Single-Machine Scheduling of Unit-Time Jobs with Earliness and Tardiness Penalties

The problem of determining a schedule of jobs with unit time lengths on a single machine that minimizes the total weighted earliness and tardiness penalties with respect to arbitrary rational due dates is formulated as an integer programming problem We show that if the penalties meet a certain criterion called the Dominance Condition then there exists an extremal optimal solution to the LP relaxation that is integral leading to a polynomial time solution procedure The general weighted symmetric penalty structure is one cost structure that satis es the Dominance Condition we point out other commonly found penalty structures that also fall in this category