Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:10:43

Prompt:
You are an Operations Research (OR) expert in iteration 1 of an alternating optimization process. The algorithm alternates between OR expert analysis and data engineering implementation until convergence.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST remain 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
- If previous iteration introduced nonlinear elements, redesign as linear formulation
- Maintain between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and mapping analysis. Do NOT propose database changes.
ROW COUNT AWARENESS: Understand that data engineer applies 3-row minimum rule - insufficient table data gets moved to business_configuration_logic.json.


DATA AVAILABILITY CHECK: 
Before listing missing requirements, verify:
- Check current schema for required data columns
- Check business configuration logic for required parameters  
- Only list as "missing" if data is truly unavailable
- If all mappings are "good", missing_requirements should be []

CONSISTENCY RULES:
- IF all mapping_adequacy == "good" THEN missing_optimization_requirements = []
- IF missing_optimization_requirements = [] THEN complete CAN be true
- IF complete == true THEN confidence should be "high"

SELF-CHECK: Before responding, verify:
1. Does current schema contain the data I claim is missing?
2. Are my mapping assessments consistent with missing requirements?
3. Is my complete status consistent with missing requirements?

MAPPING COMPLETENESS CHECK: Ensure logical consistency between:
- All objective coefficients mapped with adequacy evaluation
- All constraint bounds mapped with adequacy evaluation  
- All decision variables mapped with adequacy evaluation
- Missing requirements list matches inadequate mappings only


CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.



CURRENT STATE (iteration 0):
{
  "iteration": 1,
  "converged": false,
  "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": "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.",
  "objective": "maximize total_sales = \u2211(sales_increase[i] * promote[i])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization data, modifying existing tables to fill mapping gaps, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Determine the missing data for promotion costs, budget, and potential sales increase to complete the optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data, modifying existing tables to fill mapping gaps, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE Song (
  SongID INTEGER,
  PotentialSalesIncrease FLOAT
);

CREATE TABLE PromotionCost (
  SongID INTEGER,
  Cost FLOAT,
  Promote BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "Song": {
      "business_purpose": "Stores information about songs including potential sales increase",
      "optimization_role": "objective_coefficients",
      "columns": {
        "SongID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each song",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "1, 2, 3"
        },
        "PotentialSalesIncrease": {
          "data_type": "FLOAT",
          "business_meaning": "Potential sales increase if the song is promoted",
          "optimization_purpose": "Objective coefficient for sales increase",
          "sample_values": "1000.0, 1500.0, 2000.0"
        }
      }
    },
    "PromotionCost": {
      "business_purpose": "Stores promotion cost for each song",
      "optimization_role": "constraint_bounds",
      "columns": {
        "SongID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each song",
          "optimization_purpose": "Index for decision variables",
          "sample_values": "1, 2, 3"
        },
        "Cost": {
          "data_type": "FLOAT",
          "business_meaning": "Cost to promote the song",
          "optimization_purpose": "Constraint coefficient for promotion cost",
          "sample_values": "500.0, 750.0, 1000.0"
        },
        "Promote": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the song is promoted",
          "optimization_purpose": "Decision variable for promotion",
          "sample_values": "true, false"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "budget": {
    "sample_value": "10000",
    "data_type": "INTEGER",
    "business_meaning": "Total budget available for promoting songs",
    "optimization_role": "Used as a constraint bound in the optimization model",
    "configuration_type": "scalar_parameter"
  },
  "max_songs_to_promote": {
    "sample_value": "5",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of songs that can be promoted",
    "optimization_role": "Used as a constraint bound in the optimization model",
    "configuration_type": "scalar_parameter"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "singer",
  "iteration": 1,
  "business_context": "Updated realistic business scenario description that supports linear optimization",
  "optimization_problem_description": "Refined description of LINEAR optimization problem", 
  "optimization_formulation": {
    "objective": "refined linear minimize/maximize with mathematical precision (sum of weighted variables only)",
    "decision_variables": "clearly defined controllable linear variables (continuous or integer)",
    "constraints": "mathematically precise LINEAR constraint definitions (no variable products or divisions) - maintain 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 still needed for linear formulation (should be [] if all mappings are good)"
  ],
  
  "iteration_status": {
    "complete": true/false based on linear formulation completeness,
    "confidence": "updated confidence level",
    "next_focus": "What needs refinement for linear optimization OR 'Ready for convergence'"
  }
}

Response:
{
  "database_id": "singer",
  "iteration": 1,
  "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(PotentialSalesIncrease[i] * Promote[i])",
    "decision_variables": "Promote[i] for each song i, where Promote[i] is a binary variable indicating if song i is promoted",
    "constraints": [
      "\u2211(Cost[i] * Promote[i]) <= budget",
      "\u2211(Promote[i]) <= max_songs_to_promote"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "PotentialSalesIncrease[i]": {
        "currently_mapped_to": "Song.PotentialSalesIncrease",
        "mapping_adequacy": "good",
        "description": "Potential sales increase if the song is promoted"
      }
    },
    "constraint_bounds": {
      "budget": {
        "currently_mapped_to": "business_configuration_logic.budget",
        "mapping_adequacy": "good",
        "description": "Total budget available for promoting songs"
      },
      "max_songs_to_promote": {
        "currently_mapped_to": "business_configuration_logic.max_songs_to_promote",
        "mapping_adequacy": "good",
        "description": "Maximum number of songs that can be promoted"
      }
    },
    "decision_variables": {
      "Promote[i]": {
        "currently_mapped_to": "PromotionCost.Promote",
        "mapping_adequacy": "good",
        "description": "Indicates if the song is promoted",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
