Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:32:00

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: theme_gallery

```sql
CREATE TABLE artist (
  Artist_ID NUMBER,
  Name TEXT,
  Country TEXT,
  Year_Join NUMBER,
  Age NUMBER
);
```

```sql
CREATE TABLE exhibition (
  Exhibition_ID NUMBER,
  Year NUMBER,
  Theme TEXT,
  Artist_ID NUMBER,
  Ticket_Price NUMBER
);
```

```sql
CREATE TABLE exhibition_record (
  Exhibition_ID NUMBER,
  Date 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": "theme_gallery",
  "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": "theme_gallery",
  "iteration": 0,
  "business_context": "A theme gallery aims to maximize its annual revenue from exhibitions by optimizing the allocation of artists to exhibitions based on their popularity and ticket prices, while respecting constraints on artist availability and exhibition capacity.",
  "optimization_problem_description": "The gallery needs to decide how many exhibitions each artist should participate in to maximize total revenue, considering ticket prices and expected attendance, while ensuring no artist is overbooked and each exhibition has a minimum number of artists.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Ticket_Price \u00d7 Attendance \u00d7 x_ij) where x_ij is the number of exhibitions artist i participates in in year j",
    "decision_variables": "x_ij: number of exhibitions artist i participates in in year j (integer)",
    "constraints": [
      "\u2211(x_ij) \u2264 Max_Exhibitions_Per_Artist for each artist i (no artist is overbooked)",
      "\u2211(x_ij) \u2265 Min_Artists_Per_Exhibition for each exhibition j (each exhibition has a minimum number of artists)",
      "x_ij \u2265 0 for all i, j (non-negativity)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Ticket_Price[j]": {
        "currently_mapped_to": "exhibition.Ticket_Price",
        "mapping_adequacy": "good",
        "description": "Ticket price for exhibition j"
      },
      "Attendance[j]": {
        "currently_mapped_to": "exhibition_record.Attendance",
        "mapping_adequacy": "good",
        "description": "Expected attendance for exhibition j"
      }
    },
    "constraint_bounds": {
      "Max_Exhibitions_Per_Artist[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of exhibitions artist i can participate in"
      },
      "Min_Artists_Per_Exhibition[j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum number of artists required for exhibition j"
      }
    },
    "decision_variables": {
      "x_ij[i,j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Number of exhibitions artist i participates in in year j",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "Max_Exhibitions_Per_Artist for each artist",
    "Min_Artists_Per_Exhibition for each exhibition"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define and map missing constraint bounds and decision variables"
  }
}
