Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:25:55

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: race_track

```sql
CREATE TABLE race (
  Race_ID NUMBER,
  Name TEXT,
  Class TEXT,
  Date TEXT,
  Track_ID TEXT
);
```

```sql
CREATE TABLE track (
  Track_ID NUMBER,
  Name TEXT,
  Location TEXT,
  Seating NUMBER,
  Year_Opened 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": "race_track",
  "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": "race_track",
  "iteration": 0,
  "business_context": "A race track management company wants to maximize the total seating capacity utilization across all races in a given year, considering constraints on the number of races per track and the availability of seating.",
  "optimization_problem_description": "The goal is to maximize the total seating capacity utilization by deciding the number of races to be held at each track, subject to constraints on the maximum number of races per track and the total available seating capacity.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Seating \u00d7 Races_per_Track)",
    "decision_variables": "Races_per_Track[Track_ID] (integer)",
    "constraints": [
      "Races_per_Track[Track_ID] \u2264 Max_Races_per_Track[Track_ID] for each Track_ID",
      "\u2211(Seating \u00d7 Races_per_Track[Track_ID]) \u2264 Total_Seating_Capacity",
      "Races_per_Track[Track_ID] \u2265 0 for each Track_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Seating[Track_ID]": {
        "currently_mapped_to": "track.Seating",
        "mapping_adequacy": "good",
        "description": "Seating capacity of each track"
      }
    },
    "constraint_bounds": {
      "Max_Races_per_Track[Track_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of races allowed per track"
      },
      "Total_Seating_Capacity": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total available seating capacity across all tracks"
      }
    },
    "decision_variables": {
      "Races_per_Track[Track_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Number of races to be held at each track",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "Max_Races_per_Track[Track_ID]",
    "Total_Seating_Capacity"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Identify and map missing parameters for constraints and decision variables"
  }
}
