Branch and bound and dynamic programming to minimize the total completion times on a single machine with availability constraints

In this paper we consider the single machine scheduling problem with availability constraints in order to minimize the total completion times of jobs. We propose two exact approaches to solve the problem: a dynamic programming and a branch and bound method. The study of these approaches is carried out in this article and a concluding analysis based on several experimental results allows us to select the most suitable method according to the studied instance.