In this paper we develop approximations for the distribution of the total time spent in a dynamic job shop. In particular, using an exponential limit theorem and an heuristic decomposition of open queueing networks, we show that for a large class of dynamic job shops, the total time spent in a dynamic job shop can be approximated by an exponential random variable with an appropriate mean. Approximations for job shops that do not belong to this class are also developed. Numerical results show that the proposed approximations are in general very good. Application of these approximations in the assignment of due-dates is also illustrated.