# 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.  

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic market share data for browsers, compatibility scores reflecting real-world scenarios, and a maximum number of accelerators that aligns with business constraints.

-- Realistic data for browser
INSERT INTO browser (browser_id, market_share) VALUES (1, 0.35);
INSERT INTO browser (browser_id, market_share) VALUES (2, 0.25);
INSERT INTO browser (browser_id, market_share) VALUES (3, 0.15);

-- Realistic data for accelerator_compatible_browser
INSERT INTO accelerator_compatible_browser (accelerator_id, browser_id, compatibility_score, last_updated_date) VALUES (1, 1, 0.9, 2023-10-01);
INSERT INTO accelerator_compatible_browser (accelerator_id, browser_id, compatibility_score, last_updated_date) VALUES (1, 2, 0.8, 2023-10-01);
INSERT INTO accelerator_compatible_browser (accelerator_id, browser_id, compatibility_score, last_updated_date) VALUES (2, 1, 0.85, 2023-10-02);
INSERT INTO accelerator_compatible_browser (accelerator_id, browser_id, compatibility_score, last_updated_date) VALUES (2, 3, 0.7, 2023-10-02);
INSERT INTO accelerator_compatible_browser (accelerator_id, browser_id, compatibility_score, last_updated_date) VALUES (3, 2, 0.75, 2023-10-03);
INSERT INTO accelerator_compatible_browser (accelerator_id, browser_id, compatibility_score, last_updated_date) VALUES (3, 3, 0.65, 2023-10-03);
```