This paper deals with the earliness-tardiness common due date model of
minimizing the sum of earliness and tardiness penalties. We assume th
at those penalties vary from job to job and that the ratios of process
ing times and penalties satisfy certain (called agreeable) conditions.
Three types of schedules (V-0, V-1, and W) are identified where the c
omplexity of W schedules far exceeds the complexity of the remaining t
ypes. Conditions are derived that significantly improve the existing m
ethods to find the best W schedule. This improvement is demonstrated o
n 1500 test problems of the sizes n = 10, 20, 50, 70 and 100.