Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:45:14

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either 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
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.

Database: flight_4

```sql
CREATE TABLE routes (
  rid NUMBER,
  dst_apid NUMBER,
  dst_ap TEXT,
  src_apid NUMBER,
  src_ap TEXT,
  alid NUMBER,
  airline TEXT,
  codeshare TEXT
);
```

```sql
CREATE TABLE airports (
  apid NUMBER,
  name TEXT,
  city TEXT,
  country TEXT,
  x NUMBER,
  y NUMBER,
  elevation NUMBER,
  iata TEXT,
  icao TEXT
);
```

```sql
CREATE TABLE airlines (
  alid NUMBER,
  name TEXT,
  iata TEXT,
  icao TEXT,
  callsign TEXT,
  country TEXT,
  active TEXT
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "flight_4",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 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 needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "flight_4",
  "iteration": 0,
  "business_context": "Optimizing airline route assignments to minimize total operational costs while ensuring coverage of all required destinations.",
  "optimization_problem_description": "The goal is to assign flights to routes in a way that minimizes the total cost of operations, considering factors like distance and airline-specific costs, while ensuring all destinations are covered and no airline exceeds its capacity.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_airline_route \u00d7 assign_airline_route)",
    "decision_variables": "assign_airline_route: binary variable indicating whether an airline is assigned to a specific route",
    "constraints": [
      "\u2211(assign_airline_route) = 1 for each route (each route must be assigned to exactly one airline)",
      "\u2211(assign_airline_route) \u2264 capacity_airline for each airline (no airline exceeds its capacity)",
      "assign_airline_route \u2208 {0, 1} for all airline-route pairs (binary decision variables)"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_airline_route[alid, rid]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "cost of assigning a specific airline to a specific route"
      }
    },
    "constraint_bounds": {
      "capacity_airline[alid]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of routes an airline can handle"
      }
    },
    "decision_variables": {
      "assign_airline_route[alid, rid]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "binary decision variable indicating assignment of airline to route",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "cost_airline_route: cost data for each airline-route pair",
    "capacity_airline: capacity data for each airline"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Obtain cost and capacity data for airlines and routes to complete the optimization model."
  }
}
