Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:28:17

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": "Optimizing the selection of wrestlers for a wrestling event to maximize the total number of days their reigns have been held, while ensuring a balanced team composition and limiting the number of eliminations per wrestler.",
  "optimization_problem": "The goal is to maximize the total days held by selected wrestlers, subject to constraints on the number of wrestlers per team and the maximum number of eliminations allowed per wrestler.",
  "objective": "maximize \u2211(Days_held_i \u00d7 x_i) where x_i is a binary decision variable indicating if wrestler i is selected",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for team assignments and eliminations, modifying the wrestler table to include optimization-relevant data, and adding business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine constraints and ensure all necessary data is available for the optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for team assignments and eliminations, modifying the wrestler table to include optimization-relevant data, and adding business configuration logic for scalar parameters and formulas.

CREATE TABLE wrestler (
  Days_held INTEGER,
  selection_status BOOLEAN
);

CREATE TABLE wrestler_team (
  wrestler_id INTEGER,
  team STRING
);

CREATE TABLE wrestler_eliminations (
  wrestler_id INTEGER,
  eliminations INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "wrestler": {
      "business_purpose": "Stores wrestler information relevant to optimization",
      "optimization_role": "decision_variables/objective_coefficients",
      "columns": {
        "Days_held": {
          "data_type": "INTEGER",
          "business_meaning": "Number of days the wrestler's reign has been held",
          "optimization_purpose": "Objective coefficient for maximizing total days held",
          "sample_values": "100, 200, 300"
        },
        "selection_status": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the wrestler is selected",
          "optimization_purpose": "Decision variable x_i",
          "sample_values": "true, false"
        }
      }
    },
    "wrestler_team": {
      "business_purpose": "Team assignments for each wrestler",
      "optimization_role": "business_data",
      "columns": {
        "wrestler_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the wrestler",
          "optimization_purpose": "Links wrestler to team",
          "sample_values": "1, 2, 3"
        },
        "team": {
          "data_type": "STRING",
          "business_meaning": "Team assignment (Team A or Team B)",
          "optimization_purpose": "Used in team composition constraints",
          "sample_values": "Team A, Team B"
        }
      }
    },
    "wrestler_eliminations": {
      "business_purpose": "Number of eliminations per wrestler",
      "optimization_role": "business_data",
      "columns": {
        "wrestler_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the wrestler",
          "optimization_purpose": "Links wrestler to eliminations",
          "sample_values": "1, 2, 3"
        },
        "eliminations": {
          "data_type": "INTEGER",
          "business_meaning": "Number of eliminations by the wrestler",
          "optimization_purpose": "Used in elimination constraints",
          "sample_values": "5, 10, 15"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_wrestlers": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of wrestlers to be selected",
    "optimization_role": "Constraint bound for total wrestlers",
    "configuration_type": "scalar_parameter"
  },
  "max_eliminations": {
    "sample_value": 20,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of eliminations allowed",
    "optimization_role": "Constraint bound for total eliminations",
    "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": "wrestler",
  "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": "wrestler",
  "iteration": 1,
  "business_context": "Optimizing the selection of wrestlers for a wrestling event to maximize the total number of days their reigns have been held, while ensuring a balanced team composition and limiting the number of eliminations per wrestler.",
  "optimization_problem_description": "Maximize the total days held by selected wrestlers, subject to constraints on the number of wrestlers per team and the maximum number of eliminations allowed per wrestler.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Days_held_i \u00d7 x_i) where x_i is a binary decision variable indicating if wrestler i is selected",
    "decision_variables": "x_i \u2208 {0, 1} for each wrestler i, indicating selection status",
    "constraints": [
      "\u2211(x_i) \u2264 max_wrestlers: Total number of selected wrestlers must not exceed the maximum allowed",
      "\u2211(eliminations_i \u00d7 x_i) \u2264 max_eliminations: Total eliminations by selected wrestlers must not exceed the maximum allowed",
      "\u2211(x_i | team = 'Team A') = \u2211(x_i | team = 'Team B'): Number of wrestlers selected from Team A must equal the number selected from Team B"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Days_held_i": {
        "currently_mapped_to": "wrestler.Days_held",
        "mapping_adequacy": "good",
        "description": "Number of days the wrestler's reign has been held"
      }
    },
    "constraint_bounds": {
      "max_wrestlers": {
        "currently_mapped_to": "business_configuration_logic.max_wrestlers",
        "mapping_adequacy": "good",
        "description": "Maximum number of wrestlers to be selected"
      },
      "max_eliminations": {
        "currently_mapped_to": "business_configuration_logic.max_eliminations",
        "mapping_adequacy": "good",
        "description": "Maximum number of eliminations allowed"
      }
    },
    "decision_variables": {
      "x_i": {
        "currently_mapped_to": "wrestler.selection_status",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if wrestler i is selected",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
