Polynomial time algorithms for special open shop problems with precedence constraints and unit processing times

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In this paper we consider different open shop problems with unit processing times. For the problem with two machines and arbitrary precedence constraints among the jobs, we give a polynomial time algorithm for the minimization of the makespan with a better worst case complexity than a previous algorithm known from the literature if the number of arcs is of linear order. The complexity of the open shop problem with unit processing times and intree constraints among the jobs was open up to now if the sum of completion times of the jobs has to be minimized. By means of the first result we give a polynomial time algorithm for this problem with two machines.