Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 21:43:21

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": "An airline company wants to optimize its flight schedule to minimize operational costs while ensuring all scheduled flights are covered by available aircraft.",
  "optimization_problem": "The goal is to minimize the total operational cost of flights by selecting the optimal set of flights to operate, considering constraints such as aircraft availability, flight coverage, and airport capacity.",
  "objective": "minimize total_operational_cost = sum(cost_flight[i] * x[i] for all flights i)",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization data, modifying existing tables to fill mapping gaps, and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Gather missing data for cost coefficients and constraint bounds",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data, modifying existing tables to fill mapping gaps, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE FlightCosts (
  FlightNo STRING,
  Cost FLOAT
);

CREATE TABLE MandatoryFlights (
  FlightNo STRING
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "FlightCosts": {
      "business_purpose": "Stores operational cost data for each flight",
      "optimization_role": "objective_coefficients",
      "columns": {
        "FlightNo": {
          "data_type": "STRING",
          "business_meaning": "Unique identifier for each flight",
          "optimization_purpose": "Links cost to specific flights",
          "sample_values": "FL123, FL456"
        },
        "Cost": {
          "data_type": "FLOAT",
          "business_meaning": "Operational cost for operating the flight",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "1000.0, 1500.0"
        }
      }
    },
    "MandatoryFlights": {
      "business_purpose": "Stores list of mandatory flights that must be operated",
      "optimization_role": "constraint_bounds",
      "columns": {
        "FlightNo": {
          "data_type": "STRING",
          "business_meaning": "Unique identifier for each mandatory flight",
          "optimization_purpose": "Ensures these flights are always operated",
          "sample_values": "FL789, FL101"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_departures": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of departures allowed from an airport",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "max_arrivals": {
    "sample_value": 10,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of arrivals allowed at an airport",
    "optimization_role": "Used as a constraint bound in optimization model",
    "configuration_type": "scalar_parameter"
  },
  "max_flights_airline": {
    "sample_value": 50,
    "data_type": "INTEGER",
    "business_meaning": "Maximum number of flights an airline can operate",
    "optimization_role": "Used as a constraint bound 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": "flight_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": "flight_2",
  "iteration": 1,
  "business_context": "An airline company aims to optimize its flight schedule to minimize operational costs while ensuring all scheduled flights are covered by available aircraft and adhering to airport capacity constraints.",
  "optimization_problem_description": "The objective is to minimize the total operational cost of flights by selecting the optimal set of flights to operate, considering constraints such as aircraft availability, mandatory flight coverage, and airport capacity limits.",
  "optimization_formulation": {
    "objective": "minimize total_operational_cost = sum(Cost[FlightNo] * x[FlightNo] for all FlightNo in FlightCosts)",
    "decision_variables": "x[FlightNo] for all FlightNo in FlightCosts, where x[FlightNo] is binary indicating if flight is operated",
    "constraints": [
      "sum(x[FlightNo] for all FlightNo in FlightCosts) <= max_flights_airline",
      "sum(x[FlightNo] for FlightNo in MandatoryFlights) = |MandatoryFlights|",
      "sum(x[FlightNo] for all FlightNo departing from an airport) <= max_departures",
      "sum(x[FlightNo] for all FlightNo arriving at an airport) <= max_arrivals"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Cost[FlightNo]": {
        "currently_mapped_to": "FlightCosts.Cost",
        "mapping_adequacy": "good",
        "description": "Operational cost for each flight, used as a coefficient in the objective function"
      }
    },
    "constraint_bounds": {
      "max_flights_airline": {
        "currently_mapped_to": "business_configuration_logic.max_flights_airline",
        "mapping_adequacy": "good",
        "description": "Maximum number of flights the airline can operate"
      },
      "MandatoryFlights": {
        "currently_mapped_to": "MandatoryFlights.FlightNo",
        "mapping_adequacy": "good",
        "description": "List of flights that must be operated"
      },
      "max_departures": {
        "currently_mapped_to": "business_configuration_logic.max_departures",
        "mapping_adequacy": "good",
        "description": "Maximum number of departures allowed from an airport"
      },
      "max_arrivals": {
        "currently_mapped_to": "business_configuration_logic.max_arrivals",
        "mapping_adequacy": "good",
        "description": "Maximum number of arrivals allowed at an airport"
      }
    },
    "decision_variables": {
      "x[FlightNo]": {
        "currently_mapped_to": "FlightCosts.FlightNo",
        "mapping_adequacy": "good",
        "description": "Binary variable indicating if a flight is operated",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
