How can I query the occupation of a plant on a specific date range

In an industrial plant, I would like to make statistics to determine how much machines are occupied for a given date range (daily, monthly, quarterly, yearly or else )

In my database I have a list of tasks with the following details:

{
  "task": "task_1"
  "machine_id": 1,
  "start_date": "2018-01-29 12:30:00",
  "end_date": "2018-01-31 08:56:00",        
}

I've written code to determine which tasks where active for a given week and what where there occupation time :

$week_number = 5;
$year = 2018;

//Monday
$start_range = date("Y-m-d", strtotime($year . "W" . sprintf("%02d", $week_number)));

//Sunday at 23:59:00
$end_range = Carbon::parse($start_range)->addDays(7)->subSecond()->toDateTimeString();

$task_machine_occupation = GanttTask::where('task_type', 'task')
  ->select(DB::raw('machine_id, start_date, end_date, 

    CASE
      WHEN start_date> "' . $start_range . '" 
      AND end_date> "' . $end_range . '" then TIMEDIFF("' . $end_range . '" , start_date)/60

      WHEN start_date> "' . $start_range . '" 
      AND end_date< "' . $end_range . '" then TIMEDIFF(end_date , start_date)/60

      WHEN start_date< "' . $start_range . '" 
      AND end_date> "' . $end_range . '" then TIMEDIFF("' . $start_range . '"  , "' . $end_range . '")/60

      WHEN start_date> "' . $start_range . '" 
      AND end_date> "' . $end_range . '" then TIMEDIFF(start_date  , "' . $end_range . '")/60

    END AS minutes_active

    '))

  //Overlapping conditions
  ->where('end_date', '>', $start_range)
  ->where('start_date', '<', $end_range)
  ->get()
;
return $task_machine_occupation;

It works, but I'm sure I'm doing it the wrong way:

1. it's not very Eloquent
2. it returns time occupation by task and not by machine

Could I set custom parametrized attribute in the GanttTask model to get the occupation time by task and the sum it / group it by machine ?

via Chebli Mohamed