One of the problems in the single-objective optimisation models (SOOMs) for optimising geodetic networks is the contradiction of the controlling constraints, which may lead to their violation or infeasibility in the optimisation process. One way to solve this problem is to use a bi-objective optimisation model (BOOM) instead of SOOMs. In this paper, we will use the BOOM of precision and reliability and investigate the influence of the controlling constraints in a two-dimensional simulated network. Our studies show that the unconstrained BOOM is a good model, which almost fulfils our precision and reliability demands of the network. This model is also economical as more observables are removed from the plan whilst adding the controlling constraints leads to including more observables, which have no significant role