Iteration final - SOLVER_ANALYSIS
Sequence: 7
Timestamp: 2025-07-27 23:32:33

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 \( x_{ij} \) be a binary decision variable where \( x_{ij} = 1 \) if employee \( i \) is assigned to shop \( j \), and \( x_{ij} = 0 \) otherwise.

#### Objective Function
Maximize the total bonuses awarded to employees:
\[
\text{Maximize } \sum_{i} \sum_{j} \text{Bonus}_i \times x_{ij}
\]
where \(\text{Bonus}_i\) is the bonus for employee \( i \) from the `evaluation` table.

#### Constraints
1. **Each employee is assigned to exactly one shop:**
   \[
   \sum_{j} x_{ij} = 1 \quad \forall i
   \]
   This ensures that each employee is assigned to exactly one shop.

2. **Each shop meets its minimum staffing requirement:**
   \[
   \sum_{i} x_{ij} \geq \text{Min\_Employees}_j \quad \forall j
   \]
   where \(\text{Min\_Employees}_j\) is the minimum number of employees required for shop \( j \) from the `shop_requirements` table.

3. **Binary assignment constraint:**
   \[
   x_{ij} \in \{0, 1\} \quad \forall i, j
   \]
   This ensures that the decision variable \( x_{ij} \) is binary, indicating whether an employee is assigned to a shop or not.

Data Source Verification:
- **Bonuses (\(\text{Bonus}_i\))**: Retrieved from `evaluation.Bonus`.
- **Minimum Employees (\(\text{Min\_Employees}_j\))**: Retrieved from `shop_requirements.Min_Employees`.

This formulation provides a complete linear model that can be solved using linear programming techniques to determine the optimal assignment of employees to shops, maximizing the total bonuses while satisfying all constraints.

SOLVER EXECUTION RESULTS:
{
  "gurobipy": {
    "status": "infeasible",
    "optimal_value": null,
    "execution_time": 0.2509913444519043,
    "error_message": "Problem is infeasible",
    "retry_attempt": 4
  },
  "docplex": {
    "status": "infeasible",
    "optimal_value": null,
    "execution_time": 2.14654803276062,
    "error_message": "Problem is infeasible",
    "retry_attempt": 4
  },
  "pyomo": {
    "status": "infeasible",
    "optimal_value": null,
    "execution_time": 1.181511640548706,
    "error_message": "Problem is infeasible",
    "retry_attempt": 4
  }
}

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

RESPONSE FORMAT (JSON only):

{
  "database_id": "employee_hire_evaluation",
  "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": "employee_hire_evaluation",
  "solver_analysis": {
    "gurobipy_analysis": {
      "status": "infeasible",
      "optimal_value": null,
      "decision_variables": {},
      "reliability": "high",
      "notes": "Gurobipy consistently reports the problem as infeasible, indicating a potential issue with the constraints or data."
    },
    "docplex_analysis": {
      "status": "infeasible",
      "optimal_value": null,
      "decision_variables": {},
      "reliability": "high",
      "notes": "DOCplex also reports infeasibility, suggesting that the problem formulation or data constraints are not satisfiable."
    },
    "pyomo_analysis": {
      "status": "infeasible",
      "optimal_value": null,
      "decision_variables": {},
      "reliability": "high",
      "notes": "Pyomo's infeasibility result aligns with the other solvers, reinforcing the likelihood of an issue with the problem setup."
    }
  },
  "consistency_evaluation": {
    "values_consistent": true,
    "tolerance": 1e-06,
    "major_vote_optimal_value": null,
    "consistent_solvers": [
      "gurobipy",
      "docplex",
      "pyomo"
    ],
    "inconsistent_solvers": [],
    "potential_issues": [
      "The constraints may be too strict, particularly the minimum staffing requirements.",
      "Data errors in the `evaluation` or `shop_requirements` tables.",
      "Logical errors in the problem formulation."
    ]
  },
  "final_recommendation": {
    "recommended_optimal_value": null,
    "recommended_decision_variables": {},
    "confidence": "high",
    "business_interpretation": "The current problem setup cannot be solved as it stands, indicating that the staffing requirements or employee bonuses need to be re-evaluated.",
    "solver_preference": "multiple",
    "reasoning": "All solvers consistently report infeasibility, suggesting a fundamental issue with the problem constraints or data."
  },
  "business_insights": {
    "decision_variable_meanings": {
      "x_0": "Assignment of employee 0 to a shop, which cannot be determined due to infeasibility.",
      "x_1": "Assignment of employee 1 to a shop, which cannot be determined due to infeasibility.",
      "x_2": "Assignment of employee 2 to a shop, which cannot be determined due to infeasibility."
    },
    "objective_value_interpretation": "The objective value cannot be interpreted as the problem is infeasible.",
    "resource_allocation_summary": "Current resource allocation requirements cannot be met; reassessment of staffing needs and employee bonuses is necessary.",
    "implementation_recommendations": "Review and potentially relax the minimum staffing requirements for shops. Verify the accuracy of the bonus data and ensure all constraints are logically sound."
  }
}
