Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:27:23

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 college soccer team aims to select players for tryouts to maximize the overall skill level while respecting constraints on the number of players per position and the total number of players.",
  "optimization_problem": "The objective is to maximize the total skill level of selected players for tryouts, considering constraints on the number of players per position and the total number of players.",
  "objective": "maximize \u2211(skill_level[pID] * select[pID])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating tables for player skills and position limits, and moving scalar parameters to business configuration logic."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define and map skill levels and position limits for complete optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for player skills and position limits, and moving scalar parameters to business configuration logic.

CREATE TABLE player_skills (
  player_id INTEGER,
  skill_level FLOAT,
  select BOOLEAN
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "player_skills": {
      "business_purpose": "Skill levels of players for tryouts",
      "optimization_role": "objective_coefficients",
      "columns": {
        "player_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each player",
          "optimization_purpose": "Index for decision variables",
          "sample_values": [
            1,
            2,
            3
          ]
        },
        "skill_level": {
          "data_type": "FLOAT",
          "business_meaning": "Skill level of the player",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": [
            8.5,
            7.2,
            9.0
          ]
        },
        "select": {
          "data_type": "BOOLEAN",
          "business_meaning": "Whether the player is selected for tryouts",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": [
            true,
            false,
            true
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_players_limit": {
    "sample_value": 20,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of players to be selected",
    "optimization_role": "Constraint bound for total players",
    "configuration_type": "scalar_parameter"
  },
  "forwards_limit": {
    "sample_value": 5,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of forwards to be selected",
    "optimization_role": "Constraint bound for forwards",
    "configuration_type": "scalar_parameter"
  },
  "midfielders_limit": {
    "sample_value": 7,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of midfielders to be selected",
    "optimization_role": "Constraint bound for midfielders",
    "configuration_type": "scalar_parameter"
  },
  "defenders_limit": {
    "sample_value": 6,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of defenders to be selected",
    "optimization_role": "Constraint bound for defenders",
    "configuration_type": "scalar_parameter"
  },
  "goalkeepers_limit": {
    "sample_value": 2,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of goalkeepers to be selected",
    "optimization_role": "Constraint bound for goalkeepers",
    "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": "soccer_2",
  "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": "soccer_2",
  "iteration": 1,
  "business_context": "A college soccer team aims to select players for tryouts to maximize the overall skill level while respecting constraints on the number of players per position and the total number of players.",
  "optimization_problem_description": "Maximize the total skill level of selected players for tryouts, considering constraints on the number of players per position and the total number of players.",
  "optimization_formulation": {
    "objective": "maximize \u2211(skill_level[pID] * select[pID])",
    "decision_variables": "select[pID]: binary variable indicating whether player pID is selected for tryouts",
    "constraints": "\u2211(select[pID]) \u2264 total_players_limit, \u2211(select[pID] where pID is a forward) \u2264 forwards_limit, \u2211(select[pID] where pID is a midfielder) \u2264 midfielders_limit, \u2211(select[pID] where pID is a defender) \u2264 defenders_limit, \u2211(select[pID] where pID is a goalkeeper) \u2264 goalkeepers_limit"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "skill_level[pID]": {
        "currently_mapped_to": "player_skills.skill_level",
        "mapping_adequacy": "good",
        "description": "Skill level of player pID"
      }
    },
    "constraint_bounds": {
      "total_players_limit": {
        "currently_mapped_to": "business_configuration_logic.total_players_limit",
        "mapping_adequacy": "good",
        "description": "Maximum number of players to be selected"
      },
      "forwards_limit": {
        "currently_mapped_to": "business_configuration_logic.forwards_limit",
        "mapping_adequacy": "good",
        "description": "Maximum number of forwards to be selected"
      },
      "midfielders_limit": {
        "currently_mapped_to": "business_configuration_logic.midfielders_limit",
        "mapping_adequacy": "good",
        "description": "Maximum number of midfielders to be selected"
      },
      "defenders_limit": {
        "currently_mapped_to": "business_configuration_logic.defenders_limit",
        "mapping_adequacy": "good",
        "description": "Maximum number of defenders to be selected"
      },
      "goalkeepers_limit": {
        "currently_mapped_to": "business_configuration_logic.goalkeepers_limit",
        "mapping_adequacy": "good",
        "description": "Maximum number of goalkeepers to be selected"
      }
    },
    "decision_variables": {
      "select[pID]": {
        "currently_mapped_to": "player_skills.select",
        "mapping_adequacy": "good",
        "description": "Whether player pID is selected for tryouts",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
