Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 21:50:50

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 political organization wants to optimize the allocation of speakers to debates to maximize the total audience reached, considering constraints on the number of debates each speaker can attend and the total number of speakers available for each debate.",
  "optimization_problem": "The goal is to maximize the total number of audience members reached by optimally assigning speakers to debates. Each speaker can participate in a limited number of debates, and each debate can have a limited number of speakers.",
  "objective": "maximize \u2211(Num_of_Audience[Debate_ID] \u00d7 x[Debate_ID, People_ID])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for decision variables and constraint bounds, modifying existing tables to fill mapping gaps, and moving scalar parameters to configuration logic."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Determine the maximum number of debates each speaker can attend and the maximum number of speakers per debate",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for decision variables and constraint bounds, modifying existing tables to fill mapping gaps, and moving scalar parameters to configuration logic.

CREATE TABLE debate (
  Debate_ID INTEGER,
  Num_of_Audience INTEGER
);

CREATE TABLE decision_variables (
  Debate_ID INTEGER,
  People_ID INTEGER,
  assignment BOOLEAN
);

CREATE TABLE constraint_bounds (
  Constraint_Name STRING,
  Value INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "debate": {
      "business_purpose": "Stores information about debates including audience size",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Debate_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each debate",
          "optimization_purpose": "Index for debates in optimization",
          "sample_values": "1, 2, 3"
        },
        "Num_of_Audience": {
          "data_type": "INTEGER",
          "business_meaning": "Number of audience members for each debate",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "100, 200, 300"
        }
      }
    },
    "decision_variables": {
      "business_purpose": "Stores binary decision variables for speaker assignments",
      "optimization_role": "decision_variables",
      "columns": {
        "Debate_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for debate",
          "optimization_purpose": "Index for debates in decision variables",
          "sample_values": "1, 2, 3"
        },
        "People_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for speaker",
          "optimization_purpose": "Index for speakers in decision variables",
          "sample_values": "101, 102, 103"
        },
        "assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a speaker is assigned to a debate",
          "optimization_purpose": "Binary decision variable",
          "sample_values": "true, false"
        }
      }
    },
    "constraint_bounds": {
      "business_purpose": "Stores constraint bounds for debates and speakers",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Constraint_Name": {
          "data_type": "STRING",
          "business_meaning": "Name of the constraint",
          "optimization_purpose": "Identifies the constraint type",
          "sample_values": "Max_Debates_Per_Speaker, Max_Speakers_Per_Debate"
        },
        "Value": {
          "data_type": "INTEGER",
          "business_meaning": "Value of the constraint bound",
          "optimization_purpose": "Bound value for constraints",
          "sample_values": "3, 5"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "Max_Debates_Per_Speaker": {
    "sample_value": "3",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of debates a speaker can attend",
    "optimization_role": "Constraint bound for speaker participation",
    "configuration_type": "scalar_parameter"
  },
  "Max_Speakers_Per_Debate": {
    "sample_value": "5",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of speakers allowed per debate",
    "optimization_role": "Constraint bound for debate participation",
    "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": "debate",
  "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": "debate",
  "iteration": 1,
  "business_context": "A political organization wants to optimize the allocation of speakers to debates to maximize the total audience reached, considering constraints on the number of debates each speaker can attend and the total number of speakers available for each debate.",
  "optimization_problem_description": "The goal is to maximize the total number of audience members reached by optimally assigning speakers to debates. Each speaker can participate in a limited number of debates, and each debate can have a limited number of speakers.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Num_of_Audience[Debate_ID] \u00d7 x[Debate_ID, People_ID])",
    "decision_variables": "x[Debate_ID, People_ID] are binary variables indicating if a speaker is assigned to a debate",
    "constraints": [
      "\u2211(x[Debate_ID, People_ID]) \u2264 Max_Debates_Per_Speaker for each People_ID",
      "\u2211(x[Debate_ID, People_ID]) \u2264 Max_Speakers_Per_Debate for each Debate_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Num_of_Audience[Debate_ID]": {
        "currently_mapped_to": "debate.Num_of_Audience",
        "mapping_adequacy": "good",
        "description": "Number of audience members for each debate, used as coefficients in the objective function"
      }
    },
    "constraint_bounds": {
      "Max_Debates_Per_Speaker": {
        "currently_mapped_to": "business_configuration_logic.Max_Debates_Per_Speaker",
        "mapping_adequacy": "good",
        "description": "Maximum number of debates a speaker can attend"
      },
      "Max_Speakers_Per_Debate": {
        "currently_mapped_to": "business_configuration_logic.Max_Speakers_Per_Debate",
        "mapping_adequacy": "good",
        "description": "Maximum number of speakers allowed per debate"
      }
    },
    "decision_variables": {
      "x[Debate_ID, People_ID]": {
        "currently_mapped_to": "decision_variables.assignment",
        "mapping_adequacy": "good",
        "description": "Binary decision variable indicating if a speaker is assigned to a debate",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
