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.

JO - Bulletin of the Polish Academy of Sciences: Technical Sciences L1 - http://sd.czasopisma.pan.pl/Content/111812/PDF/%2852-2%29115.pdf L2 - http://sd.czasopisma.pan.pl/Content/111812 PY - 2004 IS - No 2 EP - 118 KW - scheduling KW - processor KW - due interval KW - cost criterion A1 - Janiak, A. VL - vol. 52 JF - Bulletin of the Polish Academy of Sciences: Technical Sciences SP - 115 T1 - Mirror image property for the optimal solutions of two single processor scheduling problems with due intervals determination DA - 2004 UR - http://sd.czasopisma.pan.pl/dlibra/docmetadata?id=111812 ER -