A simple and fast slip link model called ecoSLM is presented and applied to mixtures of short and long linear polymers. It explicitly models binary entanglements between chains as slip links and offers a natural and powerful representation of constraint release. A multichain Markov chain Monte Carlo algorithm is developed to simulate stress relaxation following a step shear in the linear viscoelastic regime. The time required for accumulated slack to equilibrate along the chain contour is subsumed into the definition of the time step. The parameters of the ecoSLM are determined from data on monodisperse linears by mapping the time and modulus scales and specifying a parameter gamma that is related to the variation of the zero-shear viscosity with molar mass. Predictions of viscosity and dynamic moduli obtained using the ecoSLM are in remarkably good agreement with experimental data on 1,4-polybutadienes. Thus, ecoSLM fills a valuable niche in describing the long and intermediate timescale dynamics of bidisperse blends in which constraint release is determined by a complex interplay of mechanisms at a computational cost that is a few orders of magnitude smaller than other, more sophisticated, slip link models.