Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:26:20

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: singer

```sql
CREATE TABLE singer (
  Singer_ID NUMBER,
  Name TEXT,
  Birth_Year NUMBER,
  Net_Worth_Millions NUMBER,
  Citizenship TEXT
);
```

```sql
CREATE TABLE song (
  Song_ID NUMBER,
  Title TEXT,
  Singer_ID NUMBER,
  Sales NUMBER,
  Highest_Position 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": "singer",
  "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": "singer",
  "iteration": 0,
  "business_context": "A music label wants to maximize the total sales of songs by selecting the optimal set of singers to promote, considering their net worth and the potential sales of their songs.",
  "optimization_problem_description": "The objective is to maximize the total sales of songs by selecting a subset of singers, subject to constraints on the total net worth of the selected singers and the number of singers that can be promoted.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Sales_i * x_i) where x_i is a binary decision variable indicating whether singer i is selected",
    "decision_variables": "x_i: binary variable indicating whether singer i is selected",
    "constraints": [
      "\u2211(Net_Worth_Millions_i * x_i) \u2264 Total_Budget: The total net worth of selected singers must not exceed the budget.",
      "\u2211(x_i) \u2264 Max_Singers: The number of selected singers must not exceed the maximum allowed.",
      "x_i \u2208 {0, 1}: Each decision variable must be binary."
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Sales_i": {
        "currently_mapped_to": "song.Sales",
        "mapping_adequacy": "good",
        "description": "Represents the sales of songs by singer i."
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The total budget available for promoting singers."
      },
      "Max_Singers": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "The maximum number of singers that can be promoted."
      }
    },
    "decision_variables": {
      "x_i": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating whether singer i is selected.",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Total_Budget: The total budget available for promoting singers.",
    "Max_Singers: The maximum number of singers that can be promoted.",
    "Binary decision variables x_i: Indicates whether singer i is selected."
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define the missing parameters (Total_Budget and Max_Singers) and ensure the decision variables are properly mapped."
  }
}
