Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:28:00

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 riding club aims to maximize the total points earned across all clubs in a season by optimally allocating players to coaches based on their performance and coach rankings.",
  "optimization_problem": "The objective is to maximize the total points earned by all clubs by assigning players to coaches in a way that leverages the coach's rank and the player's votes. Constraints include ensuring each player is assigned to only one coach, each coach has a limited number of players they can handle, and the total points are calculated based on the player's votes and coach's rank.",
  "objective": "maximize \u2211(Player_Votes[Player_ID] \u00d7 Coach_Rank[Coach_ID] \u00d7 Assignment[Player_ID, Coach_ID])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization requirements and updating business configuration logic to handle scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define the maximum number of players per coach and establish the assignment decision variable.",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization requirements and updating business configuration logic to handle scalar parameters and formulas.

CREATE TABLE player (
  Player_ID INTEGER,
  Votes INTEGER
);

CREATE TABLE coach (
  Coach_ID INTEGER,
  Rank INTEGER
);

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


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "player": {
      "business_purpose": "Represents players in the riding club.",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Player_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each player.",
          "optimization_purpose": "Index for player in optimization model.",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "Votes": {
          "data_type": "INTEGER",
          "business_meaning": "Votes received by the player.",
          "optimization_purpose": "Coefficient in objective function.",
          "sample_values": [
            10,
            15,
            20
          ]
        }
      }
    },
    "coach": {
      "business_purpose": "Represents coaches in the riding club.",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Coach_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each coach.",
          "optimization_purpose": "Index for coach in optimization model.",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "Rank": {
          "data_type": "INTEGER",
          "business_meaning": "Rank of the coach.",
          "optimization_purpose": "Coefficient in objective function.",
          "sample_values": [
            1,
            2,
            3
          ]
        }
      }
    },
    "assignment": {
      "business_purpose": "Represents the assignment of players to coaches.",
      "optimization_role": "decision_variables",
      "columns": {
        "Player_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each player.",
          "optimization_purpose": "Index for player in optimization model.",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "Coach_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each coach.",
          "optimization_purpose": "Index for coach in optimization model.",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "Assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a player is assigned to a coach.",
          "optimization_purpose": "Decision variable in optimization model.",
          "sample_values": [
            true,
            false,
            true
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Max_Players_Per_Coach": {
    "sample_value": 5,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of players a coach can handle.",
    "optimization_role": "Constraint bound in optimization model.",
    "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": 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": "riding_club",
  "iteration": 1,
  "business_context": "A riding club aims to maximize the total points earned across all clubs in a season by optimally allocating players to coaches based on their performance and coach rankings. The optimization problem is formulated as a linear programming model to ensure computational efficiency and scalability.",
  "optimization_problem_description": "The objective is to maximize the total points earned by all clubs by assigning players to coaches in a way that leverages the coach's rank and the player's votes. Constraints include ensuring each player is assigned to only one coach, each coach has a limited number of players they can handle, and the total points are calculated based on the player's votes and coach's rank.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Player_Votes[Player_ID] \u00d7 Coach_Rank[Coach_ID] \u00d7 Assignment[Player_ID, Coach_ID])",
    "decision_variables": "Assignment[Player_ID, Coach_ID] (binary)",
    "constraints": [
      "\u2211(Assignment[Player_ID, Coach_ID] for all Coach_ID) = 1 for each Player_ID",
      "\u2211(Assignment[Player_ID, Coach_ID] for all Player_ID) \u2264 Max_Players_Per_Coach for each Coach_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Player_Votes[Player_ID]": {
        "currently_mapped_to": "player.Votes",
        "mapping_adequacy": "good",
        "description": "Votes received by the player, used as a coefficient in the objective function."
      },
      "Coach_Rank[Coach_ID]": {
        "currently_mapped_to": "coach.Rank",
        "mapping_adequacy": "good",
        "description": "Rank of the coach, used as a coefficient in the objective function."
      }
    },
    "constraint_bounds": {
      "Max_Players_Per_Coach[Coach_ID]": {
        "currently_mapped_to": "business_configuration_logic.Max_Players_Per_Coach",
        "mapping_adequacy": "good",
        "description": "Maximum number of players a coach can handle, used as a constraint bound."
      }
    },
    "decision_variables": {
      "Assignment[Player_ID, Coach_ID]": {
        "currently_mapped_to": "assignment.Assignment",
        "mapping_adequacy": "good",
        "description": "Binary decision 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"
  }
}
