Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:46:34

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 wedding planning company aims to minimize the total cost of organizing weddings across different churches while ensuring that each church is used within its capacity and that the number of weddings per year does not exceed a certain limit.",
  "optimization_problem": "The company wants to minimize the total cost of organizing weddings by deciding how many weddings to hold at each church each year, considering the church's capacity and the maximum number of weddings allowed per year.",
  "objective": "minimize \u2211(cost_per_wedding[Church_ID, Year] \u00d7 weddings[Church_ID, Year])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating tables for cost per wedding, church capacity, and maximum weddings per year. Business configuration logic updated with scalar parameters and formulas for optimization."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing data required for the optimization model, such as cost per wedding, church capacity, and maximum weddings per year.",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for cost per wedding, church capacity, and maximum weddings per year. Business configuration logic updated with scalar parameters and formulas for optimization.

CREATE TABLE cost_per_wedding (
  church_id INTEGER,
  year INTEGER,
  cost FLOAT
);

CREATE TABLE weddings (
  church_id INTEGER,
  year INTEGER,
  number_of_weddings INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "cost_per_wedding": {
      "business_purpose": "cost of organizing a wedding at a specific church in a specific year",
      "optimization_role": "objective_coefficients",
      "columns": {
        "church_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the church",
          "optimization_purpose": "index for cost per wedding",
          "sample_values": "1, 2, 3"
        },
        "year": {
          "data_type": "INTEGER",
          "business_meaning": "year of the wedding",
          "optimization_purpose": "index for cost per wedding",
          "sample_values": "2023, 2024, 2025"
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "cost of organizing a wedding",
          "optimization_purpose": "coefficient in the objective function",
          "sample_values": "5000.0, 6000.0, 7000.0"
        }
      }
    },
    "weddings": {
      "business_purpose": "number of weddings at each church each year",
      "optimization_role": "decision_variables",
      "columns": {
        "church_id": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for the church",
          "optimization_purpose": "index for number of weddings",
          "sample_values": "1, 2, 3"
        },
        "year": {
          "data_type": "INTEGER",
          "business_meaning": "year of the wedding",
          "optimization_purpose": "index for number of weddings",
          "sample_values": "2023, 2024, 2025"
        },
        "number_of_weddings": {
          "data_type": "INTEGER",
          "business_meaning": "number of weddings at the church in the year",
          "optimization_purpose": "decision variable in the optimization model",
          "sample_values": "10, 15, 20"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_weddings_per_year": {
    "sample_value": 100,
    "data_type": "INTEGER",
    "business_meaning": "maximum number of weddings allowed per year",
    "optimization_role": "constraint bound",
    "configuration_type": "scalar_parameter"
  },
  "church_capacity": {
    "sample_value": 50,
    "data_type": "INTEGER",
    "business_meaning": "maximum number of weddings a church can handle",
    "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": "wedding",
  "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": "wedding",
  "iteration": 1,
  "business_context": "A wedding planning company aims to minimize the total cost of organizing weddings across different churches while ensuring that each church is used within its capacity and that the total number of weddings per year does not exceed a certain limit.",
  "optimization_problem_description": "The company wants to minimize the total cost of organizing weddings by deciding how many weddings to hold at each church each year, considering the church's capacity and the maximum number of weddings allowed per year.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_per_wedding[Church_ID, Year] \u00d7 weddings[Church_ID, Year])",
    "decision_variables": "weddings[Church_ID, Year] = number of weddings at each church each year (integer)",
    "constraints": "\u2211(weddings[Church_ID, Year]) \u2264 max_weddings_per_year for each year, weddings[Church_ID, Year] \u2264 church_capacity for each church and year"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_per_wedding[Church_ID, Year]": {
        "currently_mapped_to": "cost_per_wedding.cost",
        "mapping_adequacy": "good",
        "description": "cost of organizing a wedding at a specific church in a specific year"
      }
    },
    "constraint_bounds": {
      "max_weddings_per_year": {
        "currently_mapped_to": "business_configuration_logic.max_weddings_per_year",
        "mapping_adequacy": "good",
        "description": "maximum number of weddings allowed per year"
      },
      "church_capacity": {
        "currently_mapped_to": "business_configuration_logic.church_capacity",
        "mapping_adequacy": "good",
        "description": "maximum number of weddings a church can handle"
      }
    },
    "decision_variables": {
      "weddings[Church_ID, Year]": {
        "currently_mapped_to": "weddings.number_of_weddings",
        "mapping_adequacy": "good",
        "description": "number of weddings at each church each year",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
