## 4. Mathematical Optimization Formulation

#### Decision Variables
- Let \( x_{ij} \) be a binary decision variable where \( x_{ij} = 1 \) if journalist \( i \) is assigned to cover event \( j \), and \( x_{ij} = 0 \) otherwise.

#### Objective Function
Maximize the total attendance at events covered by journalists:
\[
\text{Maximize } Z = 150x_{11} + 250x_{12} + 100x_{13} + 250x_{22} + 100x_{23} + 150x_{31}
\]

#### Constraints
1. Each journalist can cover a limited number of events. Assuming each journalist can cover up to 2 events:
   \[
   x_{11} + x_{12} \leq 2 \quad \text{(Journalist 1)}
   \]
   \[
   x_{22} + x_{23} \leq 2 \quad \text{(Journalist 2)}
   \]
   \[
   x_{31} \leq 2 \quad \text{(Journalist 3)}
   \]

2. Each event can be covered by a limited number of journalists. Assuming each event can be covered by up to 2 journalists:
   \[
   x_{11} + x_{31} \leq 2 \quad \text{(Event 1)}
   \]
   \[
   x_{12} + x_{22} \leq 2 \quad \text{(Event 2)}
   \]
   \[
   x_{13} + x_{23} \leq 2 \quad \text{(Event 3)}
   \]

3. Binary constraints for decision variables:
   \[
   x_{ij} \in \{0, 1\} \quad \forall i, j
   \]

Data Source Verification:
- Coefficients for the objective function (attendance figures) are sourced from the `event.Event_Attendance` column.
- Constraints on the number of events a journalist can cover are based on business configuration parameters.
- Constraints on the number of journalists per event are based on business configuration parameters.

## 5. Gurobipy Implementation

```python
# Complete GUROBIPY implementation

import gurobipy as gp
from gurobipy import GRB

def optimize_journalist_event_assignment():
    """Optimize journalist assignments to maximize event attendance"""
    
    # 1. MODEL & DATA SETUP
    model = gp.Model("news_report")
    
    # Data: Event attendance and journalist-event pairs
    event_attendance = {1: 150, 2: 250, 3: 100}
    journalist_event_pairs = [(1, 1), (1, 2), (2, 2), (2, 3), (3, 1)]
    
    # Validate data lengths
    assert len(event_attendance) == 3, "Event attendance data length mismatch"
    
    # 2. VARIABLES
    # Binary decision variables for journalist-event assignments
    x = model.addVars(journalist_event_pairs, vtype=GRB.BINARY, name="x")
    
    # 3. OBJECTIVE FUNCTION
    # Maximize total attendance at events covered by journalists
    model.setObjective(gp.quicksum(event_attendance[j] * x[i, j] for i, j in journalist_event_pairs), GRB.MAXIMIZE)
    
    # 4. CONSTRAINTS
    
    # Constraint: Each journalist can cover up to 2 events
    model.addConstrs((gp.quicksum(x[i, j] for j in event_attendance.keys() if (i, j) in journalist_event_pairs) <= 2 for i in range(1, 4)), name="journalist_event_limit")
    
    # Constraint: Each event can be covered by up to 2 journalists
    model.addConstrs((gp.quicksum(x[i, j] for i in range(1, 4) if (i, j) in journalist_event_pairs) <= 2 for j in event_attendance.keys()), name="event_journalist_limit")
    
    # 5. SOLVING & RESULTS
    model.optimize()
    
    if model.status == GRB.OPTIMAL:
        print(f"Optimal value: {model.objVal}")
        for i, j in journalist_event_pairs:
            if x[i, j].x > 1e-6:
                print(f"Journalist {i} covers Event {j}")
    elif model.status == GRB.INFEASIBLE:
        print("Problem is infeasible")
    elif model.status == GRB.UNBOUNDED:
        print("Problem is unbounded")
    
    return model

# Run the optimization
optimize_journalist_event_assignment()
```

### Execution Results
**Status**: OPTIMAL
**Optimal Value**: 900.0
**Execution Time**: 0.19 seconds
**Reliability**: high
**Analysis**: Gurobipy found an optimal solution with an objective value of 900.0. The execution time was the fastest among the solvers, indicating efficient performance.

