Assortment Optimization via Distributed Knapsack Solving
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Solution Overview
Problem
Current methods for optimizing retail product assortment are inefficient, as they fail to account for real-time changes and interactions between products and stores, and are limited by the inability to solve large-scale 'knapsack' problems in polynomial time, leading to suboptimal solutions.
Innovation Solution
A distributed processing architecture that analyzes data sets across multiple data stores, transforming optimization requests into sub-queries and aggregating results to find optimal product assortments, allowing for scalable solutions to 'knapsack'-type problems, including retail assortment optimization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional optimization methods are used to analyze product assortment, then the process can be performed with simple computational tools, but the optimization cannot account for real-time changes and interactions between all products and stores
Solution Approach 1:
The patent segments the large-scale assortment optimization problem into smaller sub-problems that can be solved independently using linear programming. The overall optimization is divided into multiple manageable components that can be processed separately and then combined, enabling real-time analysis while maintaining computational feasibility.
Solution Approach 2:
The patent introduces an intermediary computational layer that translates complex assortment optimization requirements into standard linear programming formulations. This intermediary layer handles the complexity of product interactions and real-time constraints, converting them into a form that can be solved by existing optimization algorithms without requiring direct complex computational tools.
2Productivity
If manual optimization processes are used during merchandizing and planning, then the process can be performed with existing retail expertise, but the optimization occurs only seasonally or monthly and does not maximize product sales potential
Solution Approach 1:
The patent transforms the static, periodic optimization process into a dynamic system that can respond to real-time sales changes. The linear programming framework allows for continuous or near-continuous re-optimization as sales data changes, enabling the system to adapt quickly to market conditions rather than waiting for seasonal or monthly review cycles.
Solution Approach 2:
The patent implements a feedback mechanism where real-time sales figures are continuously fed into the optimization system, which then adjusts product assortment recommendations accordingly. This closed-loop system ensures that optimization responses are timely and based on actual current performance rather than historical data alone.
3Measurement precision
If approximation algorithms for the knapsack problem are used, then polynomial time computation is achieved, but the solutions are not useful for obtaining accurate answers in real time for large scale data sets
Solution Approach 1:
The patent transforms the complex knapsack-style assortment optimization problem into a copy or equivalent linear programming formulation. By creating this mathematical equivalent, the system can leverage efficient linear programming algorithms that provide exact solutions in polynomial time, rather than relying on approximation methods that sacrifice accuracy for speed.
Data Source
AI summary
A scalable architecture to solve assortment problems. Relevant data is loaded into various data stores throughout the architecture. A user specifies the problem using an interactive user interface. A dispatcher process takes the problem and delegates it to individual data stores. The data stores solve their delegated problems and return the results to the dispatcher, which aggregates the results and presents them to the user as an optimal solution to the assortment problem.