Optimal lot-sizing policy with incentives for yield improvement

In the semiconductor manufacturing industry, the complex process of turning microchip designs using silicon discs into working electronic components has become more difficult due to the advent of new technology in applications such as chips for the video gaming industry. In this paper, we model the problem for a firm facing a target demand from its customers. The firm may either subcontract manufacturing to an external supplier or do the production at its in-house facility. In the former case, the decision is to determine the optimal order size recognizing that the supplier faces an uncertain output due to random yield. In the latter case, the decision is to choose the optimal lot-sizing policy at its own production facility. We determine such optimal decisions for the firm. In addition, we consider the possibility of using better, but more expensive, technology to improve yields, and discuss the mechanism where the firm can provide incentive to the supplier to improve the yield.