The response time variability problem (RTVP) is an NP-hard scheduling problem that has been studied intensively recently and has a wide range of real-world applications in mixed-model assembly lines, multithreaded computer systems, network environments and others. The RTVP arises whenever products, clients or jobs need to be sequenced in order to minimise the variability in the time between two successive points at which they receive the necessary resources. To date, the best exact method for solving this problem is a mixed integer linear programming (MILP) model, which solves to optimality most of instances with up to 40 units to be scheduled in a reasonable amount of time. The goal of this paper is to increase the size of the instances that can be solved to optimality. We have designed an algorithm based on the branch and bound (B&B) technique to take advantage of the particular features of the problem. Our computational experiments show that the B&B algorithm is able to solve larger instances with up to 55 units to optimality in a reasonable time.