Convert your HoH into an AoH. To do that, you need to create a second entry in your HoH that contains successors. So, your datastructure needs to look like:

$hash={
  'MEX1J' => { 
    'desc' => 'Job 2' 
    'pred' => [TEX1J],
    'succ' => [MEX2J],
  },
  'MEX2J' => { 
    'desc' => 'Job end'
    'pred' => [TEX1J,MEX1J], 
    'succ' => [],
   },
  'TEX1J' => { 
    'desc' => 'Job start'
    'pred' => [], 
    'succ' => [MEX2J],
   }
}
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That way, you can start to build your job execution tree.

Of course, I would build this using some sort of directed graph instead of a HoH. That way, predecessors and successors would be handled for you.