One-Machine Sequencing to Minimize Total Tardiness: A Fourth Theorem for Emmons

In 1969 H. Emmons provided three theorems (Emmons 1–3) for determining precedence relations between pairs of jobs for the single-machine tardiness problem. We show here a fourth straightforward theorem that uses the information when the jobs in the pair are both known to precede a third job in an optimum sequence. The new theorem augments the three Emmons theorems and is shown to be a generalization of a theorem by Elmaghraby.