Iteration final - SOLVER_ANALYSIS
Sequence: 7
Timestamp: 2025-07-25 22:27:46

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 \( x_{f,c} \) be the number of showings per day for film \( f \) in cinema \( c \).  
This is the primary decision variable, representing the number of showings per film per cinema per day.

#### Objective Function
Maximize the total revenue:  
\[
\text{Maximize } \sum_{f} \sum_{c} (\text{Price}_f \times \text{Capacity}_c \times x_{f,c})
\]  
Where:  
- \( \text{Price}_f \) is the price per showing for film \( f \) (from `schedule.Price`).  
- \( \text{Capacity}_c \) is the seating capacity of cinema \( c \) (from `cinema.Capacity`).  
- \( x_{f,c} \) is the number of showings per day for film \( f \) in cinema \( c \).

#### Constraints
1. **Maximum showings per day per cinema**:  
\[
\sum_{f} x_{f,c} \leq 12 \quad \forall c
\]  
This ensures the total number of showings per day in each cinema does not exceed 12.

2. **Total capacity per day**:  
\[
\sum_{f} (\text{Capacity}_c \times x_{f,c}) \leq \text{Capacity}_c \times 12 \quad \forall c
\]  
This ensures the total number of seats available across all showings in a day does not exceed the cinema's daily capacity.

3. **Minimum showings per film**:  
\[
x_{f,c} \geq 1 \quad \forall f, c
\]  
This ensures each film is shown at least once per day in each cinema.

#### Data Source Verification
- \( \text{Price}_f \): From `schedule.Price`.  
- \( \text{Capacity}_c \): From `cinema.Capacity`.  
- Maximum showings per day per cinema: Business configuration parameter (12).  
- Minimum showings per film: Business constraint (1).  

This is a complete, immediately solvable LINEAR mathematical model with all numerical coefficients derived from the provided data.

SOLVER EXECUTION RESULTS:
{
  "gurobipy": {
    "status": "optimal",
    "optimal_value": 66546.0,
    "execution_time": 0.20128560066223145,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "docplex": {
    "status": "optimal",
    "optimal_value": 66546.0,
    "execution_time": 1.444591760635376,
    "error_message": null,
    "retry_attempt": "N/A"
  },
  "pyomo": {
    "status": "error",
    "optimal_value": null,
    "execution_time": 0.7373442649841309,
    "error_message": "Traceback (most recent call last):\n  File \"/tmp/tmpmpjr9sds.py\", line 103, in <module>\n    cinema_scheduling_optimization()\n  File \"/tmp/tmpmpjr9sds.py\", line 42, in cinema_scheduling_optimization\n    model.capacity = pyo.Param(model.C, initialize={i+1: cinemas_data[i-1] for i in model.C})\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/block.py\", line 571, in __setattr__\n    self.add_component(name, val)\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/block.py\", line 1101, in add_component\n    val.construct(data)\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/param.py\", line 850, in construct\n    self._construct_from_rule_using_setitem()\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/indexed_component.py\", line 772, in _construct_from_rule_using_setitem\n    self[index] = rule(block, index)\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/indexed_component.py\", line 692, in __setitem__\n    index = self._validate_index(index)\n  File \"/dccstor/nl2opt/miniforge3/envs/nl2opt_optim/lib/python3.10/site-packages/pyomo/core/base/indexed_component.py\", line 870, in _validate_index\n    raise KeyError(\nKeyError: \"Index '4' is not valid for indexed component 'capacity'\"\n",
    "retry_attempt": "N/A"
  }
}

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

RESPONSE FORMAT (JSON only):

{
  "database_id": "cinema",
  "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": "cinema",
  "solver_analysis": {
    "gurobipy_analysis": {
      "status": "optimal",
      "optimal_value": 66546.0,
      "decision_variables": {},
      "reliability": "high",
      "notes": "Gurobipy successfully found an optimal solution with a high level of reliability. The execution time was the fastest among the solvers, indicating efficient performance."
    },
    "docplex_analysis": {
      "status": "optimal",
      "optimal_value": 66546.0,
      "decision_variables": {},
      "reliability": "high",
      "notes": "DOCplex also found an optimal solution with the same objective value as Gurobipy. However, the execution time was significantly longer, suggesting less efficiency compared to Gurobipy."
    },
    "pyomo_analysis": {
      "status": "error",
      "optimal_value": null,
      "decision_variables": {},
      "reliability": "low",
      "notes": "Pyomo encountered an error during execution, specifically a KeyError related to the indexed component 'capacity'. This indicates a potential issue with the data handling or model setup in Pyomo."
    }
  },
  "consistency_evaluation": {
    "values_consistent": true,
    "tolerance": 1e-06,
    "major_vote_optimal_value": 66546.0,
    "consistent_solvers": [
      "gurobipy",
      "docplex"
    ],
    "inconsistent_solvers": [
      "pyomo"
    ],
    "potential_issues": [
      "Data handling error in Pyomo",
      "Potential misconfiguration in Pyomo model setup"
    ]
  },
  "final_recommendation": {
    "recommended_optimal_value": 66546.0,
    "recommended_decision_variables": {},
    "confidence": "high",
    "business_interpretation": "The optimal revenue achievable under the given constraints is $66,546. This represents the maximum possible revenue from film showings across all cinemas.",
    "solver_preference": "gurobipy",
    "reasoning": "Gurobipy is recommended due to its optimal solution, high reliability, and fastest execution time. DOCplex also found the same optimal solution but was less efficient. Pyomo is not recommended due to its execution error."
  },
  "business_insights": {
    "decision_variable_meanings": {
      "x_0": "Number of showings for film 0 in cinema 0, optimized to maximize revenue",
      "x_1": "Number of showings for film 1 in cinema 1, optimized to maximize revenue",
      "x_2": "Number of showings for film 2 in cinema 2, optimized to maximize revenue"
    },
    "objective_value_interpretation": "The optimal objective value of $66,546 represents the maximum daily revenue achievable from film showings across all cinemas, considering the constraints on showings and capacity.",
    "resource_allocation_summary": "Resources should be allocated to ensure each film is shown at least once per day in each cinema, while maximizing the number of showings for higher-revenue films in larger cinemas.",
    "implementation_recommendations": "Implement the optimal schedule as determined by Gurobipy. Ensure that each cinema does not exceed 12 showings per day and that the total seating capacity is not exceeded. Monitor the schedule for any deviations and adjust as necessary."
  }
}
