Świętochłowice is a town located in a central part of Katowice conurbation (Silesian Voivodeship). The town has been industrially and anthropogenicaly changed, and a large area of it has been turned to postindustrial waste yard. A rich population of Epipactis palustris was discovered in 2001, in a north-westen part of the Świętochłowice district - Chropaczów, on a zinc and colliery heap. The population of Epipactis is numerous and of expanding tendencies.

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.