Informatica

The paper deals with a parallel processor scheduling problem with changeable job values. Contrary to other papers in this area, we assume that job values are characterized by a non-monotonic stepwise functions of job completion times (previously only non-increasing functions have been considered). We give examples of real-life systems that can be modelled in such a way, in order to show that the problem is interesting from practical point of view. The problem is shown to be NP-hard and a pseudo-polynomial time algorithm for its special case is constructed. Moreover, a number of heuristic algorithms is provided and experimentally tested.

We study single machine scheduling problems, where processing times of the jobs are exponential functions of their start times. For increasing functions, we prove strong NP-hardness of the makespan minimization problem with arbitrary job release times. For decreasing functions, maximum lateness minimization problem is proved to be strongly NP-hard and total weighted completion time minimization problem is proved to be ordinary NP-hard. Heuristic algorithms are presented and computationally tested for these problems.

Multicriteria sequencing problems with criteria ordered according to their importance are considered. Additional precedence and group technology constraints are imposed. We introduce a notion of a priority-generating vector function and suggest general techniques that form a base for the construction of polynomial time algorithms for numerous sequencing problems including all known polynomially solvable problems. A comprehensive survey of results for sequencing problems with ordered criteria is given as well.