There are different criteria for designing a geodetic network in an optimal way.An optimum network can be regarded as a network having high precision, reliabilityand low cost. Accordingly, corresponding to these criteria different single-objectivemodels can be defined. Each one can be subjected to two other criteria as constraints.Sometimes the constraints can be contradictory so that some of the constraints areviolated. In this contribution, these models are mathematically reviewed. It is numericallyshown how to prepare these mathematical models for optimization processthrough a simulated network. We found that the reliability model yields small positionchanges between those obtained using precision respectively. Elimination ofsome observations may happen using precision and cost model while the reliabilitymodel tries to save number of observations. In our numerical studies, no contradictionscan be seen in reliability model and this model