Iteration final - SOLVER_ANALYSIS
Sequence: 7
Timestamp: 2025-07-27 23:34:23

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 \( x_1 \) be the budget allocated to movie 1.
- Let \( x_2 \) be the budget allocated to movie 2.
- Let \( x_3 \) be the budget allocated to movie 3.

#### Objective Function
Maximize the expected increase in movie ratings:
\[ \text{Maximize } 0.15x_1 + 0.25x_2 + 0.1x_3 \]

Data Source Verification:
- Coefficients 0.15, 0.25, and 0.1 are from `promotion_sensitivity.sensitivity_value` for movies 1, 2, and 3, respectively.

#### Constraints
1. Total budget constraint:
   \[ x_1 + x_2 + x_3 \leq 65000 \]
   - Data Source Verification: The total promotional budget is the sum of current allocations from `budget_allocation.amount`.

2. Minimum budget constraints for each movie:
   \[ x_1 \geq 20000 \]
   \[ x_2 \geq 30000 \]
   \[ x_3 \geq 15000 \]
   - Data Source Verification: Minimum budget allocations are from `budget_allocation.amount` for movies 1, 2, and 3, respectively.

3. Non-negativity constraints:
   \[ x_1 \geq 0, \quad x_2 \geq 0, \quad x_3 \geq 0 \]

This linear programming model is ready to be solved using appropriate optimization software, ensuring that the promotional budget is allocated to maximize the expected increase in movie ratings while adhering to the specified constraints.

SOLVER EXECUTION RESULTS:
{
  "gurobipy": {
    "status": "optimal",
    "optimal_value": 12000.0,
    "execution_time": 0.28229641914367676,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "docplex": {
    "status": "optimal",
    "optimal_value": 12000.0,
    "execution_time": 2.517634630203247,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "pyomo": {
    "status": "optimal",
    "optimal_value": 12000.0,
    "execution_time": 1.641136646270752,
    "error_message": null,
    "retry_attempt": "N/A"
  }
}

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

RESPONSE FORMAT (JSON only):

{
  "database_id": "movie_1",
  "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": "movie_1",
  "solver_analysis": {
    "gurobipy_analysis": {
      "status": "optimal",
      "optimal_value": 12000.0,
      "decision_variables": {
        "x_1": 20000,
        "x_2": 30000,
        "x_3": 15000
      },
      "reliability": "high",
      "notes": "Gurobipy found an optimal solution quickly with the expected optimal value. The decision variables meet all constraints."
    },
    "docplex_analysis": {
      "status": "optimal",
      "optimal_value": 12000.0,
      "decision_variables": {
        "x_1": 20000,
        "x_2": 30000,
        "x_3": 15000
      },
      "reliability": "high",
      "notes": "DOCplex also found an optimal solution with the same optimal value and decision variables as Gurobipy, albeit with a longer execution time."
    },
    "pyomo_analysis": {
      "status": "optimal",
      "optimal_value": 12000.0,
      "decision_variables": {
        "x_1": 20000,
        "x_2": 30000,
        "x_3": 15000
      },
      "reliability": "high",
      "notes": "Pyomo achieved the same optimal solution and decision variables, confirming the consistency across solvers."
    }
  },
  "consistency_evaluation": {
    "values_consistent": true,
    "tolerance": 1e-06,
    "major_vote_optimal_value": 12000.0,
    "consistent_solvers": [
      "gurobipy",
      "docplex",
      "pyomo"
    ],
    "inconsistent_solvers": [],
    "potential_issues": []
  },
  "final_recommendation": {
    "recommended_optimal_value": 12000.0,
    "recommended_decision_variables": {
      "x_1": 20000,
      "x_2": 30000,
      "x_3": 15000
    },
    "confidence": "high",
    "business_interpretation": "The optimal allocation of the promotional budget maximizes the expected increase in movie ratings while adhering to budget constraints.",
    "solver_preference": "multiple",
    "reasoning": "All solvers provided consistent results, confirming the reliability of the solution. Gurobipy is preferred for its speed, but any solver can be used."
  },
  "business_insights": {
    "decision_variable_meanings": {
      "x_0": "Budget allocated to movie 1, which is set at the minimum required level of $20,000.",
      "x_1": "Budget allocated to movie 2, which is set at the minimum required level of $30,000.",
      "x_2": "Budget allocated to movie 3, which is set at the minimum required level of $15,000."
    },
    "objective_value_interpretation": "The optimal objective value of 12000 represents the maximum expected increase in movie ratings achievable with the given budget.",
    "resource_allocation_summary": "Allocate $20,000 to movie 1, $30,000 to movie 2, and $15,000 to movie 3 to achieve the optimal increase in ratings.",
    "implementation_recommendations": "Ensure the budget allocations are strictly adhered to as per the solution. Monitor the impact on movie ratings to validate the model's effectiveness."
  }
}
