Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-27 23:56:55

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 university is optimizing the allocation of students' time between playing video games and participating in sports to maximize their overall engagement while ensuring academic responsibilities are not compromised.",
  "optimization_problem": "The goal is to maximize the total engagement score of students by allocating their available hours between playing video games and participating in sports, subject to constraints on maximum hours available, minimum academic hours required, and scholarship requirements.",
  "objective": "maximize total_engagement = sum(GameEngagementScore[StuID, GameID] * x[StuID, GameID] + SportEngagementScore[StuID, SportName] * y[StuID, SportName])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for decision variables, modifying existing tables to improve mapping adequacy, and moving scalar parameters to configuration logic."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Map decision variables to schema or configuration logic",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating new tables for decision variables, modifying existing tables to improve mapping adequacy, and moving scalar parameters to configuration logic.

CREATE TABLE EngagementScores (
  StuID INTEGER,
  GameID INTEGER,
  SportName STRING,
  GameEngagementScore FLOAT,
  SportEngagementScore FLOAT
);

CREATE TABLE GameAllocation (
  StuID INTEGER,
  GameID INTEGER,
  HoursAllocated FLOAT
);

CREATE TABLE SportAllocation (
  StuID INTEGER,
  SportName STRING,
  HoursAllocated FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "EngagementScores": {
      "business_purpose": "Stores engagement scores for students.",
      "optimization_role": "objective_coefficients",
      "columns": {
        "StuID": {
          "data_type": "INTEGER",
          "business_meaning": "Student identifier.",
          "optimization_purpose": "Links engagement scores to students.",
          "sample_values": "1, 2, 3"
        },
        "GameID": {
          "data_type": "INTEGER",
          "business_meaning": "Game identifier.",
          "optimization_purpose": "Links engagement scores to games.",
          "sample_values": "101, 102, 103"
        },
        "SportName": {
          "data_type": "STRING",
          "business_meaning": "Name of the sport.",
          "optimization_purpose": "Links engagement scores to sports.",
          "sample_values": "Basketball, Soccer, Tennis"
        },
        "GameEngagementScore": {
          "data_type": "FLOAT",
          "business_meaning": "Engagement score for games.",
          "optimization_purpose": "Coefficient in objective function.",
          "sample_values": "1.5, 2.0, 2.5"
        },
        "SportEngagementScore": {
          "data_type": "FLOAT",
          "business_meaning": "Engagement score for sports.",
          "optimization_purpose": "Coefficient in objective function.",
          "sample_values": "1.0, 1.8, 2.2"
        }
      }
    },
    "GameAllocation": {
      "business_purpose": "Stores hours allocated by students to games.",
      "optimization_role": "decision_variables",
      "columns": {
        "StuID": {
          "data_type": "INTEGER",
          "business_meaning": "Student identifier.",
          "optimization_purpose": "Links allocation to students.",
          "sample_values": "1, 2, 3"
        },
        "GameID": {
          "data_type": "INTEGER",
          "business_meaning": "Game identifier.",
          "optimization_purpose": "Links allocation to games.",
          "sample_values": "101, 102, 103"
        },
        "HoursAllocated": {
          "data_type": "FLOAT",
          "business_meaning": "Hours allocated by student to game.",
          "optimization_purpose": "Decision variable in optimization model.",
          "sample_values": "2.0, 3.5, 4.0"
        }
      }
    },
    "SportAllocation": {
      "business_purpose": "Stores hours allocated by students to sports.",
      "optimization_role": "decision_variables",
      "columns": {
        "StuID": {
          "data_type": "INTEGER",
          "business_meaning": "Student identifier.",
          "optimization_purpose": "Links allocation to students.",
          "sample_values": "1, 2, 3"
        },
        "SportName": {
          "data_type": "STRING",
          "business_meaning": "Name of the sport.",
          "optimization_purpose": "Links allocation to sports.",
          "sample_values": "Basketball, Soccer, Tennis"
        },
        "HoursAllocated": {
          "data_type": "FLOAT",
          "business_meaning": "Hours allocated by student to sport.",
          "optimization_purpose": "Decision variable in optimization model.",
          "sample_values": "1.5, 2.0, 2.5"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_hours_available": {
    "sample_value": 40,
    "data_type": "INTEGER",
    "business_meaning": "Total hours a student can allocate to games and sports.",
    "optimization_role": "Used as a constraint in optimization model.",
    "configuration_type": "scalar_parameter"
  },
  "min_sport_hours": {
    "sample_value": 5,
    "data_type": "INTEGER",
    "business_meaning": "Minimum hours a student on scholarship must spend on sports.",
    "optimization_role": "Used as a constraint in optimization model.",
    "configuration_type": "scalar_parameter"
  },
  "max_game_hours": {
    "sample_value": 15,
    "data_type": "INTEGER",
    "business_meaning": "Maximum hours a student can spend on games.",
    "optimization_role": "Used as a constraint 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": "game_1",
  "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": "game_1",
  "iteration": 2,
  "business_context": "A university is optimizing the allocation of students' time between playing video games and participating in sports to maximize their overall engagement while ensuring academic responsibilities are not compromised.",
  "optimization_problem_description": "The goal is to maximize the total engagement score of students by allocating their available hours between playing video games and participating in sports, subject to constraints on maximum hours available, minimum academic hours required, and scholarship requirements.",
  "optimization_formulation": {
    "objective": "maximize total_engagement = sum(GameEngagementScore[StuID, GameID] * x[StuID, GameID] + SportEngagementScore[StuID, SportName] * y[StuID, SportName])",
    "decision_variables": "x[StuID, GameID] and y[StuID, SportName] are continuous variables representing hours allocated to games and sports respectively",
    "constraints": [
      "sum(x[StuID, GameID] + y[StuID, SportName]) <= total_hours_available for each StuID",
      "sum(y[StuID, SportName]) >= min_sport_hours for each StuID on scholarship",
      "sum(x[StuID, GameID]) <= max_game_hours for each StuID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "GameEngagementScore[StuID, GameID]": {
        "currently_mapped_to": "EngagementScores.GameEngagementScore",
        "mapping_adequacy": "good",
        "description": "Engagement score for games used as coefficient in objective function"
      },
      "SportEngagementScore[StuID, SportName]": {
        "currently_mapped_to": "EngagementScores.SportEngagementScore",
        "mapping_adequacy": "good",
        "description": "Engagement score for sports used as coefficient in objective function"
      }
    },
    "constraint_bounds": {
      "total_hours_available": {
        "currently_mapped_to": "business_configuration_logic.total_hours_available",
        "mapping_adequacy": "good",
        "description": "Total hours a student can allocate to games and sports"
      },
      "min_sport_hours": {
        "currently_mapped_to": "business_configuration_logic.min_sport_hours",
        "mapping_adequacy": "good",
        "description": "Minimum hours a student on scholarship must spend on sports"
      },
      "max_game_hours": {
        "currently_mapped_to": "business_configuration_logic.max_game_hours",
        "mapping_adequacy": "good",
        "description": "Maximum hours a student can spend on games"
      }
    },
    "decision_variables": {
      "x[StuID, GameID]": {
        "currently_mapped_to": "GameAllocation.HoursAllocated",
        "mapping_adequacy": "good",
        "description": "Hours allocated by student to game",
        "variable_type": "continuous"
      },
      "y[StuID, SportName]": {
        "currently_mapped_to": "SportAllocation.HoursAllocated",
        "mapping_adequacy": "good",
        "description": "Hours allocated by student to sport",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
