Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:27:49

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 aims to minimize the total cost of operating flights while ensuring that each flight route is covered and that the number of flights does not exceed the capacity of each airport.",
  "optimization_problem": "The objective is to minimize the total operating cost of flights, which is a linear function of the number of flights on each route. Constraints include ensuring that each route is covered by at least one flight and that the number of flights departing from and arriving at each airport does not exceed the airport's capacity.",
  "objective": "minimize \u2211(cost_per_flight[route] \u00d7 flights[route])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for cost_per_flight and airport_capacity, modifying the flights table to better map decision variables, and adding business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Identify and map missing data for cost_per_flight and airport_capacity",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for cost_per_flight and airport_capacity, modifying the flights table to better map decision variables, and adding business configuration logic for scalar parameters and formulas.

CREATE TABLE cost_per_flight (
  route STRING,
  cost INTEGER
);

CREATE TABLE airport_capacity (
  airport STRING,
  capacity INTEGER
);

CREATE TABLE flights (
  route STRING,
  flight_count INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "cost_per_flight": {
      "business_purpose": "cost of operating a flight on a specific route",
      "optimization_role": "objective_coefficients",
      "columns": {
        "route": {
          "data_type": "STRING",
          "business_meaning": "specific flight route",
          "optimization_purpose": "index for cost_per_flight",
          "sample_values": "NYC-LAX"
        },
        "cost": {
          "data_type": "INTEGER",
          "business_meaning": "cost of operating a flight on this route",
          "optimization_purpose": "coefficient in the objective function",
          "sample_values": 5000
        }
      }
    },
    "airport_capacity": {
      "business_purpose": "maximum number of flights an airport can handle",
      "optimization_role": "constraint_bounds",
      "columns": {
        "airport": {
          "data_type": "STRING",
          "business_meaning": "specific airport",
          "optimization_purpose": "index for airport_capacity",
          "sample_values": "JFK"
        },
        "capacity": {
          "data_type": "INTEGER",
          "business_meaning": "maximum number of flights this airport can handle",
          "optimization_purpose": "bound in the constraints",
          "sample_values": 100
        }
      }
    },
    "flights": {
      "business_purpose": "number of flights on a specific route",
      "optimization_role": "decision_variables",
      "columns": {
        "route": {
          "data_type": "STRING",
          "business_meaning": "specific flight route",
          "optimization_purpose": "index for flights",
          "sample_values": "NYC-LAX"
        },
        "flight_count": {
          "data_type": "INTEGER",
          "business_meaning": "number of flights on this route",
          "optimization_purpose": "decision variable in the optimization model",
          "sample_values": 3
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "cost_per_flight": {
    "sample_value": 5000,
    "data_type": "INTEGER",
    "business_meaning": "cost of operating a flight on a specific route",
    "optimization_role": "coefficient in the objective function",
    "configuration_type": "scalar_parameter"
  },
  "airport_capacity": {
    "sample_value": 100,
    "data_type": "INTEGER",
    "business_meaning": "maximum number of flights an airport can handle",
    "optimization_role": "bound in the constraints",
    "configuration_type": "scalar_parameter"
  },
  "total_operating_cost": {
    "formula_expression": "sum(cost_per_flight[route] * flights[route])",
    "data_type": "STRING",
    "business_meaning": "total cost of operating all flights",
    "optimization_role": "objective function to minimize",
    "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_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 minimize the total cost of operating flights while ensuring that each flight route is covered and that the number of flights does not exceed the capacity of each airport.",
  "optimization_problem_description": "Minimize the total operating cost of flights, which is a linear function of the number of flights on each route. Constraints include ensuring that each route is covered by at least one flight and that the number of flights departing from and arriving at each airport does not exceed the airport's capacity.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_per_flight[route] \u00d7 flights[route])",
    "decision_variables": "flights[route] (integer)",
    "constraints": [
      "flights[route] \u2265 1 for all routes",
      "\u2211(flights[route] for all routes departing from airport) \u2264 airport_capacity[airport] for all airports",
      "\u2211(flights[route] for all routes arriving at airport) \u2264 airport_capacity[airport] for all airports"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_per_flight[route]": {
        "currently_mapped_to": "cost_per_flight.cost",
        "mapping_adequacy": "good",
        "description": "cost of operating a flight on a specific route"
      }
    },
    "constraint_bounds": {
      "airport_capacity[airport]": {
        "currently_mapped_to": "airport_capacity.capacity",
        "mapping_adequacy": "good",
        "description": "maximum number of flights an airport can handle"
      }
    },
    "decision_variables": {
      "flights[route]": {
        "currently_mapped_to": "flights.flight_count",
        "mapping_adequacy": "good",
        "description": "number of flights on a specific route",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
