hello ejeg
welcome to TP
sadly many of us have faced this particular habit
Beate is right about the service - we had a Telecare system installed through the Local Authority Adult Services - there was an alarm button (dad wore his on a pendant, could have been on a wristband) and a door monitor linked up to a phone hub in the house - if dad opened the door and left it open for more than an agreed length of time, an operator called him using the hub, which acted as a speaker so dad didn't have to lift a handset or even be nearby - if the operator was at all concerned, either with what dad said in response or if there was no answer, she also called me and I could go round to his house to check on him, she stayed on the line whilst I got there (less than 5 mins by car) - it saved his bacon when he wandered off in only his pjs on a winter night - I think it cost a few pounds a week; well worth it
is the front door on a Yale lock or has it to be locked with a key - if the latter, maybe install one of these door closer mechanisms, so that at least the door closes, though it won't be locked - if on a Yale lock, not ideal as it may close and lock your dad out - you could have a keysafe installed but doubt he'd be able to use it (though very useful for emergency services, carers ... to get in)
I do agree about days at a day care centre which will keep your dad occupied and well fed, ask for transport to be arranged and the transporter can make sure your dad goes into the house and settles
just a bit of a warning - such behaviour can be the precursor to going out of the house and wandering off; it isn't always, but it is worth bearing that in mind
best wishes