In this letter, we proposed a brand-new version for investigating the optical bistability (OB) and optical multistability (OM) through electron tunneling impact in a defect one-dimensional photonic crystal (1DPC). The defect layer of 1DPC is doped with double quantum dot (DQD) nanostructure which interacts with an indirect incoherent pump and a susceptible probe incident light, respectively. By the usage of the quantum mechanical density matrix method, we first examine the refractive index properties of the defect layer through electron tunneling and indirect incoherent pumping effects. Then, through the usage of the transfer matrix methods, we acquire the reflection and transmission coefficients of the defect 1DPC. At the end, we discuss the OB and OM properties of the reflected and transmitted lighting in negative refractive index situation of the DQD. We determine that during a few parametric conditions the switching from OB to OM or vice versa is feasible for reflected and transmitted light beams.