  We introduce an intuitive and semi-analytical polaron master equation
approach to model pulse-driven population inversion and emitted single photons
from a quantum dot exciton. The master equation theory allows one to identify
important phonon-induced scattering rates analytically, and fully includes the
role of the time-dependent pump field. As an application of the theory, we
first study a quantum dot driven by a time-varying laser pulse on and off
resonance, showing the population inversion caused by acoustic phonon emission
in direct agreement with recent experiment of Quilter {\em et al.}, Phys Rev
Lett {\bf 114}, 137401 (2015). We then model quantum dots in weakly coupled
cavities and show the difference in population response between exciton-driven
and cavity-driven systems. Finally, we assess the nonresonant phonon-assisted
loading scheme with a quantum dot resonantly coupled to a cavity as a
deterministic single photon source, and compare and contrast the important
figures of merit with direct Rabi oscillation of the population using a
resonant $\pi$ pulse, where the latter is shown to be much more efficient.
