Inventory and investment in quality improvement under return on investment maximization

In this paper, we construct and analyze inventory and investment in quality improvement policies under return on investment (ROI) maximization. In our model, the level of quality is represented by the fraction of an order quantity meeting the quality requirements such as product specifications. The key contributions of this paper are the establishment of an ROI model and characterization of the unique global optimal solution. We also show how the inventory level is reduced when it is optimal to invest additional money in quality improvement. In addition, we derive the unique global optimal solutions in closed-form when the investment in quality improvement is a linear function of the quality. Various interesting managerial insights and a numerical example are provided.