Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:27:47

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: body_builder

```sql
CREATE TABLE body_builder (
  Body_Builder_ID NUMBER,
  People_ID NUMBER,
  Snatch NUMBER,
  Clean_Jerk NUMBER,
  Total NUMBER
);
```

```sql
CREATE TABLE people (
  People_ID NUMBER,
  Name TEXT,
  Height NUMBER,
  Weight NUMBER,
  Birth_Date TEXT,
  Birth_Place 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": "body_builder",
  "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": "body_builder",
  "iteration": 0,
  "business_context": "A bodybuilding competition organizer wants to select a team of bodybuilders to maximize the total score based on their Snatch and Clean & Jerk performances, while ensuring the team meets certain diversity and physical criteria.",
  "optimization_problem_description": "The goal is to maximize the total score of the selected team, which is the sum of the Snatch and Clean & Jerk scores of the chosen bodybuilders. The selection must respect constraints on the total number of bodybuilders, their average height, and their average weight.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Snatch_i + Clean_Jerk_i) * x_i, where x_i is a binary decision variable indicating whether bodybuilder i is selected",
    "decision_variables": "x_i: binary variable indicating whether bodybuilder i is selected",
    "constraints": [
      "\u2211x_i \u2264 10: The team can have at most 10 bodybuilders",
      "\u2211(Height_i * x_i) / \u2211x_i \u2265 170: The average height of the team must be at least 170 cm",
      "\u2211(Weight_i * x_i) / \u2211x_i \u2264 100: The average weight of the team must be at most 100 kg",
      "x_i \u2208 {0, 1}: Each x_i must be binary"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Snatch_i": {
        "currently_mapped_to": "body_builder.Snatch",
        "mapping_adequacy": "good",
        "description": "Snatch score of bodybuilder i"
      },
      "Clean_Jerk_i": {
        "currently_mapped_to": "body_builder.Clean_Jerk",
        "mapping_adequacy": "good",
        "description": "Clean & Jerk score of bodybuilder i"
      }
    },
    "constraint_bounds": {
      "Height_i": {
        "currently_mapped_to": "people.Height",
        "mapping_adequacy": "good",
        "description": "Height of bodybuilder i"
      },
      "Weight_i": {
        "currently_mapped_to": "people.Weight",
        "mapping_adequacy": "good",
        "description": "Weight of bodybuilder i"
      }
    },
    "decision_variables": {
      "x_i": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating whether bodybuilder i is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Binary decision variables x_i to indicate selection of bodybuilders",
    "Constraints on the total number of bodybuilders in the team"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine constraints and ensure all necessary decision variables are included"
  }
}
