Iteration final - SOLVER_ANALYSIS
Sequence: 11
Timestamp: 2025-07-25 22:36:07

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
- \( x_{i}^{ft} \): Number of full-time employees to hire for shop \( i \) (integer)  
- \( x_{i}^{pt} \): Number of part-time employees to hire for shop \( i \) (integer)  

#### Objective Function
Minimize the total hiring cost:  
\[
\text{Minimize } \sum_{i} \left( \text{cost\_full\_time}_i \times x_{i}^{ft} + \text{cost\_part\_time}_i \times x_{i}^{pt} \right)
\]  
Where:  
- \( \text{cost\_full\_time}_i \): Cost per full-time employee for shop \( i \) (from `employee_costs.cost_full_time`)  
- \( \text{cost\_part\_time}_i \): Cost per part-time employee for shop \( i \) (from `employee_costs.cost_part_time`)  

#### Constraints
1. **Minimum Staffing Requirement**:  
   For each shop \( i \):  
   \[
   x_{i}^{ft} + x_{i}^{pt} \geq \text{min\_staff}_i
   \]  
   Where \( \text{min\_staff}_i \) is the minimum staffing requirement for shop \( i \) (from `shop_staff_requirements.min_staff`).  

2. **Maximum Full-Time Employees**:  
   For each shop \( i \):  
   \[
   x_{i}^{ft} \leq \text{max\_full\_time}_i
   \]  
   Where \( \text{max\_full\_time}_i \) is the maximum allowed full-time employees for shop \( i \) (from `shop_staff_requirements.max_full_time`).  

3. **Maximum Part-Time Employees**:  
   For each shop \( i \):  
   \[
   x_{i}^{pt} \leq \text{max\_part\_time}_i
   \]  
   Where \( \text{max\_part\_time}_i \) is the maximum allowed part-time employees for shop \( i \) (from `shop_staff_requirements.max_part_time`).  

#### Data Source Verification
- \( \text{cost\_full\_time}_i \): `employee_costs.cost_full_time`  
- \( \text{cost\_part\_time}_i \): `employee_costs.cost_part_time`  
- \( \text{min\_staff}_i \): `shop_staff_requirements.min_staff`  
- \( \text{max\_full\_time}_i \): `shop_staff_requirements.max_full_time`  
- \( \text{max\_part\_time}_i \): `shop_staff_requirements.max_part_time`  

#### Complete Numerical Model
For the provided data, the model is:  

**Objective Function**:  
\[
\text{Minimize } 1500x_{1}^{ft} + 800x_{1}^{pt} + 1600x_{2}^{ft} + 850x_{2}^{pt} + 1700x_{3}^{ft} + 900x_{3}^{pt}
\]  

**Constraints**:  
1. **Minimum Staffing Requirement**:  
   \[
   x_{1}^{ft} + x_{1}^{pt} \geq 5  
   x_{2}^{ft} + x_{2}^{pt} \geq 6  
   x_{3}^{ft} + x_{3}^{pt} \geq 7  
   \]  
2. **Maximum Full-Time Employees**:  
   \[
   x_{1}^{ft} \leq 10  
   x_{2}^{ft} \leq 12  
   x_{3}^{ft} \leq 15  
   \]  
3. **Maximum Part-Time Employees**:  
   \[
   x_{1}^{pt} \leq 8  
   x_{2}^{pt} \leq 10  
   x_{3}^{pt} \leq 12  
   \]  

This is a complete, immediately solvable Mixed-Integer Linear Programming (MIP) model.

SOLVER EXECUTION RESULTS:
{
  "gurobipy": {
    "status": "optimal",
    "optimal_value": 15400.0,
    "execution_time": 0.14216232299804688,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "docplex": {
    "status": "optimal",
    "optimal_value": 15400.0,
    "execution_time": 1.076530933380127,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "pyomo": {
    "status": "optimal",
    "optimal_value": 15400.0,
    "execution_time": 0.8412282466888428,
    "error_message": null,
    "retry_attempt": "N/A"
  }
}

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": "optimal",
      "optimal_value": 15400.0,
      "decision_variables": {},
      "reliability": "high",
      "notes": "Gurobipy found the optimal solution quickly with the lowest execution time among the solvers."
    },
    "docplex_analysis": {
      "status": "optimal",
      "optimal_value": 15400.0,
      "decision_variables": {},
      "reliability": "high",
      "notes": "DOCplex also found the optimal solution but took significantly longer compared to Gurobipy."
    },
    "pyomo_analysis": {
      "status": "optimal",
      "optimal_value": 15400.0,
      "decision_variables": {},
      "reliability": "high",
      "notes": "Pyomo found the optimal solution with an execution time between Gurobipy and DOCplex."
    }
  },
  "consistency_evaluation": {
    "values_consistent": true,
    "tolerance": 1e-06,
    "major_vote_optimal_value": 15400.0,
    "consistent_solvers": [
      "gurobipy",
      "docplex",
      "pyomo"
    ],
    "inconsistent_solvers": [],
    "potential_issues": []
  },
  "final_recommendation": {
    "recommended_optimal_value": 15400.0,
    "recommended_decision_variables": {},
    "confidence": "high",
    "business_interpretation": "The optimal hiring plan minimizes the total cost while meeting all staffing requirements and constraints.",
    "solver_preference": "gurobipy",
    "reasoning": "Gurobipy is recommended due to its faster execution time while still providing the same optimal solution as the other solvers."
  },
  "business_insights": {
    "decision_variable_meanings": {
      "x_0": "Number of full-time employees to hire for shop 1",
      "x_1": "Number of part-time employees to hire for shop 1",
      "x_2": "Number of full-time employees to hire for shop 2"
    },
    "objective_value_interpretation": "The total cost of hiring employees across all shops is minimized to $15,400.",
    "resource_allocation_summary": "Allocate the minimum required staff for each shop while adhering to the maximum limits for full-time and part-time employees.",
    "implementation_recommendations": "Proceed with hiring the calculated number of full-time and part-time employees for each shop to achieve the optimal cost."
  }
}
