Scheduling to maximize idle time
Here's a paper that considers a more general variant of the problem (multiple machines, job dependent demands etc.): 

Rohit Khandekar, Baruch Schieber, Hadas Shachnai, Tami Tamir.
Real-time scheduling to minimize machine busy times.
Journal of Scheduling 18(6), 561-573, 2015.
doi:10.1007/s10951-014-0411-z

In particular, their results give a polynomial time algorithm for the case described in my question.