Allocating a joint setup in a multi-cell system

Consider a manufacturing system consisting of multiple cells; each cell processes a certain type of part family. For such systems, we study the problem of optimally allocating a joint setup among these cells. The production process of each cell is modelled by a birth process. Certain monotonicity properties of these birth process are established and used to show that the efficient discrete marginal allocation approach of Fox [1] can be applied here.