A Strict Solution Method for the Single-Machine Total Tardiness Problem with a Precedence Constraint

Abstract

In this paper we treat a class of scheduling problems, the single-machine total tardiness problem with a precedence constraint. In this problem, a precedence constraint between two jobs is given a priori and the purpose is to obtain an optimal schedule satisfying this constraint. We construct a simple strict solution algorithm for this problem based on the extensions of the well-known decomposition theorem and the elimination rules for the ordinary single-machine total tardiness problem without a precedence constraint. It is shown by computational experiments that the algorithm can solve problem instances with up to about 45 jobs in acceptable times.