Tardiness (scheduling)

In scheduling, tardiness is a measure of a delay in executing certain operations and earliness is a measure of finishing operations before due time. The operations may depend on each other and on the availability of equipment to perform them.
Typical examples include job scheduling in manufacturing and data delivery scheduling in data processing networks.
In manufacturing environment, inventory management considers both tardiness and earliness undesirable. Tardiness involves backlog issues such as customer compensation for delays and loss of goodwill. Earliness incurs expenses for storage of the manufactured items and ties up capital.
Mathematical formulations.
In an environment with multiple jobs, let the deadline be formula_1 and the completion time be formula_2 of job formula_3. Then for job formula_3
In scheduling common objective functions are formula_8 or weighted version of these sums, formula_9, where every job comes with a weight formula_10. The weight is a representation of job cost, priority, etc.
In a large number of cases the problems of optimizing these functions are NP-hard.