AI Promotion Optimization Under Mixed Constraint Complexity
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current promotional planning systems fail to optimize item promotions effectively, leading to unnecessary promotions or missed opportunities due to the complexity of combining real, integer, and Boolean variables in constraint-based optimization, which is NP-complete and cannot be solved feasibly with existing methods.
Innovation Solution
A constraint-based optimization system that encodes constraints in a graph-based approach, using machine learning to forecast demand and optimize promotions, reducing scaling from O(N^3) to O(N), and employing a branch-and-cut algorithm to solve integer programming problems efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If constraint-based optimization is used to identify optimal promotional combinations, then promotional effectiveness is improved, but computational complexity becomes NP-complete and cannot be solved feasibly
Solution Approach 1:
The patent segments the NP-complete optimization problem into two separate sub-problems: (1) a mixed-integer linear programming (MILP) problem for selecting promotional items and timing, and (2) a Boolean satisfiability (SAT) problem for determining promotion mechanics. This segmentation allows each sub-problem to be solved independently using specialized algorithms, avoiding the intractability of solving the combined problem directly.
Solution Approach 2:
The patent introduces an intermediary forecast model that predicts demand under different promotion scenarios. This forecast model acts as a mediator between the optimization objectives and the constraints, enabling the system to evaluate promotional effectiveness without directly solving the NP-complete optimization problem. The forecast model provides demand predictions that guide the optimization process while keeping computational complexity manageable.
2Measurement precision
If machine learning is combined with optimization to forecast demand and select promotions, then decision accuracy is improved, but the ML problem grows cubically with the number of variables and constraints
Solution Approach 1:
The patent segments the combined ML-optimization problem by separating the forecast generation from the optimization process. The forecast model is trained independently on historical data to predict demand under various promotion scenarios, while the optimization component uses these forecasts as inputs to select promotional strategies. This segmentation prevents the cubic growth that would occur if the ML problem directly incorporated all optimization variables and constraints.
Solution Approach 2:
The patent performs preliminary demand forecasting before executing the optimization process. By pre-computing demand forecasts for different promotion scenarios and storing them as lookup tables or preprocessed data structures, the system eliminates the need to re-run complex ML computations during the optimization phase. This preliminary action reduces the computational burden from cubic to linear scaling with respect to the number of variables and constraints.
3Productivity
If traditional linear programming is used for promotion optimization, then computational efficiency is maintained, but it cannot handle mixed constraints involving real, integer, and Boolean variables
Solution Approach 1:
The patent segments the constraint handling into two specialized components: a MILP solver that efficiently handles real and integer variables with linear constraints, and a SAT solver that efficiently handles Boolean variables and logical constraints. Each segment uses algorithms optimized for its specific constraint type, maintaining computational efficiency while achieving the versatility needed to handle mixed constraints that traditional linear programming cannot manage.
Data Source
AI summary
Systems and methods for constraint-based optimization, comprising: an AI demand forecasting engine, an optimization engine, a user-defined objective, and a user-defined set of constraints. Using historical sales data, the AI demand forecasting engine generates a plurality of entities, each entity defined by a placement of an item in a promotion platform; and forecasts the objective associated with each entity. The optimization engine generates a plurality of plans, each plan consisting of a unique subset of entities. Plans that violate at least one constraint are eliminated by the optimization engine, leaving a set of candidate solutions. An optimum plan is selected from the set of candidate solutions based on maximization of the objective.