Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-27 23:07:42

Prompt:
You are an Operations Research (OR) expert in iteration 2 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 1):
{
  "iteration": 2,
  "converged": false,
  "business_context": "A riding club aims to maximize its total points from match results by optimally assigning players to coaches, considering the constraints of coach availability and player-coach compatibility.",
  "optimization_problem": "The objective is to maximize the total points scored by the club by assigning players to coaches based on compatibility scores, while respecting coach capacity constraints and ensuring each assignment meets a minimum compatibility threshold.",
  "objective": "maximize total_points = \u2211(compatibility_score[Player_ID, Coach_ID] * assignment[Player_ID, Coach_ID])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating a table for assignment decision variables, updating configuration logic for scalar parameters, and ensuring all constraints are correctly implemented based on OR expert mapping analysis."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Map the assignment decision variable to the schema and ensure all constraints are correctly implemented",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a table for assignment decision variables, updating configuration logic for scalar parameters, and ensuring all constraints are correctly implemented based on OR expert mapping analysis.

CREATE TABLE compatibility_scores (
  Player_ID INTEGER,
  Coach_ID INTEGER,
  compatibility_score FLOAT
);

CREATE TABLE coach_constraints (
  Coach_ID INTEGER,
  max_players INTEGER
);

CREATE TABLE assignments (
  Player_ID INTEGER,
  Coach_ID INTEGER,
  assignment BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "compatibility_scores": {
      "business_purpose": "stores compatibility scores between players and coaches",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Player_ID": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for a player",
          "optimization_purpose": "index for compatibility score",
          "sample_values": "1, 2, 3"
        },
        "Coach_ID": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for a coach",
          "optimization_purpose": "index for compatibility score",
          "sample_values": "1, 2, 3"
        },
        "compatibility_score": {
          "data_type": "FLOAT",
          "business_meaning": "compatibility score between a player and a coach",
          "optimization_purpose": "coefficient in objective function",
          "sample_values": "0.8, 0.6, 0.9"
        }
      }
    },
    "coach_constraints": {
      "business_purpose": "stores constraints related to coach availability and capacity",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Coach_ID": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for a coach",
          "optimization_purpose": "index for coach constraints",
          "sample_values": "1, 2, 3"
        },
        "max_players": {
          "data_type": "INTEGER",
          "business_meaning": "maximum number of players a coach can handle",
          "optimization_purpose": "constraint bound for coach capacity",
          "sample_values": "5, 6, 4"
        }
      }
    },
    "assignments": {
      "business_purpose": "stores binary decision variables indicating player-coach assignments",
      "optimization_role": "decision_variables",
      "columns": {
        "Player_ID": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for a player",
          "optimization_purpose": "index for assignment decision variable",
          "sample_values": "1, 2, 3"
        },
        "Coach_ID": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for a coach",
          "optimization_purpose": "index for assignment decision variable",
          "sample_values": "1, 2, 3"
        },
        "assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "binary variable indicating if a player is assigned to a coach",
          "optimization_purpose": "decision variable in optimization model",
          "sample_values": "true, false"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "min_compatibility_threshold": {
    "sample_value": 0.5,
    "data_type": "FLOAT",
    "business_meaning": "minimum compatibility score required for a player-coach assignment",
    "optimization_role": "constraint bound for player-coach compatibility",
    "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": "riding_club",
  "iteration": 2,
  "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": "riding_club",
  "iteration": 2,
  "business_context": "A riding club aims to maximize its total points from match results by optimally assigning players to coaches, considering the constraints of coach availability and player-coach compatibility.",
  "optimization_problem_description": "The objective is to maximize the total points scored by the club by assigning players to coaches based on compatibility scores, while respecting coach capacity constraints and ensuring each assignment meets a minimum compatibility threshold.",
  "optimization_formulation": {
    "objective": "maximize total_points = \u2211(compatibility_score[Player_ID, Coach_ID] * assignment[Player_ID, Coach_ID])",
    "decision_variables": "assignment[Player_ID, Coach_ID] are binary variables indicating if a player is assigned to a coach",
    "constraints": [
      "\u2211(assignment[Player_ID, Coach_ID]) <= max_players[Coach_ID] for each Coach_ID",
      "compatibility_score[Player_ID, Coach_ID] * assignment[Player_ID, Coach_ID] >= min_compatibility_threshold for each Player_ID, Coach_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "compatibility_score[Player_ID, Coach_ID]": {
        "currently_mapped_to": "compatibility_scores.compatibility_score",
        "mapping_adequacy": "good",
        "description": "compatibility score between a player and a coach used as a coefficient in the objective function"
      }
    },
    "constraint_bounds": {
      "max_players[Coach_ID]": {
        "currently_mapped_to": "coach_constraints.max_players",
        "mapping_adequacy": "good",
        "description": "maximum number of players a coach can handle"
      },
      "min_compatibility_threshold": {
        "currently_mapped_to": "business_configuration_logic.min_compatibility_threshold",
        "mapping_adequacy": "good",
        "description": "minimum compatibility score required for a player-coach assignment"
      }
    },
    "decision_variables": {
      "assignment[Player_ID, Coach_ID]": {
        "currently_mapped_to": "assignments.assignment",
        "mapping_adequacy": "good",
        "description": "binary variable indicating if a player is assigned to a coach",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
