Iteration final - SOLVER_ANALYSIS
Sequence: 7
Timestamp: 2025-07-28 00:25:08

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 \( x_i \) be the amount of resources allocated to institution \( i \).
  - \( x_1 \) for institution 1
  - \( x_2 \) for institution 2
  - \( x_3 \) for institution 3

#### Objective Function
Maximize the total sequence identity:
\[ \text{Maximize } 0.85x_1 + 0.9x_2 + 0.8x_3 \]

#### Constraints
1. Total Resource Constraint:
   \[ x_1 + x_2 + x_3 \leq 600 \]
   - This constraint ensures that the total resources allocated do not exceed the total available resources.

2. Building Capacity Constraints:
   \[ x_1 \leq 600 \]
   \[ x_2 \leq 700 \]
   \[ x_3 \leq 500 \]
   - These constraints ensure that the resources allocated to each institution do not exceed the capacity of their respective buildings.

Data Source Verification:
- Objective coefficients:
  - \( 0.85 \) from `protein.sequence_identity_coefficient` for institution 1
  - \( 0.9 \) from `protein.sequence_identity_coefficient` for institution 2
  - \( 0.8 \) from `protein.sequence_identity_coefficient` for institution 3
- Total resource constraint from business configuration (assumed total available resources = 600).
- Building capacity constraints:
  - \( 600 \) from `building.building_capacity` for institution 1
  - \( 700 \) from `building.building_capacity` for institution 2
  - \( 500 \) from `building.building_capacity` for institution 3

This linear model is immediately solvable using standard linear programming techniques, ensuring that the allocation of resources maximizes the total sequence identity while respecting the constraints.

SOLVER EXECUTION RESULTS:
{
  "gurobipy": {
    "status": "optimal",
    "optimal_value": 540.0,
    "execution_time": 0.6687581539154053,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "docplex": {
    "status": "optimal",
    "optimal_value": 540.0,
    "execution_time": 2.609788656234741,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "pyomo": {
    "status": "optimal",
    "optimal_value": 540.0,
    "execution_time": 3.0800564289093018,
    "error_message": null,
    "retry_attempt": "N/A"
  }
}

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

RESPONSE FORMAT (JSON only):

{
  "database_id": "protein_institute",
  "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": "protein_institute",
  "solver_analysis": {
    "gurobipy_analysis": {
      "status": "optimal",
      "optimal_value": 540.0,
      "decision_variables": {
        "x_1": 0,
        "x_2": 600,
        "x_3": 0
      },
      "reliability": "high",
      "notes": "Gurobipy found an optimal solution quickly with the highest reliability due to its robust performance and industry reputation."
    },
    "docplex_analysis": {
      "status": "optimal",
      "optimal_value": 540.0,
      "decision_variables": {
        "x_1": 0,
        "x_2": 600,
        "x_3": 0
      },
      "reliability": "high",
      "notes": "DOCplex also found the optimal solution, albeit with a longer execution time compared to Gurobipy, but still reliable."
    },
    "pyomo_analysis": {
      "status": "optimal",
      "optimal_value": 540.0,
      "decision_variables": {
        "x_1": 0,
        "x_2": 600,
        "x_3": 0
      },
      "reliability": "high",
      "notes": "Pyomo achieved the optimal solution with the longest execution time, but the results are consistent with other solvers."
    }
  },
  "consistency_evaluation": {
    "values_consistent": true,
    "tolerance": 1e-06,
    "major_vote_optimal_value": 540.0,
    "consistent_solvers": [
      "gurobipy",
      "docplex",
      "pyomo"
    ],
    "inconsistent_solvers": [],
    "potential_issues": []
  },
  "final_recommendation": {
    "recommended_optimal_value": 540.0,
    "recommended_decision_variables": {
      "x_1": 0,
      "x_2": 600,
      "x_3": 0
    },
    "confidence": "high",
    "business_interpretation": "Allocate all available resources to institution 2 to maximize sequence identity.",
    "solver_preference": "gurobipy",
    "reasoning": "Gurobipy is preferred due to its faster execution time and high reliability, making it suitable for time-sensitive applications."
  },
  "business_insights": {
    "decision_variable_meanings": {
      "x_0": "Resources allocated to institution 1, which is optimal at 0.",
      "x_1": "Resources allocated to institution 2, which is optimal at 600.",
      "x_2": "Resources allocated to institution 3, which is optimal at 0."
    },
    "objective_value_interpretation": "The optimal objective value of 540.0 represents the maximum achievable sequence identity given the constraints.",
    "resource_allocation_summary": "All resources should be allocated to institution 2 to achieve the highest sequence identity.",
    "implementation_recommendations": "Implement the solution by reallocating resources to institution 2, ensuring compliance with the building capacity and total resource constraints."
  }
}
