Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-28 00:07:10

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": "Optimize the assignment of wrestlers to events to maximize the total number of days titles are held, considering constraints on wrestler participation and event scheduling.",
  "optimization_problem": "The goal is to maximize the total number of days titles are held by assigning wrestlers to events, ensuring that each wrestler can only participate in a limited number of events and that each event has a limited number of participants.",
  "objective": "maximize total_days_held = \u2211(days_held_coefficient[i] * x[i])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for decision variables and constraint bounds, modifying existing tables to fill mapping gaps, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine the mapping of decision variables and constraints to existing schema or business logic",
  "mapping_adequacy_summary": "needs_improvement"
}

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

CREATE TABLE Wrestler (
  WrestlerID INTEGER,
  Days_held INTEGER,
  MaxEvents INTEGER
);

CREATE TABLE WrestlerEventAssignment (
  WrestlerID INTEGER,
  EventID INTEGER,
  Assigned BOOLEAN
);

CREATE TABLE EventConstraints (
  EventID INTEGER,
  MaxParticipants INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "Wrestler": {
      "business_purpose": "Stores information about wrestlers",
      "optimization_role": "objective_coefficients",
      "columns": {
        "WrestlerID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each wrestler",
          "optimization_purpose": "Index for decision variables and coefficients",
          "sample_values": "1, 2, 3"
        },
        "Days_held": {
          "data_type": "INTEGER",
          "business_meaning": "Number of days a title is held by the wrestler",
          "optimization_purpose": "Objective coefficient",
          "sample_values": "30, 45, 60"
        },
        "MaxEvents": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of events a wrestler can participate in",
          "optimization_purpose": "Constraint bound",
          "sample_values": "5, 6, 7"
        }
      }
    },
    "WrestlerEventAssignment": {
      "business_purpose": "Tracks wrestler assignments to events",
      "optimization_role": "decision_variables",
      "columns": {
        "WrestlerID": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the wrestler",
          "optimization_purpose": "Index for decision variable",
          "sample_values": "1, 2, 3"
        },
        "EventID": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the event",
          "optimization_purpose": "Index for decision variable",
          "sample_values": "101, 102, 103"
        },
        "Assigned": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the wrestler is assigned to the event",
          "optimization_purpose": "Decision variable",
          "sample_values": "true, false"
        }
      }
    },
    "EventConstraints": {
      "business_purpose": "Stores constraints related to event participation",
      "optimization_role": "constraint_bounds",
      "columns": {
        "EventID": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the event",
          "optimization_purpose": "Index for constraint",
          "sample_values": "101, 102, 103"
        },
        "MaxParticipants": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of participants allowed per event",
          "optimization_purpose": "Constraint bound",
          "sample_values": "10, 12, 15"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_events_per_wrestler": {
    "sample_value": "5",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of events a wrestler can participate in",
    "optimization_role": "Constraint bound for wrestler participation",
    "configuration_type": "scalar_parameter"
  },
  "max_participants_per_event": {
    "sample_value": "10",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of participants allowed per event",
    "optimization_role": "Constraint bound for event participation",
    "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": "Optimize the assignment of wrestlers to events to maximize the total number of days titles are held, considering constraints on wrestler participation and event scheduling.",
  "optimization_problem_description": "Maximize the total number of days titles are held by assigning wrestlers to events, ensuring that each wrestler can only participate in a limited number of events and that each event has a limited number of participants.",
  "optimization_formulation": {
    "objective": "maximize total_days_held = \u2211(Days_held[i] * Assigned[i, j])",
    "decision_variables": "Assigned[i, j]: binary variable indicating if wrestler i is assigned to event j",
    "constraints": [
      "\u2211(Assigned[i, j]) <= MaxEvents[i] for each wrestler i",
      "\u2211(Assigned[i, j]) <= MaxParticipants[j] for each event j"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Days_held[i]": {
        "currently_mapped_to": "Wrestler.Days_held",
        "mapping_adequacy": "good",
        "description": "Number of days a title is held by wrestler i"
      }
    },
    "constraint_bounds": {
      "MaxEvents[i]": {
        "currently_mapped_to": "Wrestler.MaxEvents",
        "mapping_adequacy": "good",
        "description": "Maximum number of events wrestler i can participate in"
      },
      "MaxParticipants[j]": {
        "currently_mapped_to": "EventConstraints.MaxParticipants",
        "mapping_adequacy": "good",
        "description": "Maximum number of participants allowed in event j"
      }
    },
    "decision_variables": {
      "Assigned[i, j]": {
        "currently_mapped_to": "WrestlerEventAssignment.Assigned",
        "mapping_adequacy": "good",
        "description": "Indicates if wrestler i is assigned to event j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
