# Complete Optimization Problem and Solution: browser_web

## 1. Problem Context and Goals

### Context  
The company is focused on optimizing the deployment of web client accelerators to various browsers to enhance market share coverage. Each accelerator has the potential to be compatible with multiple browsers, and the objective is to select a combination of accelerators that maximizes the total market share of the browsers they support. The decision-making process involves determining whether a browser is covered by an accelerator, represented by the binary decision variable 'x_b', and whether an accelerator is selected, represented by the binary decision variable 'y_a'. The operational goal is to maximize the total market share by considering the market share of each browser and ensuring that the number of selected accelerators does not exceed the predefined limit. The business configuration specifies the total number of accelerators that can be selected, which serves as a constraint in the optimization model. This approach ensures that the decision-making process is linear, focusing on maximizing market share without involving complex nonlinear relationships.

### Goals  
The primary goal of the optimization is to maximize the total market share covered by the selected accelerators. This involves maximizing the sum of the market shares of the browsers that are covered by the accelerators. The success of this optimization is measured by the total market share achieved, which is directly linked to the market share data of each browser. The objective is clearly defined in linear terms, focusing on maximizing the total market share without involving any complex mathematical expressions.

## 2. Constraints    

The optimization problem is subject to specific constraints that ensure the solution is feasible and aligns with business requirements. The first constraint is the compatibility constraint, which limits the total number of accelerators that can be selected to the predefined maximum. This ensures that the selection of accelerators is within the operational limits set by the business. The second constraint is the coverage constraint, which ensures that a browser can only be considered covered if there is at least one selected accelerator that is compatible with it. These constraints are expressed in business terms that naturally lead to linear mathematical forms, avoiding any nonlinear relationships.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Incorporated market share data into the schema, updated configuration logic for scalar parameters, and ensured all tables meet the 3-row minimum rule.

CREATE TABLE accelerator_compatible_browser (
  accelerator_id INTEGER,
  browser_id INTEGER
);

CREATE TABLE decision_variables (
  x_b BOOLEAN,
  y_a BOOLEAN
);

CREATE TABLE browser_market_share (
  browser_id INTEGER,
  market_share FLOAT
);
```

### Data Dictionary  
The data dictionary provides a comprehensive mapping of tables and columns to their business purposes and roles in the optimization process:

- **Accelerator Compatible Browser Table**: This table defines the compatibility between accelerators and browsers. Each entry indicates which accelerators can work with which browsers, serving as critical business data for determining compatibility in the optimization model.

  - **Accelerator ID**: A unique identifier for each accelerator, used to determine compatibility with browsers.
  - **Browser ID**: A unique identifier for each browser, used to link market share data and compatibility information.

- **Decision Variables Table**: This table stores the decision variables used in the optimization process.

  - **x_b**: A binary variable indicating whether a browser is covered by a selected accelerator.
  - **y_a**: A binary variable indicating whether an accelerator is selected for deployment.

- **Browser Market Share Table**: This table contains market share data for each browser, which serves as the coefficient in the objective function.

  - **Browser ID**: A unique identifier for each browser, linking market share data to the optimization process.
  - **Market Share**: The market share percentage of each browser, used as a coefficient in the objective function to maximize total market share.

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical market share distributions and compatibility scenarios in the web browser and accelerator industry. The goal was to ensure a diverse set of browsers with varying market shares and a realistic number of accelerators that can cover these browsers.

-- Realistic data for accelerator_compatible_browser
INSERT INTO accelerator_compatible_browser (accelerator_id, browser_id) VALUES (1, 101);
INSERT INTO accelerator_compatible_browser (accelerator_id, browser_id) VALUES (1, 102);
INSERT INTO accelerator_compatible_browser (accelerator_id, browser_id) VALUES (2, 103);
INSERT INTO accelerator_compatible_browser (accelerator_id, browser_id) VALUES (3, 101);
INSERT INTO accelerator_compatible_browser (accelerator_id, browser_id) VALUES (3, 104);

-- Realistic data for decision_variables
INSERT INTO decision_variables (x_b, y_a) VALUES (True, True);
INSERT INTO decision_variables (x_b, y_a) VALUES (False, False);
INSERT INTO decision_variables (x_b, y_a) VALUES (True, False);

-- Realistic data for browser_market_share
INSERT INTO browser_market_share (browser_id, market_share) VALUES (101, 0.4);
INSERT INTO browser_market_share (browser_id, market_share) VALUES (102, 0.3);
INSERT INTO browser_market_share (browser_id, market_share) VALUES (103, 0.15);
INSERT INTO browser_market_share (browser_id, market_share) VALUES (104, 0.1);
```