LAUSR

This article systematically establishes a new category of assignment problems by reviewing and extending the problems related to group role assignment (GRA) from a novel vision. After reviewing seven related GRA with Constraints (GRA+) problems, this article specifies three new major assignment problems to make GRA+ problems complete and coherent. In addition, this article proves a series of new related theorems, proposes new conditions for the specified problems to have feasible solutions, and verifies the hardness of the newly specified problems. This article finally verifies the value of the presented theoretical work and provides a generalized formalization of this category of problems, i.e., the one highly abstract optimization problem, which is specified the first time. This article contributes to the literature of assignment problems with a novel category of well-defined problems, i.e., GRA+. The presented problem category is original, consistent, but far from complete. It will initiate further innovations in assignment research along with the presented directions. This article again demonstrates the power of the methodology role-based collaboration (RBC), and the environments—classes, agents, roles, groups, and objects (E-CARGO) model.