Exam scheduling is a complex problem. Traditional ways are using either graph-based heuristic algorithms or mixed linear programming (MLP) plus human intelligence. The heuristics could not always guarantee an optimal solution, and MLP, due to its generality, needs human schedulers to model for special requirements. Role-Based Collaboration (RBC) and its Environments - Classes, Agents, Roles, Groups, and Objects (E-CARGO) model and Group Role Assignment with Constraints (GRA+) are tools well suited to tackle such a problem. With RBC E-CARGO, and GRA⁺, human schedulers save a lot of effort to create symbols and the relationships among the components. This paper formalizes the problem of exam scheduling as an extended GRA with Conflicting Agents on Roles (GRACAR) problem, proposes practical solutions by using a Linear Programming (LP) solver, i.e., the IBM ILOG CPLEX Optimization Package (CPLEX). The proposed solution is verified by a real-world case study, and provides technical support for human schedulers in solving similar problems.