The problem of sizing the resources of a production system is widely encountered both in the literature and in practice. Simulation is a very useful method to identify the necessary number of resources. However, if there are numerous resources, it can become impossible to make a sound 'trial-and-error' analysis with simulation models, so that strategies using simulation optimization appear as an attractive approach. Unfortunately, it is necessary to specify a cost function, and, in practice, it is often very difficult to formalize such a function which is used to determine the number of resources that will minimize this cost. In this article, we propose a different modelling approach, which aims at sizing the resources so as to meet the design specifications. In this respect, we search for the minimum number of resources of each type, while satisfying the performance requirements specified in the design project. As a result, the problem is formulated as a stochastic multi-objective optimization problem with constraints. The approach used here is based on simulation, used in conjunction with a bootstrap approach which accounts for the stochastic aspect of the model, and with regression meta-modelling in order to derive an analytical formulation of the constraints together. Different multi-objective optimization methods can then be used to solve the problem. An illustrative example is given.