## 6. DOCplex Implementation

```python
# Complete DOCPLEX implementation

from docplex.mp.model import Model

def optimize_journalist_event_assignment():
    """Optimize the assignment of journalists to events to maximize attendance."""
    
    # 1. MODEL & DATA SETUP
    mdl = Model(name="news_report")
    
    # Data: Event attendance and journalist-event assignments
    event_attendance = [150, 250, 100]  # Attendance for events 1, 2, 3
    journalist_event_pairs = [(1, 1), (1, 2), (2, 2), (2, 3), (3, 1)]
    
    # Validate array lengths to prevent IndexError
    assert len(event_attendance) == 3, "Event attendance array length mismatch"
    
    # Safe range for indexing
    safe_range = range(len(journalist_event_pairs))
    
    # 2. VARIABLES
    # Binary decision variables for journalist-event assignments
    x = {(i, j): mdl.binary_var(name=f"x_{i}_{j}") for i, j in journalist_event_pairs}
    
    # 3. OBJECTIVE FUNCTION
    # Maximize total attendance at events covered by journalists
    objective = mdl.sum(event_attendance[j-1] * x[i, j] for i, j in journalist_event_pairs)
    mdl.maximize(objective)
    
    # 4. CONSTRAINTS
    
    # Each journalist can cover up to 2 events
    mdl.add_constraint(x[1, 1] + x[1, 2] <= 2, ctname="journalist_1_limit")
    mdl.add_constraint(x[2, 2] + x[2, 3] <= 2, ctname="journalist_2_limit")
    mdl.add_constraint(x[3, 1] <= 2, ctname="journalist_3_limit")
    
    # Each event can be covered by up to 2 journalists
    mdl.add_constraint(x[1, 1] + x[3, 1] <= 2, ctname="event_1_limit")
    mdl.add_constraint(x[1, 2] + x[2, 2] <= 2, ctname="event_2_limit")
    mdl.add_constraint(x[2, 3] <= 2, ctname="event_3_limit")
    
    # 5. SOLVING & RESULTS
    solution = mdl.solve()
    
    if solution:
        print(f"Optimal value: {solution.objective_value}")
        for i, j in journalist_event_pairs:
            value = solution.get_value(x[i, j])
            if value > 1e-6:
                print(f"x[{i},{j}] = {value:.3f}")
    else:
        print("No solution found")
        print(f"Status: {mdl.solve_details.status}")
    
    return mdl

# Run the optimization
optimize_journalist_event_assignment()
```

### Execution Results
**Status**: OPTIMAL
**Optimal Value**: 900.0
**Execution Time**: 2.16 seconds
**Reliability**: high
**Analysis**: DOCplex also found an optimal solution with an objective value of 900.0. The execution time was longer than Gurobipy but still reasonable.

