=== Problem Context ===
# Complete Optimization Problem and Solution: browser_web

## 1. Problem Context and Goals

### Context  
A company is focused on optimizing the selection of web client accelerators to ensure maximum compatibility with the most widely used browsers. The decision-making process involves determining which accelerators are compatible with which browsers, with the goal of maximizing the overall market share of compatible browsers. The company has a limited number of accelerators it can feasibly implement and maintain, as defined by a maximum number of accelerators that can be selected. This limit is a key operational constraint.  

The compatibility between accelerators and browsers is evaluated using a compatibility score, which is calculated based on the market share of the browser and a predefined weighting formula. This score ensures that the selection process prioritizes browsers with higher market shares, aligning with the company’s goal of maximizing user coverage.  

The business configuration includes a scalar parameter that defines the maximum number of accelerators that can be selected, currently set to three. Additionally, the compatibility score formula incorporates the market share of the browser and a compatibility weight, divided by a total weight, to determine the final score. This formula ensures that the decision variables are calculated in a way that supports linear optimization.  

### Goals  
The primary goal of this optimization problem is to maximize the total market share of browsers that are compatible with the selected accelerators. This is achieved by selecting accelerators that are compatible with the most widely used browsers, as measured by their market share. Success is measured by the extent to which the selected accelerators cover the highest possible market share of browsers, ensuring broad user compatibility.  

## 2. Constraints  

The optimization problem is subject to two key constraints:  
1. **Maximum Accelerators Constraint**: The total number of accelerators selected cannot exceed the predefined maximum number of accelerators, which is currently set to three. This ensures that the company does not exceed its operational capacity for implementing and maintaining accelerators.  
2. **Minimum Compatibility Constraint**: Each selected accelerator must be compatible with at least one browser. This ensures that no accelerator is selected without providing compatibility benefits to at least one browser.  

These constraints are designed to align with the company’s operational limitations and ensure that the optimization process remains feasible and practical.  

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding a max_accelerators parameter to business_configuration_logic.json, enhancing the accelerator_compatible_browser table with additional attributes, and ensuring all tables meet the 3-row minimum rule. Configuration logic updates include scalar parameters and formulas for optimization constraints and metrics.

CREATE TABLE browser (
  browser_id INTEGER,
  market_share FLOAT
);

CREATE TABLE accelerator_compatible_browser (
  accelerator_id INTEGER,
  browser_id INTEGER,
  compatibility_score FLOAT,
  last_updated_date DATE
);
```

### Data Dictionary  
- **browser**:  
  - **Business Purpose**: Stores browser market share data, which is critical for determining the optimization objective.  
  - **Optimization Role**: Provides the coefficients for the objective function, ensuring that the optimization process prioritizes browsers with higher market shares.  
  - **Columns**:  
    - **browser_id**: Unique identifier for each browser, used to index the objective coefficients.  
    - **market_share**: Percentage of the market share for each browser, used as the coefficient in the objective function.  

- **accelerator_compatible_browser**:  
  - **Business Purpose**: Stores compatibility data between accelerators and browsers, which is essential for determining the decision variables.  
  - **Optimization Role**: Provides the data used to calculate the decision variables, ensuring that the optimization process selects accelerators that are compatible with the most widely used browsers.  
  - **Columns**:  
    - **accelerator_id**: Unique identifier for each accelerator, used to index the decision variables.  
    - **browser_id**: Unique identifier for each browser, used to index the decision variables.  
    - **compatibility_score**: Score indicating the compatibility between an accelerator and a browser, used in the calculation of the decision variables.  
    - **last_updated_date**: Ensures that the compatibility data is current and reliable.  


=== Schema ===
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding a max_accelerators parameter to business_configuration_logic.json, enhancing the accelerator_compatible_browser table with additional attributes, and ensuring all tables meet the 3-row minimum rule. Configuration logic updates include scalar parameters and formulas for optimization constraints and metrics.

CREATE TABLE browser (
  browser_id INTEGER,
  market_share FLOAT
);

CREATE TABLE accelerator_compatible_browser (
  accelerator_id INTEGER,
  browser_id INTEGER,
  compatibility_score FLOAT,
  last_updated_date DATE
);



=== LLM Response ===
```sql
-- Query Description: Retrieve the market share of each browser, which is crucial for the objective function coefficients.
-- This data helps prioritize browsers with higher market shares in the optimization process.
SELECT browser_id, market_share
FROM browser;

-- Query Description: Retrieve the compatibility scores between accelerators and browsers, which are essential for determining decision variables.
-- This data helps identify which accelerators are compatible with which browsers and their respective compatibility scores.
SELECT accelerator_id, browser_id, compatibility_score
FROM accelerator_compatible_browser;

-- Query Description: Retrieve the total number of compatible browsers for each accelerator, which helps in applying the minimum compatibility constraint.
-- This ensures that each selected accelerator is compatible with at least one browser.
SELECT accelerator_id, COUNT(browser_id) AS num_compatible_browsers
FROM accelerator_compatible_browser
GROUP BY accelerator_id;

-- Query Description: Retrieve the total market share covered by each accelerator, which helps in evaluating the potential impact of selecting each accelerator.
-- This data is useful for identifying accelerators that cover the highest market share.
SELECT acb.accelerator_id, SUM(b.market_share) AS total_market_share_covered
FROM accelerator_compatible_browser acb
JOIN browser b ON acb.browser_id = b.browser_id
GROUP BY acb.accelerator_id;

-- Query Description: Retrieve the top 3 accelerators based on the total market share they cover, considering the maximum accelerators constraint.
-- This query helps in identifying the most impactful accelerators within the operational limit.
SELECT acb.accelerator_id, SUM(b.market_share) AS total_market_share_covered
FROM accelerator_compatible_browser acb
JOIN browser b ON acb.browser_id = b.browser_id
GROUP BY acb.accelerator_id
ORDER BY total_market_share_covered DESC
LIMIT 3;

-- Query Description: Retrieve the compatibility scores and market shares for each accelerator-browser pair, which is useful for detailed analysis and optimization.
-- This data combines compatibility scores with market shares to provide a comprehensive view of each pair's contribution to the objective function.
SELECT acb.accelerator_id, acb.browser_id, acb.compatibility_score, b.market_share
FROM accelerator_compatible_browser acb
JOIN browser b ON acb.browser_id = b.browser_id;

-- Query Description: Retrieve the most recent compatibility data to ensure the optimization is based on up-to-date information.
-- This query filters the compatibility data to include only the most recent entries, ensuring reliability.
SELECT accelerator_id, browser_id, compatibility_score
FROM accelerator_compatible_browser
WHERE last_updated_date = (SELECT MAX(last_updated_date) FROM accelerator_compatible_browser);

-- Query Description: Retrieve the average compatibility score for each accelerator, which can be used to assess the overall compatibility of each accelerator.
-- This data helps in understanding the general compatibility level of each accelerator across all browsers.
SELECT accelerator_id, AVG(compatibility_score) AS avg_compatibility_score
FROM accelerator_compatible_browser
GROUP BY accelerator_id;
```

These queries are designed to retrieve the most relevant data for the optimization problem, including objective function coefficients, decision variables, and constraint parameters. They also provide aggregated and detailed views to support comprehensive analysis and decision-making.
