Iteration final - SOLVER_ANALYSIS
Sequence: 7
Timestamp: 2025-07-27 23:27:52

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
- \( x_i \): Binary variable indicating whether game \( i \) is scheduled (1 if scheduled, 0 otherwise).
- \( y_j \): Integer variable representing the number of home games scheduled at stadium \( j \).

#### Objective Function
Maximize total attendance while minimizing injury risk:
\[ \text{Maximize } \sum_{j} \text{Average_Attendance}_j \times y_j - \sum_{i} \text{Risk}_i \times x_i \]

Data Source Verification:
- \(\text{Average_Attendance}_j\) from `stadium.Average_Attendance`
- \(\text{Risk}_i\) from `injury_risk.Risk`

#### Constraints
1. Total number of home games scheduled across all stadiums must not exceed the league's predefined limit:
   \[ \sum_{j} y_j \leq \text{Total_Home_Games_Limit} \]

2. Cumulative injury risk associated with the scheduled games must remain within the maximum allowable limit:
   \[ \sum_{i} \text{Risk}_i \times x_i \leq \text{Max_Allowable_Injury_Risk} \]

3. Number of home games scheduled at each stadium must not exceed the stadium's capacity:
   \[ y_j \leq \text{Capacity_Percentage}_j \times \text{Total_Home_Games_Limit} \]

4. Each game can only be scheduled once:
   \[ x_i \in \{0, 1\} \]

5. Number of home games scheduled at each stadium must be non-negative and integer:
   \[ y_j \geq 0, \quad y_j \in \mathbb{Z}^+ \]

Data Source Verification:
- \(\text{Capacity_Percentage}_j\) from `stadium.Capacity_Percentage`
- \(\text{Total_Home_Games_Limit}\) and \(\text{Max_Allowable_Injury_Risk}\) are parameters from business configuration.

This formulation ensures that the optimization problem is both meaningful and solvable by balancing attendance and injury risk while adhering to the constraints set by the league's operational parameters.

SOLVER EXECUTION RESULTS:
{
  "gurobipy": {
    "status": "optimal",
    "optimal_value": 297000.0,
    "execution_time": 0.49564123153686523,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "docplex": {
    "status": "optimal",
    "optimal_value": 297000.0,
    "execution_time": 5.812991380691528,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "pyomo": {
    "status": "optimal",
    "optimal_value": 297000.0,
    "execution_time": 2.1465721130371094,
    "error_message": null,
    "retry_attempt": "N/A"
  }
}

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

RESPONSE FORMAT (JSON only):

{
  "database_id": "game_injury",
  "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": "game_injury",
  "solver_analysis": {
    "gurobipy_analysis": {
      "status": "optimal",
      "optimal_value": 297000.0,
      "decision_variables": {},
      "reliability": "high",
      "notes": "Gurobipy found an optimal solution quickly with a very short execution time, indicating efficient performance and reliability."
    },
    "docplex_analysis": {
      "status": "optimal",
      "optimal_value": 297000.0,
      "decision_variables": {},
      "reliability": "high",
      "notes": "DOCplex also found an optimal solution, but with a longer execution time compared to Gurobipy, suggesting it is reliable but less efficient."
    },
    "pyomo_analysis": {
      "status": "optimal",
      "optimal_value": 297000.0,
      "decision_variables": {},
      "reliability": "high",
      "notes": "Pyomo achieved an optimal solution with a moderate execution time, indicating a balance between efficiency and reliability."
    }
  },
  "consistency_evaluation": {
    "values_consistent": true,
    "tolerance": 1e-06,
    "major_vote_optimal_value": 297000.0,
    "consistent_solvers": [
      "gurobipy",
      "docplex",
      "pyomo"
    ],
    "inconsistent_solvers": [],
    "potential_issues": []
  },
  "final_recommendation": {
    "recommended_optimal_value": 297000.0,
    "recommended_decision_variables": {},
    "confidence": "high",
    "business_interpretation": "The optimal solution maximizes attendance while minimizing injury risk, adhering to all constraints.",
    "solver_preference": "gurobipy",
    "reasoning": "Gurobipy is preferred due to its high reliability and the fastest execution time, making it the most efficient choice for this problem."
  },
  "business_insights": {
    "decision_variable_meanings": {
      "x_0": "Indicates whether game 0 is scheduled; optimal value determines its inclusion in the schedule.",
      "x_1": "Indicates whether game 1 is scheduled; optimal value determines its inclusion in the schedule.",
      "x_2": "Indicates whether game 2 is scheduled; optimal value determines its inclusion in the schedule."
    },
    "objective_value_interpretation": "The optimal objective value of 297000.0 represents the maximum achievable attendance minus the weighted injury risk, reflecting the best trade-off between these factors.",
    "resource_allocation_summary": "Resources should be allocated to schedule games that maximize attendance while keeping injury risk within acceptable limits.",
    "implementation_recommendations": "Implement the schedule as determined by the optimal solution, ensuring compliance with all constraints and monitoring injury risk closely."
  }
}
