Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:24:49

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: entrepreneur

```sql
CREATE TABLE entrepreneur (
  Entrepreneur_ID NUMBER,
  People_ID NUMBER,
  Company TEXT,
  Money_Requested NUMBER,
  Investor TEXT
);
```

```sql
CREATE TABLE people (
  People_ID NUMBER,
  Name TEXT,
  Height NUMBER,
  Weight NUMBER,
  Date_of_Birth TEXT
);
```



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": "entrepreneur",
  "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": "entrepreneur",
  "iteration": 0,
  "business_context": "An investor wants to allocate a fixed budget across multiple entrepreneurs to maximize the total expected return on investment, while ensuring that no single entrepreneur receives more than a specified maximum amount and that the total investment does not exceed the budget.",
  "optimization_problem_description": "The goal is to maximize the total expected return on investment by deciding how much money to allocate to each entrepreneur. The constraints include not exceeding the total budget and ensuring that no entrepreneur receives more than a predefined maximum amount.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Return_Rate_i \u00d7 Investment_i)",
    "decision_variables": "Investment_i: Amount of money allocated to entrepreneur i (continuous)",
    "constraints": [
      "\u2211(Investment_i) \u2264 Total_Budget",
      "Investment_i \u2264 Max_Investment_i for all i",
      "Investment_i \u2265 0 for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Return_Rate_i": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Expected return rate for entrepreneur i"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total available budget for investment"
      },
      "Max_Investment_i": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum amount that can be allocated to entrepreneur i"
      }
    },
    "decision_variables": {
      "Investment_i": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Amount of money allocated to entrepreneur i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Return_Rate_i: Expected return rate for each entrepreneur",
    "Total_Budget: Total available budget for investment",
    "Max_Investment_i: Maximum amount that can be allocated to each entrepreneur"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Identify and map the missing data/parameters required for the optimization model"
  }
}
