Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 23:10:43

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 production company wants to maximize the total sales of songs by selecting a subset of songs to promote, considering the constraints on the number of songs that can be promoted and the budget available for promotion.",
  "optimization_problem_description": "The company aims to maximize the total sales of selected songs by deciding which songs to promote. Each song has a potential sales increase if promoted, and there is a cost associated with promoting each song. The company has a limited budget for promotion and can only promote a certain number of songs.",
  "optimization_formulation": {
    "objective": "maximize total_sales = \u2211(sales_increase[i] * promote[i])",
    "decision_variables": "promote[i] (binary) - whether to promote song i or not",
    "constraints": [
      "\u2211(promotion_cost[i] * promote[i]) \u2264 budget",
      "\u2211(promote[i]) \u2264 max_songs_to_promote"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "sales_increase[i]": {
        "currently_mapped_to": "song.Sales",
        "mapping_adequacy": "partial",
        "description": "potential sales increase if song i is promoted"
      }
    },
    "constraint_bounds": {
      "budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "total budget available for promoting songs"
      },
      "max_songs_to_promote": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of songs that can be promoted"
      }
    },
    "decision_variables": {
      "promote[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary decision variable indicating whether to promote song i",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Promotion cost for each song",
    "Budget for promotion",
    "Maximum number of songs that can be promoted",
    "Potential sales increase for each song if promoted"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Determine the missing data for promotion costs, budget, and potential sales increase to complete the optimization model"
  }
}
