Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-25 22:34:33

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 decoration competition is held among colleges, where each college sends members to participate in rounds with different themes. The goal is to maximize the overall ranking of a college by strategically assigning members to rounds based on their strengths in specific themes.",
  "optimization_problem": "The optimization problem aims to maximize the total ranking points of a college by assigning members to rounds in a way that leverages their strengths in specific decoration themes. The objective is linear, and constraints ensure that each member is assigned to a limited number of rounds and that each round has a specific number of participants.",
  "objective": "maximize \u2211(Rank_in_Round[Member_ID, Round_ID] \u00d7 Assignment_Indicator[Member_ID, Round_ID])",
  "table_count": 1,
  "key_changes": [
    "Added a new table for ranking points to address the missing optimization requirement. Updated business configuration logic to include scalar parameters and formulas. Ensured all tables meet the 3-row minimum rule."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Add data for Rank_in_Round[Member_ID, Round_ID] to complete the linear formulation.",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Added a new table for ranking points to address the missing optimization requirement. Updated business configuration logic to include scalar parameters and formulas. Ensured all tables meet the 3-row minimum rule.

CREATE TABLE assignment_indicator (
  Member_ID INTEGER,
  Round_ID INTEGER,
  Assignment_Indicator BOOLEAN
);

CREATE TABLE member_limit (
  Member_ID INTEGER,
  Member_Limit INTEGER
);

CREATE TABLE round_requirement (
  Round_ID INTEGER,
  Round_Requirement INTEGER
);

CREATE TABLE rank_in_round (
  Member_ID INTEGER,
  Round_ID INTEGER,
  Rank_in_Round INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "assignment_indicator": {
      "business_purpose": "Tracks which members are assigned to which rounds.",
      "optimization_role": "decision_variables",
      "columns": {
        "Member_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a member.",
          "optimization_purpose": "Used to identify the member in the assignment decision.",
          "sample_values": "1, 2, 3"
        },
        "Round_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a round.",
          "optimization_purpose": "Used to identify the round in the assignment decision.",
          "sample_values": "1, 2, 3"
        },
        "Assignment_Indicator": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if the member is assigned to the round.",
          "optimization_purpose": "Binary decision variable in the optimization model.",
          "sample_values": "true, false"
        }
      }
    },
    "member_limit": {
      "business_purpose": "Stores the maximum number of rounds each member can participate in.",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Member_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a member.",
          "optimization_purpose": "Used to identify the member in the constraint.",
          "sample_values": "1, 2, 3"
        },
        "Member_Limit": {
          "data_type": "INTEGER",
          "business_meaning": "The maximum number of rounds the member can participate in.",
          "optimization_purpose": "Used in the constraint to limit member participation.",
          "sample_values": "1, 1, 1"
        }
      }
    },
    "round_requirement": {
      "business_purpose": "Stores the number of participants required for each round.",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Round_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a round.",
          "optimization_purpose": "Used to identify the round in the constraint.",
          "sample_values": "1, 2, 3"
        },
        "Round_Requirement": {
          "data_type": "INTEGER",
          "business_meaning": "The number of participants required for the round.",
          "optimization_purpose": "Used in the constraint to ensure the round has the required number of participants.",
          "sample_values": "1, 1, 1"
        }
      }
    },
    "rank_in_round": {
      "business_purpose": "Stores the ranking points a member achieves in a specific round.",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Member_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a member.",
          "optimization_purpose": "Used to identify the member in the ranking calculation.",
          "sample_values": "1, 2, 3"
        },
        "Round_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for a round.",
          "optimization_purpose": "Used to identify the round in the ranking calculation.",
          "sample_values": "1, 2, 3"
        },
        "Rank_in_Round": {
          "data_type": "INTEGER",
          "business_meaning": "The ranking points a member achieves in a specific round.",
          "optimization_purpose": "Used in the objective function to maximize total ranking points.",
          "sample_values": "10, 20, 30"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "member_limit": {
    "sample_value": 1,
    "data_type": "INTEGER",
    "business_meaning": "The maximum number of rounds a member can participate in.",
    "optimization_role": "Used in the constraint to limit member participation.",
    "configuration_type": "scalar_parameter"
  },
  "round_requirement": {
    "sample_value": 1,
    "data_type": "INTEGER",
    "business_meaning": "The number of participants required for each round.",
    "optimization_role": "Used in the constraint to ensure each round has the required number of participants.",
    "configuration_type": "scalar_parameter"
  },
  "rank_in_round_formula": {
    "formula_expression": "Rank_in_Round[Member_ID, Round_ID]",
    "data_type": "STRING",
    "business_meaning": "The ranking points a member achieves in a specific round.",
    "optimization_role": "Used in the objective function to maximize total ranking points.",
    "configuration_type": "business_logic_formula"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "decoration_competition",
  "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": "decoration_competition",
  "iteration": 2,
  "business_context": "A decoration competition is held among colleges, where each college sends members to participate in rounds with different themes. The goal is to maximize the overall ranking of a college by strategically assigning members to rounds based on their strengths in specific themes.",
  "optimization_problem_description": "The optimization problem aims to maximize the total ranking points of a college by assigning members to rounds in a way that leverages their strengths in specific decoration themes. The objective is linear, and constraints ensure that each member is assigned to a limited number of rounds and that each round has a specific number of participants.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Rank_in_Round[Member_ID, Round_ID] \u00d7 Assignment_Indicator[Member_ID, Round_ID])",
    "decision_variables": "Assignment_Indicator[Member_ID, Round_ID] (binary)",
    "constraints": [
      "\u2211(Assignment_Indicator[Member_ID, Round_ID] for each Round_ID) \u2264 Member_Limit[Member_ID] for each Member_ID",
      "\u2211(Assignment_Indicator[Member_ID, Round_ID] for each Member_ID) = Round_Requirement[Round_ID] for each Round_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Rank_in_Round[Member_ID, Round_ID]": {
        "currently_mapped_to": "rank_in_round.Rank_in_Round",
        "mapping_adequacy": "good",
        "description": "The ranking points a member achieves in a specific round."
      }
    },
    "constraint_bounds": {
      "Member_Limit[Member_ID]": {
        "currently_mapped_to": "member_limit.Member_Limit",
        "mapping_adequacy": "good",
        "description": "The maximum number of rounds a member can participate in."
      },
      "Round_Requirement[Round_ID]": {
        "currently_mapped_to": "round_requirement.Round_Requirement",
        "mapping_adequacy": "good",
        "description": "The number of participants required for each round."
      }
    },
    "decision_variables": {
      "Assignment_Indicator[Member_ID, Round_ID]": {
        "currently_mapped_to": "assignment_indicator.Assignment_Indicator",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if a member is assigned to a round.",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
