Due to the limited amount of resources available for the next release of the current product under development not all stakeholders requests can be included in the next product to deliver. This optimization problem, known as the Next Release Problem (NRP), has customers satisfaction and development costs as the basic optimization objectives, and has been the subject of many research works. However, there are additional issues that deserve to be considered and included in the definition of the NRP, such as supplementary optimization objectives including the elicited properties about the requirements, or the analysis of the non-dominated solution sets found to decide which solution is preferred. This paper presents a generic formulation for this problem that allows the management of the currently agreed properties and relationships between requirements. It provides an open formulation that is capable of growing as the scope of the NRP grows. We specify how our proposal can be used in software product projects when requirements selection has to be performed. We also describe how our formulation has been instantiated to cover previous solving approaches to this problem, using six case studies to demonstrate the successful customization of the generic formulation.