In this paper, we study a fair resource scheduling problem involving the assignment of a set of interval jobs among a group of heterogeneous machines. Each job is associated with a release time, a deadline, and a processing time. A machine can process a job if the entire processing period falls within the release time and deadline of the job. Each machine can process at most one job at any given time, and different jobs yield different utilities for the machines. The goal is to find a fair and efficient schedule of the jobs. We discuss the compatibility between envy-freeness up to any item (EFX) and various efficiency concepts. Additionally, we present polynomial-time algorithms for various settings.