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Complaint letters addressed to the CEO always get resolved quickly
I've done this many times -. Professional letter to the CEO gets you a relatively high up director contacting you personally with their contact details and almost immediate resolution / explanation / compensation.
I'm under no illusion that the CEO actually read it or anything, but it's definitely worth the cost of a special delivery letter.
I work for a big BS. Complaint letters addressed to the CEO always get resolved quickly.