blocked <- data.frame(
  crossing(i = 1:n, j = 1:m) %>%
    mutate(blocked = 1) %>%
    spread(j, blocked) %>%
    select(-i)
)
# student 10 cannot take course 4
blocked[10, 4] <- 0

# student 25 cannot take course 1 or 3
blocked[25, 1] <- 0
blocked[25, 3] <- 0

model <- MIPModel() %>%
  
  # 1 iff student i is assigned to course m
  add_variable(x[i, j], i = 1:n, j = 1:m, type = "binary") %>%
  
  # maximize the preferences
  set_objective(sum_expr(weight(i, j) * x[i, j], i = 1:n, j = 1:m)) %>%
  
  # we cannot exceed the capacity of a course
  add_constraint(sum_expr(x[i, j], i = 1:n) <= capacity[j], j = 1:m) %>% 
  
  # each student needs to be assigned to one course
  add_constraint(sum_expr(x[i, j], j = 1:m) == 1, i = 1:n) %>%

  # NEW: some students are blocked from certain courses
  add_constraint(x[i, j] <= blocked[i, j], i = 1:n, j = 1)

  # NEW: some students are blocked from certain courses
  set_bounds(x[i, j], ub = blocked[i, j])

  # some students are blocked from certain courses
  set_bounds(x[blocked[i, j]], ub = 0, i = 1:n, j = 1:m)

MIPModel() %>%
  add_variable(x[a, b], a=1:2, b=1:5, type = "integer", lb = 0, ub = 5) %>%
  set_objective(sum_expr(x[a, b], a=1:2, b=1:5), "max") %>%
  # add_constraint(x[i, i] == 0, i = 1:2) %>%
  set_bounds(x[i, i], i=1:2, ub = 0) %>%
  solve_model(with_ROI(solver = "glpk")) %>%
  get_solution(x[a, b])

   variable a b value
1         x 1 1     0
2         x 1 2     5
3         x 1 3     5
4         x 1 4     0
5         x 1 5     5
6         x 2 1     5
7         x 2 2     5
8         x 2 3     5
9         x 2 4     5
10        x 2 5     5

MIPModel() %>%
  add_variable(x[a, b], a=1:2, b=1:5, type = "integer", lb = 0, ub = 5) %>%
  set_objective(sum_expr(x[a, b], a=1:2, b=1:5), "max") %>%
  add_constraint(x[i, i] == 0, i = 1:2) %>%
  # set_bounds(x[i, i], i=1:2, ub = 0) %>%
  solve_model(with_ROI(solver = "glpk")) %>%
  get_solution(x[a, b])

   variable a b value
1         x 1 1     0
2         x 1 2     5
3         x 1 3     5
4         x 1 4     5
5         x 1 5     5
6         x 2 1     5
7         x 2 2     0
8         x 2 3     5
9         x 2 4     5
10        x 2 5     5