Optimal ordering policies and capital investment in setup reduction for continuous review inventory system with random yields

In existing production/inventory models with random yields, the setup cost is given and fixed. However, in many practice situations, they can be reduced by investment in modern production technology. In this study, we attempt to determine the optimal capital investment in setup cost reduction for ( Q, ") inventory system, jointly with the optimal ordering policies. We assume that the setup cost is the function of capital expenditure. Furthermore, we show that the expected total annual cost function with capital investment is convex. With the convexity, an algorithm is developed to determine the optimal order quantity and reorder point, and then to find the optimal setup cost. Finally, numerical results are presented to illustrate the algorithm procedure and compared to the results without considering capital investment. Our results evidently show that substantial cost saving might be obtained through capital investment in setup reduction.