Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:42:07

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 political campaign wants to maximize the overall support rate for a candidate by strategically allocating resources to different poll sources based on their effectiveness in converting unsure voters to supporters.",
  "optimization_problem": "The campaign aims to maximize the total support rate across all poll sources by deciding how much to invest in each poll source, considering constraints on budget, minimum investment per source, and the conversion rates of unsure voters to supporters.",
  "objective": "maximize \u2211(Support_rate[i] + Conversion_rate[i] * Investment[i])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization parameters and updating business configuration logic to handle scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing parameters such as Conversion_rate, Total_Budget, Minimum_Investment, and Maximum_Support_Rate 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 parameters and updating business configuration logic to handle scalar parameters and formulas.

CREATE TABLE poll_source_conversion_rates (
  Poll_Source_ID INTEGER,
  Conversion_rate FLOAT
);

CREATE TABLE candidate (
  Poll_Source_ID INTEGER,
  Support_rate FLOAT
);

CREATE TABLE poll_source_investments (
  Poll_Source_ID INTEGER,
  Investment FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "poll_source_conversion_rates": {
      "business_purpose": "Conversion rates for each poll source",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Poll_Source_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for poll source",
          "optimization_purpose": "Index for poll source",
          "sample_values": "1, 2, 3"
        },
        "Conversion_rate": {
          "data_type": "FLOAT",
          "business_meaning": "Rate at which unsure voters convert to supporters per unit investment in poll source",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "0.05, 0.07, 0.1"
        }
      }
    },
    "candidate": {
      "business_purpose": "Initial support rates for candidate in each poll source",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Poll_Source_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for poll source",
          "optimization_purpose": "Index for poll source",
          "sample_values": "1, 2, 3"
        },
        "Support_rate": {
          "data_type": "FLOAT",
          "business_meaning": "Initial support rate for candidate in poll source",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "0.3, 0.4, 0.5"
        }
      }
    },
    "poll_source_investments": {
      "business_purpose": "Investment amounts for each poll source",
      "optimization_role": "decision_variables",
      "columns": {
        "Poll_Source_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for poll source",
          "optimization_purpose": "Index for poll source",
          "sample_values": "1, 2, 3"
        },
        "Investment": {
          "data_type": "FLOAT",
          "business_meaning": "Amount of money invested in poll source",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "1000, 2000, 3000"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Total_Budget": {
    "sample_value": 100000,
    "data_type": "INTEGER",
    "business_meaning": "Total budget available for investment across all poll sources",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "Minimum_Investment": {
    "sample_value": 1000,
    "data_type": "INTEGER",
    "business_meaning": "Minimum required investment in poll source i",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "Maximum_Support_Rate": {
    "sample_value": 0.8,
    "data_type": "FLOAT",
    "business_meaning": "Maximum achievable support rate for candidate in poll source i",
    "optimization_role": "constraint bound",
    "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": "candidate_poll",
  "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": "candidate_poll",
  "iteration": 1,
  "business_context": "A political campaign aims to maximize the overall support rate for a candidate by strategically allocating resources to different poll sources based on their effectiveness in converting unsure voters to supporters, while adhering to budget and investment constraints.",
  "optimization_problem_description": "Maximize the total support rate across all poll sources by deciding how much to invest in each poll source, considering constraints on budget, minimum investment per source, and the conversion rates of unsure voters to supporters.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Support_rate[i] + Conversion_rate[i] * Investment[i])",
    "decision_variables": "Investment[i]: continuous variable representing the amount of money invested in poll source i",
    "constraints": [
      "\u2211(Investment[i]) \u2264 Total_Budget",
      "Investment[i] \u2265 Minimum_Investment for all i",
      "Support_rate[i] + Conversion_rate[i] * Investment[i] \u2264 Maximum_Support_Rate for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Support_rate[i]": {
        "currently_mapped_to": "candidate.Support_rate",
        "mapping_adequacy": "good",
        "description": "Initial support rate for candidate in poll source i"
      },
      "Conversion_rate[i]": {
        "currently_mapped_to": "poll_source_conversion_rates.Conversion_rate",
        "mapping_adequacy": "good",
        "description": "Rate at which unsure voters convert to supporters per unit investment in poll source i"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "business_configuration_logic.Total_Budget",
        "mapping_adequacy": "good",
        "description": "Total budget available for investment across all poll sources"
      },
      "Minimum_Investment": {
        "currently_mapped_to": "business_configuration_logic.Minimum_Investment",
        "mapping_adequacy": "good",
        "description": "Minimum required investment in poll source i"
      },
      "Maximum_Support_Rate": {
        "currently_mapped_to": "business_configuration_logic.Maximum_Support_Rate",
        "mapping_adequacy": "good",
        "description": "Maximum achievable support rate for candidate in poll source i"
      }
    },
    "decision_variables": {
      "Investment[i]": {
        "currently_mapped_to": "poll_source_investments.Investment",
        "mapping_adequacy": "good",
        "description": "Amount of money invested in poll source i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
