Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 22:52:42

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either Linear Programming (LP) or Mixed-Integer Programming (MIP)
- Objective function MUST be linear: minimize/maximize ∑(coefficient × variable)
- All constraints MUST be linear: ∑(coefficient × variable) ≤/≥/= constant
- Decision variables can be continuous (LP) or mixed continuous/integer (MIP)
- NO variable products, divisions, or other nonlinear relationships
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.

Database: browser_web

```sql
CREATE TABLE Web_client_accelerator (
  id NUMBER,
  name TEXT,
  Operating_system TEXT,
  Client TEXT,
  Connection TEXT
);
```

```sql
CREATE TABLE browser (
  id NUMBER,
  name TEXT,
  market_share NUMBER
);
```

```sql
CREATE TABLE accelerator_compatible_browser (
  accelerator_id NUMBER,
  browser_id NUMBER,
  compatible_since_year NUMBER
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "browser_web",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 2 to 20 constraints"
  },
  
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "coefficient_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this coefficient represents in the optimization model"
      }
    },
    "constraint_bounds": {
      "constraint_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing", 
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this constraint bound represents"
      }
    },
    "decision_variables": {
      "variable_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate", 
        "description": "what this decision variable represents",
        "variable_type": "continuous/integer/binary"
      }
    }
  },
  
  "missing_optimization_requirements": [
    "List what data/parameters are needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "browser_web",
  "iteration": 0,
  "business_context": "A company wants to optimize the allocation of web client accelerators to browsers to maximize market share coverage. Each accelerator can be compatible with multiple browsers, and the goal is to select a combination of accelerators that maximizes the total market share of the compatible browsers.",
  "optimization_problem_description": "The problem is to select a set of web client accelerators such that the total market share of the browsers they are compatible with is maximized. Each accelerator can be used only once, and the compatibility is defined by the 'accelerator_compatible_browser' table.",
  "optimization_formulation": {
    "objective": "maximize total_market_share = \u2211(market_share[b] * x[b]) for all browsers b",
    "decision_variables": "x[b] is a binary variable indicating whether browser b is covered by selected accelerators",
    "constraints": [
      "\u2211(x[b] for all b) <= total_number_of_accelerators",
      "x[b] <= \u2211(y[a] * compatibility[a][b] for all a) for all browsers b",
      "y[a] is a binary variable indicating whether accelerator a is selected"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "market_share[b]": {
        "currently_mapped_to": "browser.market_share",
        "mapping_adequacy": "good",
        "description": "Represents the market share of browser b"
      }
    },
    "constraint_bounds": {
      "total_number_of_accelerators": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Represents the total number of accelerators that can be selected"
      }
    },
    "decision_variables": {
      "x[b]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary variable indicating if browser b is covered",
        "variable_type": "binary"
      },
      "y[a]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary variable indicating if accelerator a is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Total number of accelerators available for selection",
    "Compatibility matrix indicating which accelerators are compatible with which browsers"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define the total number of accelerators and establish compatibility matrix"
  }
}
