Optimizing the concurrency for a group of design activities

This research focuses upon the optimization of the concurrency between upstream product design activity and downstream process design activities in the concurrent engineering product development pattern. First, a new model of concurrent product development process, i.e., the design activity group model, is built. In this model, the product and process design activities are carried out concurrently with the whole design process divided into several stages, every two of which are separated by a design review activity. The design review activities may lead to design iterations at a certain rate of probability. Therefore, a probability theory-based method is proposed to compute the mean duration of the design activity group and the mean workloads of all the design and review activities, with design iterations taken into consideration. Then, the problem of concurrency optimization is defined mathematically, whose objective is to minimize the total costs for delay of design activity group completion time and unnecessary design revision workloads. Our research proves that the cost function is convex with respect to the concurrent (or overlap) degree between design activities and that it must have a minimum value at a unique optimum point. Based on this property, a one-dimensional search algorithm that is exponentially converged is finally proposed for solving the problem.