Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 21:44:00

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 flight company wants to optimize the allocation of its flights to different airports to minimize the total operational cost while ensuring that each airport can handle the assigned flights within its capacity.",
  "optimization_problem": "The goal is to minimize the total operational cost of flights by optimally assigning flights to airports. The cost is influenced by factors such as distance, airport fees, and operational constraints. The company must ensure that each airport does not exceed its capacity and that all flights are assigned to an airport.",
  "objective": "minimize total_cost = sum(c_ij * x_ij) for all flights i and airports j",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for objective coefficients and constraint bounds, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Gather missing cost and capacity data to complete the optimization model",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for objective coefficients and constraint bounds, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE Flights (
  flight_id INTEGER,
  airport_id INTEGER,
  assignment BOOLEAN
);

CREATE TABLE Airports (
  airport_id INTEGER,
  capacity INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "Flights": {
      "business_purpose": "Represents the assignment of flights to airports",
      "optimization_role": "decision_variables",
      "columns": {
        "flight_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each flight",
          "optimization_purpose": "Identifies flights in optimization model",
          "sample_values": "1, 2, 3"
        },
        "airport_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for the assigned airport",
          "optimization_purpose": "Links flights to airports in optimization model",
          "sample_values": "101, 102, 103"
        },
        "assignment": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if a flight is assigned to an airport",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        }
      }
    },
    "Airports": {
      "business_purpose": "Contains data about airports including their capacity",
      "optimization_role": "business_data",
      "columns": {
        "airport_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each airport",
          "optimization_purpose": "Identifies airports in optimization model",
          "sample_values": "101, 102, 103"
        },
        "capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of flights an airport can handle",
          "optimization_purpose": "Constraint bound in optimization model",
          "sample_values": "100, 150, 200"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "airport_capacity": {
    "sample_value": "100",
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of flights an airport can handle",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "cost_coefficient_formula": {
    "formula_expression": "distance * fee_rate",
    "data_type": "STRING",
    "business_meaning": "Formula to calculate cost of assigning a flight to an airport",
    "optimization_role": "Used to calculate objective coefficients in optimization model",
    "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": "flight_company",
  "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": "flight_company",
  "iteration": 1,
  "business_context": "A flight company aims to optimize the allocation of its flights to different airports to minimize the total operational cost while ensuring that each airport can handle the assigned flights within its capacity.",
  "optimization_problem_description": "The objective is to minimize the total operational cost of flights by optimally assigning flights to airports. The cost is influenced by factors such as distance and airport fees. The company must ensure that each airport does not exceed its capacity and that all flights are assigned to an airport.",
  "optimization_formulation": {
    "objective": "minimize total_cost = sum(c_ij * x_ij) for all flights i and airports j",
    "decision_variables": "x_ij: binary variable indicating if flight i is assigned to airport j",
    "constraints": [
      "sum(x_ij for all j) = 1 for each flight i",
      "sum(x_ij for all i) <= capacity_j for each airport j"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "c_ij": {
        "currently_mapped_to": "business_configuration_logic.cost_coefficient_formula",
        "mapping_adequacy": "partial",
        "description": "Cost of assigning flight i to airport j, calculated using distance and fee rate"
      }
    },
    "constraint_bounds": {
      "capacity_j": {
        "currently_mapped_to": "Airports.capacity",
        "mapping_adequacy": "good",
        "description": "Maximum number of flights airport j can handle"
      }
    },
    "decision_variables": {
      "x_ij": {
        "currently_mapped_to": "Flights.assignment",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if flight i is assigned to airport j",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "distance data for cost calculation",
    "fee rate data for cost calculation"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Gather missing distance and fee rate data to complete the linear optimization model"
  }
}
