These are all mind-numbingly administrative details that can be automated and Google Calendar, which is available as part of the Google Apps for Work suite.
One of my favourite features of Google Calendar is appointment slots, whereby you can indicate your availability for meetings and allow others to book those slots. Another great feature is resource booking so rooms and equipment can't be double booked.
Google Apps costs less than £4 / user / month and offers work based emails and office productivity apps (including Calendar) as part of the price.
Free trial of Google Apps for Work
A good way to find out more is to take advantage of the 30 day free trial of Google Apps for Work that lets you try out these features for yourself.