  We consider the Cauchy problem associated to the fourth-order nonlinear
Schr\"{o}dinger-Hartree equation with variable dispersion coefficients. The
variable dispersion coefficients are assumed to be continuous or periodic and
piecewise constant in time functions. We prove local and global well-posedness
results for initial data in $H^s$-spaces. We also analyze the scaling limit of
fast dispersion management and the convergence to a model with averaged
dispersions.
