Abstract: Parallel machine scheduling problems, which are important discrete optimization problems, may occur in many applications. For example, load balancing in network communication channel assignment, parallel processing in large-size computing, task arrangement in flexible manufacturing systems, etc., are multiprocessor scheduling problem. In the traditional parallel machine scheduling problems, it is assumed that the problems are considered in offline or online environment. But in practice, problems are often not really offline or online but somehow in-between. This means that, with respect to the online problem, some further information about the tasks is available, which allows the improvement of the performance of the best possible algorithms. Problems of this class are called semi-online ones. In this paper, the semi-online problem P2|decr|l_p (p>1) is considered where jobs come in non-increasing order of their processing times and the objective is to minimize the sum of the l_p norm of every machine’s load. It is shown that LS algorithm is optimal for any l_p norm, which extends the results known in the literature. Furthermore, randomized lower bounds for the problems P2|online|l_p and P2|decr|l_p are presented.

Key words: Semi-online, Scheduling, Randomization, Competitive ratio

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