Late reply ...
Thanks to all who responded, also in private email.
MRBS at http://mrbs.sourceforge.net/
seems to fit the bill quite nicely.
Lars Hecking writes:
>> I am looking for web-based software for resource scheduling.
> E.g. to let people book/unbook/view bookings of rooms, equipment,
> and so on. I couldn't find anything obvious on php.net's project page.
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