Inventory and investment in setup operations under return on investment maximization

In this paper, we construct and analyze inventory and investment in setup operations policies under return on investment (ROI) maximization. The key contributing features of this paper are the establishment of an ROI model and characterization of the unique global optimal solution when there exists an option to invest in setup operations. We also show how the inventory level is reduced when it is optimal to invest additional money in setup operations and derive the unique optimal solutions in closed-form when the setup cost is a rational or linear function of the level of investment. Various interesting managerial insights are provided.