Given the questionable financial capacity of the current public pension systems to meet the economic needs that workers regularly demand after they have ceased working, governments are increasingly and more generally promoting the development of social welfare systems that complement, as far as possible, these shortcomings. To this end, so-called integrated pension schemes have been gradually developed in some countries, the main purpose of which is to provide workers who have already retired with a level of income which, together with that provided by the public pension system, guarantees income similar to that which they had before retirement. Two types of methods, Offset and Excess, are commonly used for the integration of these public and private social welfare systems, the analysis of which is the main objective of this work. To this end, we set up a model whose structure reflects the main characteristics and variables of these systems and, subsequently, we will examine the most common methods of integration.