Near field cosmology is practiced by studying the Local Group (LG) and its neighbourhood. The present paper describes a framework for simulating the near field on the computer. Assuming the LCDM model as a prior and applying the Bayesian tools of the Wiener filter (WF) and constrained realizations of Gaussian fields to the Cosmicflows-2 (CF2) survey of peculiar velocities, constrained simulations of our cosmic environment are performed. The aim of these simulations is to reproduce the LG and its local environment. Our main result is that the LG is likely a robust outcome of the LCDM scenario when subjected to the constraint derived from CF2 data, emerging in an environment akin to the observed one. Three levels of criteria are used to define the simulated LGs. At the base level, pairs of halos must obey specific isolation, mass and separation criteria. At the second level the orbital angular momentum and energy are constrained and on the third one the phase of the orbit is constrained. Out of the 300 constrained simulations 146 LGs obey the first set of criteria, 51 the second and 6 the third. The robustness of our LG factory enables the construction of a large ensemble of simulated LGs. Suitable candidates for high resolution hydrodynamical simulations of the LG can be drawn from this ensemble, which can be used to perform comprehensive studies of the formation of the LG