Due date assignment in repetitive projects

This paper is concerned with the study of the constant due-date assignment policy in repetitive projects, where the activity durations are exponentially distributed random variables. It is then extended to the case where activity durations follow generalized Erlang distributions. The main feature of this research over the classical PERT networks is that the projects are generated according to a renewal process and share the same facilities. Our approach is first to obtain the project completion time distribution, for each generated project, by constructing a proper continuous-time Markov chain, and then to compute the optimal constant lead time for each particular project. The repetitive projects are represented as proper networks of queues, where the service times represent the durations of the corresponding activities and the arrival stream to each node follows a renewal process. It is assumed that each project's end result has a penalty cost that is some linear function of its due-date and its actual completion time. The due date is found by adding a constant to the time that the order for a project's end result arrives. This constant value is the constant lead time that a project might expect between its starting and completion times. Then, the optimal constant lead time is computed by minimizing the expected aggregate cost per project. Finally, the results are verified by Monte Carlo simulation.