large customer populations and numerous offer combinations, making it difficult to determine the best course of action for offering products through different channels.
Innovation Solution
A computer-implemented system that uses a combination of aggregate constraints and objective coefficients to generate offer sets for customers, employing techniques like Lagrange relaxation and subgradient algorithms to maximize the objective function while satisfying individual and aggregate constraints, and iteratively refining offer sets based on upper bound objective values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the system considers more customers and offer combinations to maximize objective function, then the optimization quality improves, but the computational complexity increases
Solution Approach 1:
The patent segments the optimization problem by separating aggregate constraints from individual customer constraints. Aggregate constraints are handled through Lagrange relaxation and subgradient algorithms, while individual customer offer selections are made independently. This segmentation allows the system to manage large customer populations and numerous offer combinations without overwhelming computational complexity.
Solution Approach 2:
The patent introduces Lagrange multipliers as an intermediary mechanism to handle aggregate constraints. By transforming aggregate constraints into penalty terms in the objective function through Lagrange relaxation, the system can efficiently incorporate global constraints without directly solving the complex constrained optimization problem, thus reducing computational burden while maintaining optimization quality.
2Measurement precision
If the system uses sophisticated predictive models with high degree of sophistication, then the response probability prediction improves, but the model complexity and data requirements increase
Solution Approach 1:
The patent transforms the optimization problem by changing the parameters being optimized. Instead of directly optimizing complex predictive models, the system optimizes the objective function coefficients and constraint parameters. This parameter transformation allows sophisticated predictive models to be incorporated without increasing the complexity of the optimization framework itself, as the models serve as input data rather than components of the optimization algorithm.
3Reliability
If the system satisfies all aggregate and contact policy constraints simultaneously, then the solution feasibility improves, but the optimization flexibility decreases
Solution Approach 1:
The patent employs dynamic optimization through iterative subgradient algorithms that adjust Lagrange multipliers based on constraint violations. This dynamic approach allows the system to satisfy aggregate constraints while maintaining flexibility in individual customer offer selections. The algorithm can adaptively balance constraint satisfaction with optimization objectives, providing both feasibility and flexibility simultaneously.
Solution Approach 2:
The patent applies partial satisfaction of constraints through Lagrange relaxation, where aggregate constraints are satisfied approximately rather than exactly. This partial action approach allows the system to meet the spirit of constraints while maintaining optimization flexibility, and can refine to exact satisfaction if needed. The method avoids the rigidity of exact constraint satisfaction while ensuring feasibility through iterative improvement.
Data Source
AI summary
Computer-implemented systems and methods are provided for determining an action item from a global set of action items for a plurality of customers based on an objective function, a plurality of individual constraints, and a plurality of aggregate constraints. A plurality of offer sets is generated for each customer. An approximate highest reduced adjusted objective for each of the offer sets for each customer is calculated, and the customers are bucketed based on the highest adjusted objective value associated with each customer. The buckets are collapsed into a single bucket record containing a plurality of aggregate offer set columns, and an aggregate offer set column is selected from each bucket record for each bucket. Each bucket associated with a selected offer set is disaggregated, and the action item included in the selected offer set is stored in a computer-readable memory.