Focusing on electron transport through a periodically driven resonant tunneling diode, we study the generation of a non-vanishing dc-current by applying symmetry breaking external ac fields with phase difference phi in a statically unbiased system. The effect of an environment is investigated using the system-bath Hamiltonian represented by the electron system coupled to harmonic oscillator modes with a Drude-Lorentz spectral density. To carry out simulations, we use the hierarchal equations of motion approach in the Wigner representation including a self-consistently constructed electric field that is determined from the electron distribution using the Poisson equation. We show that the maximal pumping current at a phase difference near phi = pi/2 is strongly influenced by the system-bath coupling strength. The effect of dissipation is diminished if the self-consistent part of the potential is ignored.