|The In the paper, we investigate two single processor problems, which deal with the process of negotiation between a producer and
a customer about delivery time of ﬁnal products. This process is modelled by a due interval, which is a generalization of well known classical
due date and describes a time interval, in which a job should be ﬁnished. In this paper we consider two
diffierent mathematical models of due intervals. In both considered problems we should
ﬁnd such a schedule of jobs and such a determination of due intervals to each job, that the
generalized cost function is minimized. The cost function is the maximum of the following three weighted parts: the maximum tardiness, the
maximum earliness and the maximum due interval size. For the ﬁrst problem we proved several properties of its optimal solution and next we
show the mirror image property for both of considered problems, which helps us to provide an optimal solution for the second problem.