An exact algorithm for the precedence-constrained single-machine scheduling problem

This study proposes an exact algorithm for the precedence-constrained singlemachine scheduling problem to minimize total job completion cost where machine idle time is forbidden. The proposed algorithm is an extension of the authors’ previous algorithms for the problem without precedence-constraints and is based on the SSDP (Successive Sublimation Dynamic Programming) method. Numerical experiments will show that it can solve all instances with up to 50 jobs of the precedence-constrained total weighted tardiness and total weighted earliness-tardiness problems, and most instances with 100 jobs of the former problem.