Iteration final - SOLVER_ANALYSIS
Sequence: 7
Timestamp: 2025-07-25 22:47:08

Prompt:
You are an operations research expert analyzing the results from three different optimization solvers. Based on the original mathematical formulation and solver execution results, provide a comprehensive analysis and final recommendation.

ORIGINAL MATHEMATICAL FORMULATION:
## 4. Mathematical Optimization Formulation

#### Decision Variables
Let \( x_{ij} \) be the number of aircraft of type \( i \) assigned to airport \( j \), where:
- \( i \in \{ \text{Boeing 737}, \text{Airbus A320}, \text{Boeing 777} \} \) (aircraft types)
- \( j \in \{ \text{JFK}, \text{LAX}, \text{ORD} \} \) (airport codes)

#### Objective Function
Minimize the total operational cost:
\[
\text{Minimize } Z = \sum_{i} \sum_{j} c_{ij} \cdot x_{ij}
\]
where \( c_{ij} \) is the operational cost of assigning aircraft type \( i \) to airport \( j \).

#### Constraints
1. **Passenger Demand Constraint**: For each airport \( j \), the total passenger capacity of all assigned aircraft must meet or exceed the airport's passenger demand:
\[
\sum_{i} p_i \cdot x_{ij} \geq d_j \quad \forall j
\]
where \( p_i \) is the passenger capacity of aircraft type \( i \), and \( d_j \) is the passenger demand at airport \( j \).

2. **Aircraft Movement Constraint**: For each airport \( j \), the total number of assigned aircraft must not exceed the airport's maximum number of aircraft movements:
\[
\sum_{i} x_{ij} \leq m_j \quad \forall j
\]
where \( m_j \) is the maximum number of aircraft movements at airport \( j \).

3. **Non-Negativity Constraint**: The number of aircraft assigned must be non-negative:
\[
x_{ij} \geq 0 \quad \forall i, j
\]

#### Data Source Verification
- \( c_{ij} \): `operational_costs.cost` (operational cost of assigning aircraft type \( i \) to airport \( j \))
- \( p_i \): `aircraft_capacity.passenger_capacity` (passenger capacity of aircraft type \( i \))
- \( d_j \): `airport.passenger_demand` (passenger demand at airport \( j \))
- \( m_j \): `airport.aircraft_movements` (maximum number of aircraft movements at airport \( j \))

#### Numerical Coefficients from Data
- **Operational Costs (\( c_{ij} \))**:
  - Boeing 737 at JFK: 5000.0
  - Airbus A320 at JFK: 5500.0
  - Boeing 777 at JFK: 8000.0
  - Boeing 737 at LAX: 4800.0
  - Airbus A320 at LAX: 5200.0

- **Passenger Capacities (\( p_i \))**:
  - Boeing 737: 150
  - Airbus A320: 180
  - Boeing 777: 300

- **Passenger Demands (\( d_j \))**:
  - JFK: 15000
  - LAX: 20000
  - ORD: 18000

- **Aircraft Movements (\( m_j \))**:
  - JFK: 50
  - LAX: 60
  - ORD: 55

This formulation provides a complete, immediately solvable LINEAR mathematical model with all numerical coefficients derived from the provided data.

SOLVER EXECUTION RESULTS:
{
  "gurobipy": {
    "status": "error",
    "optimal_value": null,
    "execution_time": 0.18592000007629395,
    "error_message": "Traceback (most recent call last):\n  File \"/tmp/tmp9zwwqvft.py\", line 81, in <module>\n    aircraft_assignment_optimization()\n  File \"/tmp/tmp9zwwqvft.py\", line 45, in aircraft_assignment_optimization\n    gp.quicksum(operational_costs[(i, j)] * x[i, j] for i in aircraft_types for j in airports),\n  File \"src/gurobipy/_helpers.pyx\", line 41, in gurobipy._helpers.quicksum\n  File \"/tmp/tmp9zwwqvft.py\", line 45, in <genexpr>\n    gp.quicksum(operational_costs[(i, j)] * x[i, j] for i in aircraft_types for j in airports),\nKeyError: ('Boeing 777', 'LAX')\n",
    "retry_attempt": 4
  },
  "docplex": {
    "status": "infeasible",
    "optimal_value": null,
    "execution_time": 1.0410196781158447,
    "error_message": "Problem is infeasible",
    "retry_attempt": 4
  },
  "pyomo": {
    "status": "error",
    "optimal_value": null,
    "execution_time": 0.8514814376831055,
    "error_message": "Traceback (most recent call last):\n  File \"/tmp/tmpofbro04n.py\", line 102, in <module>\n    aircraft_assignment_optimization()\n  File \"/tmp/tmpofbro04n.py\", line 62, in aircraft_assignment_optimization\n    model.objective = pyo.Objective(rule=obj_rule, sense=pyo.minimize)\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/block.py\", line 571, in __setattr__\n    self.add_component(name, val)\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/block.py\", line 1101, in add_component\n    val.construct(data)\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/objective.py\", line 336, in construct\n    ans = self._setitem_when_not_present(index, rule(block, index))\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/initializer.py\", line 485, in __call__\n    return self._fcn(parent)\n  File \"/tmp/tmpofbro04n.py\", line 61, in obj_rule\n    return sum(model.operational_costs[i, j] * model.x[i, j] for i in model.aircraft_types for j in model.airports)\n  File \"/tmp/tmpofbro04n.py\", line 61, in <genexpr>\n    return sum(model.operational_costs[i, j] * model.x[i, j] for i in model.aircraft_types for j in model.airports)\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/param.py\", line 1012, in __getitem__\n    return super().__getitem__(args)\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/indexed_component.py\", line 662, in __getitem__\n    return self._getitem_when_not_present(index)\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/param.py\", line 627, in _getitem_when_not_present\n    raise ValueError(\nValueError: Error retrieving immutable Param value (operational_costs[('Boeing 777', 'LAX')]):\n\tThe Param value is undefined and no default value is specified.\n",
    "retry_attempt": 4
  }
}

TASK: Analyze the three solver results and provide structured recommendations.

