A queueing model for due date control in a multi server repair shop with subcontracting

This paper deals with a repair shop with multiple parallel servers, which has to carry out planned overhauls, consisting of a lot of maintenance jobs. These overhauls are disturbed by randomly arriving emergency jobs. To control the delivery performance of the overhauls, knowledge about the overhaul makespan distribution should be available. However, past approaches do not have an answer to this problem. Using a 2-dimensional Markov model, we derive theoretical solutions for the first and second moment of the overhaul makespan for the case that the repair times of all overhaul jobs are identically and exponentially distributed. In case of non identical repair time distributions, an approximation for the moments is presented. These moments are used to approximate the makespan distribution by a mixture of two Erlang distributions. We show by simulation that this approximation gives very good results