Exam scheduling infeasible solutions?

Hi all,

I am trying to solve an examination timetabling problem (ITC 2007 track 1 instances, using only a subset of the original constraints) 

I am trying to run below code but for some reason not all exams get assigned a room and a period, even though I have a constraint taking care of that every exam needs to be scheduled for exactly 1 room and 1 period. Could anyone perhaps help me out with this?

# Create the model within the Gurobi environment
model = gp.Model(env=env)
model.setParam('PoolSearchMode', 2)  # Find multiple solutions
model.setParam('PoolSolutions', 40)  # Maximum number of solutions to store in the pool

# Decision Variables
num_exams = timetable_instance.meta['Exams']
num_periods = timetable_instance.meta['Periods']
num_rooms = timetable_instance.meta['Rooms']
imm = timetable_instance.imm
durations = timetable_instance.durations
# Calculate the maximum number of invigilators
num_max_invigilators = sum(math.ceil(len(timetable_instance.imm[exam]) / 30) for exam in range(num_exams))

x = gp.tuplelist([(exam, room, period) for exam in range(num_exams) for room in range(num_rooms) for period in range(num_periods)])
x = model.addVars(x, vtype=GRB.BINARY, name="x")

model.update()

# Constraints
# Constraint: Each exam is assigned to exactly one room and one period
for exam in range(num_exams):
    model.addConstr(gp.quicksum(x[exam, room, period] for room in range(num_rooms) for period in range(num_periods)) == 1,
                    f'exam_assignment[{exam}]')

model.update()

# Constraint: Room capacities are never to be exceeded
for room in range(num_rooms):
    for period in range(num_periods):
        # Create a list to hold expressions for each exam in the current room and period
        exam_expressions = []
        for exam in range(num_exams):
            expr = gp.LinExpr()
            expr.addTerms(len(timetable_instance.imm[exam]), x[exam, room, period])
            exam_expressions.append(expr)
        
        # Sum up the expressions for all exams in the current room and period
        total_students_expr = gp.LinExpr()
        for expr in exam_expressions:
            total_students_expr.add(expr)
            
        # Add a constraint that the total students should not exceed the room's capacity
        model.addConstr(total_students_expr <= timetable_instance.rooms[room]['capacity'],
                        f'room_capacity[{room},{period}]')

model.update()

#Constraint: Each student can only be assigned to one exam in a period
student_exams = {}
for i in range(len(timetable_instance.imm)):
    for student_number in timetable_instance.imm[i]:
        if student_number not in student_exams:
            student_exams[student_number] = []
        student_exams[student_number].append(i)

for student, ex in student_exams.items():
    num_exams_this_student = len(ex)
    if num_exams_this_student>1:
        for i in range(num_exams_this_student - 1):
            exam1 = ex[i]
            for j in range(i + 1, num_exams_this_student):
                exam2 = ex[j]
                for period in range(num_periods):
                    model.addConstr(gp.quicksum(x[exam1, room, period] + \
                                                x[exam2, room, period] for room in range(num_rooms))\
                                    <= 1, f'student_{student}_period_{period}_constraint')
model.update()

# Constraint: Period lengths respected
for exam in range(num_exams):
    for room in range(num_rooms):
        for period in range(num_periods):
            if durations[exam] > timetable_instance.periods[period]['duration']:
                model.addConstr(x[exam, room, period] == 0, f'duration_constraint[{exam},{room},{period}]')

model.update()

model.setParam('FeasibilityTol', 1e-9)
model.params.TimeLimit = 1800  # setting a time limit of 300 seconds

solutions_dfs = []

# Optimize the model
model.optimize()

if model.Status == GRB.INFEASIBLE:
    model.computeIIS()

    # Print out the IIS constraints and variables
    print('\nThe following constraints and variables are in the IIS:')
    for c in model.getConstrs():
        if c.IISConstr:
            print(f'\t{c.constrname}: {model.getRow(c)} {c.Sense} {c.RHS}')

    for v in model.getVars():
        if v.IISLB:
            print(f'\t{v.varname} ≥ {v.LB}')
        if v.IISUB:
            print(f'\t{v.varname} ≤ {v.UB}')
else:
    num_solutions = model.SolCount
    print("Number of solutions found:", num_solutions)
    print('runtime is',model.Runtime)
    # Getting % usage of virtual_memory ( 3rd field)
    print('RAM memory % used:', psutil.virtual_memory()[2])

    solution_pool_size = model.getAttr('SolCount')
    print(f"Solution pool contains {solution_pool_size} solutions")

    # Access every solution from the Gurobi solution pool
    solution_dataframes = []
    count_0s=0
    for solution_index in range(solution_pool_size):
        model.params.SolutionNumber = solution_index

        # Create a DataFrame to store variable values for this solution
        solution_vars_df = pd.DataFrame(columns=['Exam', 'Room', 'Period','Invigilators'])

        # Retrieve and store variable values for this solution
        for exam in range(num_exams):
            for room in range(num_rooms):
                for period in range(num_periods):
                    if exam==0:
                        if x[exam, room, period].Xn == 1:
                            count_0s+=1 
                    if x[exam, room, period].Xn == 1:
                        solution_vars_df = solution_vars_df.append({
                            'Exam': exam,
                            'Room': room,
                            'Period': period,
                        }, ignore_index=True)

        # Store the DataFrame for this solution
        solution_dataframes.append(solution_vars_df)