Optimal periodic run quantities for a set of cells under joint setup

Considered is a set of manufacturing cells that are jointly setup for production. Each cell is capable of producing a specific type of part family and periodically a joint setup is performed at each of these cells for production. We model the production process of each cell by a self-exciting point process. Using some structural properties of this process, an efficient algorithm is developed to obtain the optimal run quantity and the inter-setup time.