Total late work criteria for shop scheduling problems

Scheduling theory is concerned with problems of the allocation of resources to perform a set of activities in order to achieve a certain goal. The purpose of the scheduling process could be attained by finding a feasible solution of the considered problem as well as by determining the best solution in the reference to a given optimality criterion. There are a few classical performance measures broadly studied such as schedule length, mean or mean weighted how time, maximum lateness etc. However, trying to cover more realistic problems, new parameters and criteria must be considered. The performance measure based on the amount of late work in the system is an example of such a non-classical criterion involving due dates. Classical criteria such as e.g, maximum lateness or mean tardiness calculate the penalty for late tasks with respect to the time of their completion, whereas in some applications, the penalty should be determined with the reference to the amount of the late work independently of the time of its completion. The criteria based on late work were first proposed in the context of parallel processors and then applied in a one machine scheduling problem. In the paper, new results are presented concerning general complexity of scheduling problems with the late work criteria and some special cases in the shop environment.