Iteration final - SOLVER_ANALYSIS
Sequence: 9
Timestamp: 2025-07-27 22:09:50

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 \( x_i \) be the effort allocated to poll source \( i \).
- \( x_i \) is a continuous variable representing the level of effort for each poll source.

#### Objective Function
Maximize the total support rate:
\[ \text{Maximize } Z = 0.55x_1 + 0.75x_2 + 0.6x_3 \]

#### Constraints
1. Total effort constraint (budget constraint):
   \[ x_1 + x_2 + x_3 \leq \text{Total Budget} \]

2. Minimum and maximum effort constraints for each poll source:
   \[
   \begin{align*}
   5.0 & \leq x_1 \leq 20.0 \\
   10.0 & \leq x_2 \leq 30.0 \\
   7.5 & \leq x_3 \leq 25.0 \\
   \end{align*}
   \]

Data Source Verification:
- Objective coefficients (support rates) are from `PollSupportRates.support_rate`.
- Minimum and maximum effort constraints are from `PollConstraints.min_effort` and `PollConstraints.max_effort`.
- The total budget constraint is a parameter that should be defined based on the campaign's available resources.

SOLVER EXECUTION RESULTS:
{
  "gurobipy": {
    "status": "optimal",
    "optimal_value": 34.25,
    "execution_time": 0.4200870990753174,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "docplex": {
    "status": "optimal",
    "optimal_value": 34.25,
    "execution_time": 7.570535182952881,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "pyomo": {
    "status": "optimal",
    "optimal_value": 34.25,
    "execution_time": 3.09859299659729,
    "error_message": null,
    "retry_attempt": "N/A"
  }
}

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

RESPONSE FORMAT (JSON only):

{
  "database_id": "candidate_poll",
  "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": "candidate_poll",
  "solver_analysis": {
    "gurobipy_analysis": {
      "status": "optimal",
      "optimal_value": 34.25,
      "decision_variables": {},
      "reliability": "high",
      "notes": "Gurobipy found an optimal solution quickly with a short execution time, indicating high efficiency and reliability."
    },
    "docplex_analysis": {
      "status": "optimal",
      "optimal_value": 34.25,
      "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": 34.25,
      "decision_variables": {},
      "reliability": "high",
      "notes": "Pyomo achieved the 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": 34.25,
    "consistent_solvers": [
      "gurobipy",
      "docplex",
      "pyomo"
    ],
    "inconsistent_solvers": [],
    "potential_issues": []
  },
  "final_recommendation": {
    "recommended_optimal_value": 34.25,
    "recommended_decision_variables": {},
    "confidence": "high",
    "business_interpretation": "The optimal allocation of resources maximizes the total support rate effectively.",
    "solver_preference": "gurobipy",
    "reasoning": "Gurobipy is preferred due to its high reliability and the shortest execution time, making it the most efficient choice for this problem."
  },
  "business_insights": {
    "decision_variable_meanings": {
      "x_0": "Effort allocated to poll source 1, optimizing its contribution to the support rate.",
      "x_1": "Effort allocated to poll source 2, optimizing its contribution to the support rate.",
      "x_2": "Effort allocated to poll source 3, optimizing its contribution to the support rate."
    },
    "objective_value_interpretation": "The optimal objective value of 34.25 represents the maximum achievable support rate given the constraints.",
    "resource_allocation_summary": "Resources should be allocated to maximize the support rate while adhering to budget and effort constraints.",
    "implementation_recommendations": "Implement the solution by allocating resources according to the optimal decision variables, ensuring compliance with all constraints."
  }
}
