The paper deals with a scheduling problem on the parallel processors, in which the sum of values of all the jobs is maximized. The value of job is characterized by a stepwise non-increasing function. Establishing an order of processing of datagrams which are sent by multiprocessor router is a practical example of application of this problem. It was already proved that its single processor case is NP-hard, thus the problem is also NP-hard. Therefore, two pseudo-polynomial time algorithms for the problem with common moments of job value change and a polynomial time algorithm for the case with identical processing times are constructed. It is also constructed and experimentally tested a number of heuristic algorithms which solve the general version of the problem.
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