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scheduling A schedule or a timetable, as a basic time-management tool, consists of a list of times at which possible tasks, events, or actions are intended to take place, or of a sequence of events in the chronological order in which such things are ...
, 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 Field inventory management commonly known as inventory management is the function of understanding the stock mix of a company and the different demands on that stock. The demands are influenced by both external and internal factors and are bal ...
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 d_i and the completion time be C_i of job i. Then for job i * lateness is L_i=C_i-d_i, * earliness is E_i = \max(0, d_i-C_i), * tardiness is T_i = \max(0, C_i-d_i). In scheduling common
objective function In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cos ...
s are C_\max, L_\max, E_\max, T_\max, \sum C_i, \sum L_i, \sum E_i, \sum T_i or weighted version of these sums, w_iC_\max, w_iL_\max, w_iE_\max, w_iT_\max, \sum w_iC_i, \sum w_iL_i, \sum w_iE_i, \sum w_iT_i, where every job comes with a weight w_i. 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 In computational complexity theory, NP-hardness ( non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard pr ...
."Complexity results for scheduling problems"
University of Osnabrueck


References

{{reflist Time management Scheduling (computing) Schedule (project management) Theoretical computer science