(eng): The existence of the fast/slow phenomena in (bio)chemical reaction systems rep- resents difficulties for numerical simulation. However, it provides opportunities to reduce the system order. A well-known example of a classical model reduction method is the so-called quasi-steady-state approximation (QSSA) method, usually applied to a system of ODEs describing chemical reaction networks where one or more reactions are so fast that a quasi-steady-state for some species concentration is reached almost instantaneously. In this contribution, we develop and test a novel model reduction method, the delayed quasi-steady-state approximation (D-QSSA) method, which was first pro- posed by Vejchodský [1], [2] and further developed by Matonoha and Papáček [3]. While Vejchodský et al. developed their method for the generally time-dependent delays, we newly analyzed theoretical and numerical issues related to the existence and setting of constant delays in some sense optimal. As a numerical case study, we took the paradigmatic example of the Michaelis-Menten kinetics with a simple transport process. The results of the comparison of the full non-reduced system behavior with nine respective variants of reduced models are discussed.