## 7. Pyomo Implementation

```python
# Complete PYOMO implementation

import pyomo.environ as pyo
from pyomo.opt import SolverFactory

def news_report_optimization():
    """Optimize journalist assignments to maximize event attendance"""
    
    # 1. MODEL CREATION
    model = pyo.ConcreteModel()
    
    # 2. DATA SETUP
    # Event attendance data
    event_attendance = {1: 150, 2: 250, 3: 100}
    # Journalists and events
    journalists = [1, 2, 3]
    events = [1, 2, 3]
    
    # CRITICAL: Validate data lengths before indexing
    assert len(event_attendance) == len(events), "Event data length mismatch"
    
    # 3. SETS
    model.Journalists = pyo.Set(initialize=journalists)
    model.Events = pyo.Set(initialize=events)
    
    # 4. PARAMETERS
    model.EventAttendance = pyo.Param(model.Events, initialize=event_attendance)
    
    # 5. VARIABLES
    model.x = pyo.Var(model.Journalists, model.Events, within=pyo.Binary)
    
    # 6. OBJECTIVE FUNCTION
    def obj_rule(model):
        return sum(model.EventAttendance[j] * model.x[i, j] for i in model.Journalists for j in model.Events)
    model.objective = pyo.Objective(rule=obj_rule, sense=pyo.maximize)
    
    # 7. CONSTRAINTS
    
    # Each journalist can cover up to 2 events
    def journalist_constraint_rule(model, i):
        return sum(model.x[i, j] for j in model.Events) <= 2
    model.journalist_constraint = pyo.Constraint(model.Journalists, rule=journalist_constraint_rule)
    
    # Each event can be covered by up to 2 journalists
    def event_constraint_rule(model, j):
        return sum(model.x[i, j] for i in model.Journalists) <= 2
    model.event_constraint = pyo.Constraint(model.Events, rule=event_constraint_rule)
    
    # 8. SOLVING WITH GUROBI
    solver = SolverFactory('gurobi')
    
    # Optional: Set solver options
    solver.options['TimeLimit'] = 300  # 5 minutes
    solver.options['MIPGap'] = 0.01    # 1% gap
    
    # Solve the model
    results = solver.solve(model, tee=True)
    
    # 9. RESULT PROCESSING
    # Check solver status
    if results.solver.termination_condition == pyo.TerminationCondition.optimal:
        print("Optimal solution found!")
        print(f"Optimal value: {pyo.value(model.objective)}")
        
        # Extract variable values
        print("\nAssignment of journalists to events:")
        for i in model.Journalists:
            for j in model.Events:
                x_val = pyo.value(model.x[i, j])
                if x_val > 0.5:  # Only print assignments
                    print(f"Journalist {i} covers Event {j}")
        
    elif results.solver.termination_condition == pyo.TerminationCondition.infeasible:
        print("Problem is infeasible")
    elif results.solver.termination_condition == pyo.TerminationCondition.unbounded:
        print("Problem is unbounded")
    else:
        print(f"Solver terminated with condition: {results.solver.termination_condition}")
    
    return model

# Run the optimization
news_report_optimization()
```

### Execution Results
**Status**: OPTIMAL
**Optimal Value**: 1000.0
**Execution Time**: 2.01 seconds
**Reliability**: medium
**Analysis**: Pyomo reported an optimal solution with an objective value of 1000.0, which is inconsistent with the other solvers. This discrepancy suggests potential issues with the model setup or solver configuration.

## 8. Cross-Solver Analysis and Final Recommendation

### Solver Results Comparison

| Solver | Status | Optimal Value | Execution Time | Decision Variables | Retry Attempt |
|--------|--------|---------------|----------------|-------------------|---------------|
| Gurobipy | OPTIMAL | 900.00 | 0.19s | N/A | N/A |
| Docplex | OPTIMAL | 900.00 | 2.16s | N/A | N/A |
| Pyomo | OPTIMAL | 1000.00 | 2.01s | N/A | N/A |

### Solver Consistency Analysis
**Result**: Solvers produced inconsistent results
**Consistent Solvers**: gurobipy, docplex
**Inconsistent Solvers**: pyomo
**Potential Issues**:
- Pyomo might have a different interpretation of constraints or objective function.
- There could be a bug or misconfiguration in the Pyomo model setup.
- Numerical precision or solver-specific settings might have affected Pyomo's results.
**Majority Vote Optimal Value**: 900.0

### Final Recommendation
**Recommended Optimal Value**: 900.0
**Confidence Level**: HIGH
**Preferred Solver(s)**: gurobipy
**Reasoning**: Gurobipy provided a consistent and optimal solution with the fastest execution time, indicating reliability and efficiency.

### Business Interpretation
**Overall Strategy**: The optimal solution suggests that the maximum achievable attendance is 900, given the constraints on journalist and event assignments.
**Objective Value Meaning**: The optimal objective value of 900 represents the maximum total attendance at events covered by journalists, optimizing resource allocation.
**Resource Allocation Summary**: Journalists should be assigned to events in a way that maximizes total attendance while respecting the constraints on the number of events each journalist can cover and the number of journalists per event.
**Implementation Recommendations**: Ensure accurate data input and model configuration. Use Gurobipy for solving similar optimization problems due to its reliability and efficiency.