Iteration final - SOLVER_ANALYSIS
Sequence: 7
Timestamp: 2025-07-25 22:30:24

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 \( x_{p,c} \) be the number of roller coasters of type \( c \) to install in park \( p \), where:
- \( p \in \{1, 2, 3\} \) (park IDs)
- \( c \in \{\text{Wooden}, \text{Steel}, \text{Inverted}\} \) (roller coaster types)

#### Objective Function
Maximize the total visitor satisfaction:
\[
\text{Maximize} \quad \sum_{p=1}^{3} \sum_{c} \text{visitor\_satisfaction\_scores.score}_{p,c} \times x_{p,c}
\]
Data Source Verification:
- Coefficients \( \text{visitor\_satisfaction\_scores.score}_{p,c} \) come from the `visitor_satisfaction_scores.score` column.

#### Constraints
1. **Budget Constraint**: The total cost of roller coasters in each park must not exceed the park’s budget.
\[
\sum_{c} 500000 \times x_{p,c} \leq \text{park\_budgets.budget}_p \quad \forall p
\]
Data Source Verification:
- Coefficient \( 500000 \) is the fixed cost per roller coaster (business configuration).
- Right-hand side \( \text{park\_budgets.budget}_p \) comes from the `park_budgets.budget` column.

2. **Space Constraint**: The total space occupied by roller coasters in each park must not exceed the park’s available space.
\[
\sum_{c} 2000 \times x_{p,c} \leq \text{park\_available\_space.space}_p \quad \forall p
\]
Data Source Verification:
- Coefficient \( 2000 \) is the fixed space requirement per roller coaster (business configuration).
- Right-hand side \( \text{park\_available\_space.space}_p \) comes from the `park_available_space.space` column.

3. **Maximum Roller Coasters Constraint**: The total number of roller coasters in each park must not exceed the park’s maximum capacity.
\[
\sum_{c} x_{p,c} \leq \text{park\_max\_coasters.max\_coasters}_p \quad \forall p
\]
Data Source Verification:
- Right-hand side \( \text{park\_max\_coasters.max\_coasters}_p \) comes from the `park_max_coasters.max_coasters` column.

4. **Non-Negativity Constraint**: The number of roller coasters cannot be negative.
\[
x_{p,c} \geq 0 \quad \forall p, c
\]

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

SOLVER EXECUTION RESULTS:
{
  "gurobipy": {
    "status": "optimal",
    "optimal_value": 82.5,
    "execution_time": 0.16910600662231445,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "docplex": {
    "status": "optimal",
    "optimal_value": 82.5,
    "execution_time": 1.1225271224975586,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "pyomo": {
    "status": "optimal",
    "optimal_value": 82.5,
    "execution_time": 1.02946138381958,
    "error_message": null,
    "retry_attempt": "N/A"
  }
}

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

RESPONSE FORMAT (JSON only):

{
  "database_id": "roller_coaster",
  "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": "roller_coaster",
  "solver_analysis": {
    "gurobipy_analysis": {
      "status": "optimal",
      "optimal_value": 82.5,
      "decision_variables": {},
      "reliability": "high",
      "notes": "Gurobipy achieved the optimal solution efficiently with the fastest execution time."
    },
    "docplex_analysis": {
      "status": "optimal",
      "optimal_value": 82.5,
      "decision_variables": {},
      "reliability": "high",
      "notes": "DOCplex also achieved the optimal solution but with a longer execution time compared to Gurobipy."
    },
    "pyomo_analysis": {
      "status": "optimal",
      "optimal_value": 82.5,
      "decision_variables": {},
      "reliability": "high",
      "notes": "Pyomo achieved the optimal solution with an execution time slightly better than DOCplex but still slower than Gurobipy."
    }
  },
  "consistency_evaluation": {
    "values_consistent": true,
    "tolerance": 1e-06,
    "major_vote_optimal_value": 82.5,
    "consistent_solvers": [
      "gurobipy",
      "docplex",
      "pyomo"
    ],
    "inconsistent_solvers": [],
    "potential_issues": []
  },
  "final_recommendation": {
    "recommended_optimal_value": 82.5,
    "recommended_decision_variables": {},
    "confidence": "high",
    "business_interpretation": "The optimal visitor satisfaction score of 82.5 indicates the best possible allocation of roller coasters across the parks within the given constraints.",
    "solver_preference": "gurobipy",
    "reasoning": "Gurobipy is recommended due to its optimal solution and significantly faster execution time compared to DOCplex and Pyomo."
  },
  "business_insights": {
    "decision_variable_meanings": {
      "x_0": "Number of Wooden roller coasters to install in Park 1",
      "x_1": "Number of Steel roller coasters to install in Park 2",
      "x_2": "Number of Inverted roller coasters to install in Park 3"
    },
    "objective_value_interpretation": "The optimal objective value of 82.5 represents the maximum total visitor satisfaction achievable with the given constraints.",
    "resource_allocation_summary": "Resources should be allocated to install the optimal number of each type of roller coaster in each park, ensuring budget, space, and capacity constraints are not exceeded.",
    "implementation_recommendations": "Proceed with the installation of roller coasters as per the optimal solution, ensuring all constraints are adhered to. Monitor the execution to ensure alignment with the planned resource allocation."
  }
}
