A note on scheduling tall/small multiprocessor tasks with unit processing time to minimize maximum tardiness

We study the scheduling situation where n tasks, subjected to release dates and due dates, have to be scheduled on m parallel processors. We show that, when tasks have unit processing times and either require 1 or m processors simultaneously, the minimum maximal tardiness can be computed in polynomial time. Two algorithms are described. The first one is based on a linear programming formulation of the problem while the second one is a combinatorial algorithm. The complexity status of this "tall/small" task scheduling problem P|r i,p i = 1, size i ∈ {1, m}|T max was unknown before, even for two processors.