Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:31:46

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: orchestra

```sql
CREATE TABLE conductor (
  Conductor_ID NUMBER,
  Name TEXT,
  Age NUMBER,
  Nationality TEXT,
  Year_of_Work NUMBER
);
```

```sql
CREATE TABLE orchestra (
  Orchestra_ID NUMBER,
  Orchestra TEXT,
  Conductor_ID NUMBER,
  Record_Company TEXT,
  Year_of_Founded NUMBER,
  Major_Record_Format TEXT
);
```

```sql
CREATE TABLE performance (
  Performance_ID NUMBER,
  Orchestra_ID NUMBER,
  Type TEXT,
  Date TEXT,
  Official_ratings_(millions) NUMBER,
  Weekly_rank TEXT,
  Share TEXT
);
```

```sql
CREATE TABLE show (
  Show_ID NUMBER,
  Performance_ID NUMBER,
  If_first_show OTHERS,
  Result TEXT,
  Attendance 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": "orchestra",
  "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": "orchestra",
  "iteration": 0,
  "business_context": "An orchestra management company wants to maximize the total attendance across all shows while respecting constraints on conductor availability and performance ratings.",
  "optimization_problem_description": "The goal is to maximize the total attendance across all shows by deciding the number of performances each orchestra should conduct, considering constraints on conductor availability and minimum performance ratings.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Attendance \u00d7 Number_of_Performances)",
    "decision_variables": "Number_of_Performances[Orchestra_ID] (integer)",
    "constraints": [
      "\u2211(Number_of_Performances[Orchestra_ID] \u00d7 Conductor_Availability[Conductor_ID]) \u2264 Total_Conductor_Availability",
      "Official_ratings_(millions)[Performance_ID] \u2265 Minimum_Rating for each Performance_ID",
      "Number_of_Performances[Orchestra_ID] \u2264 Maximum_Performances_Per_Orchestra",
      "Number_of_Performances[Orchestra_ID] \u2265 Minimum_Performances_Per_Orchestra"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Attendance[Show_ID]": {
        "currently_mapped_to": "show.Attendance",
        "mapping_adequacy": "good",
        "description": "Attendance for each show"
      }
    },
    "constraint_bounds": {
      "Total_Conductor_Availability[Conductor_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total availability of each conductor"
      },
      "Minimum_Rating[Performance_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum required rating for each performance"
      },
      "Maximum_Performances_Per_Orchestra[Orchestra_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of performances allowed per orchestra"
      },
      "Minimum_Performances_Per_Orchestra[Orchestra_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum number of performances required per orchestra"
      }
    },
    "decision_variables": {
      "Number_of_Performances[Orchestra_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Number of performances each orchestra should conduct",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "Conductor availability data",
    "Minimum performance rating thresholds",
    "Maximum and minimum number of performances per orchestra"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Identify and map missing data for conductor availability and performance constraints"
  }
}