RESPONSE FORMAT (JSON only):

{
  "database_id": "aircraft",
  "solver_analysis": {
    "gurobipy_analysis": {
      "status": "optimal/infeasible/error/timeout",
      "optimal_value": null,
      "decision_variables": {},
      "reliability": "high/medium/low",
      "notes": "Analysis of Gurobipy results"
    },
    "docplex_analysis": {
      "status": "optimal/infeasible/error/timeout", 
      "optimal_value": null,
      "decision_variables": {},
      "reliability": "high/medium/low",
      "notes": "Analysis of DOCplex results"
    },
    "pyomo_analysis": {
      "status": "optimal/infeasible/error/timeout",
      "optimal_value": null,
      "decision_variables": {},
      "reliability": "high/medium/low", 
      "notes": "Analysis of Pyomo results"
    }
  },
  "consistency_evaluation": {
    "values_consistent": false,
    "tolerance": 1e-6,
    "major_vote_optimal_value": null,
    "consistent_solvers": [],
    "inconsistent_solvers": [],
    "potential_issues": ["List potential reasons for inconsistencies"]
  },
  "final_recommendation": {
    "recommended_optimal_value": null,
    "recommended_decision_variables": {},
    "confidence": "high/medium/low",
    "business_interpretation": "What these results mean in business terms",
    "solver_preference": "gurobipy/docplex/pyomo/multiple",
    "reasoning": "Why this recommendation is made"
  },
  "business_insights": {
    "decision_variable_meanings": {
      "x_0": "Business meaning of x[0] and its optimal value",
      "x_1": "Business meaning of x[1] and its optimal value",
      "x_2": "Business meaning of x[2] and its optimal value"
    },
    "objective_value_interpretation": "What the optimal objective value means in business context",
    "resource_allocation_summary": "Summary of how resources should be allocated",
    "implementation_recommendations": "Practical steps for implementing this solution"
  }
}

Response:
{
  "database_id": "aircraft",
  "solver_analysis": {
    "gurobipy_analysis": {
      "status": "error",
      "optimal_value": null,
      "decision_variables": {},
      "reliability": "low",
      "notes": "Gurobipy encountered a KeyError due to missing operational cost data for ('Boeing 777', 'LAX'). This indicates incomplete data input or a data preparation issue."
    },
    "docplex_analysis": {
      "status": "infeasible",
      "optimal_value": null,
      "decision_variables": {},
      "reliability": "medium",
      "notes": "DOCplex reported the problem as infeasible, suggesting that the constraints cannot be satisfied with the given data. This could be due to overly restrictive constraints or incorrect data."
    },
    "pyomo_analysis": {
      "status": "error",
      "optimal_value": null,
      "decision_variables": {},
      "reliability": "low",
      "notes": "Pyomo encountered a ValueError due to undefined operational cost for ('Boeing 777', 'LAX'). Similar to Gurobipy, this points to missing or incomplete data."
    }
  },
  "consistency_evaluation": {
    "values_consistent": false,
    "tolerance": 1e-06,
    "major_vote_optimal_value": null,
    "consistent_solvers": [],
    "inconsistent_solvers": [
      "gurobipy",
      "docplex",
      "pyomo"
    ],
    "potential_issues": [
      "Missing operational cost data for ('Boeing 777', 'LAX')",
      "Infeasible constraints due to incorrect or overly restrictive data",
      "Data preparation errors leading to undefined parameters"
    ]
  },
  "final_recommendation": {
    "recommended_optimal_value": null,
    "recommended_decision_variables": {},
    "confidence": "low",
    "business_interpretation": "The optimization problem cannot be solved due to data issues or infeasible constraints. This prevents determining the optimal aircraft assignment and operational cost.",
    "solver_preference": "none",
    "reasoning": "All solvers failed due to data-related issues or infeasibility. The problem must be revisited to ensure complete and accurate data, and to verify the feasibility of constraints."
  },
  "business_insights": {
    "decision_variable_meanings": {
      "x_0": "Number of Boeing 737 aircraft assigned to JFK",
      "x_1": "Number of Airbus A320 aircraft assigned to LAX",
      "x_2": "Number of Boeing 777 aircraft assigned to ORD"
    },
    "objective_value_interpretation": "The total operational cost of assigning aircraft to airports, which could not be determined due to solver errors.",
    "resource_allocation_summary": "Resource allocation cannot be determined until the data issues are resolved and the problem is feasible.",
    "implementation_recommendations": [
      "Verify and complete the operational cost data for all aircraft-airport combinations.",
      "Review passenger demand and aircraft movement constraints to ensure they are realistic and feasible.",
      "Re-run the optimization with corrected data and constraints."
    ]
  }
}
