Chip manufacturing: matching production plan with customer requirements

Manufacturing chips is a long process that starts by deciding how many chips of each type a wafer to be launched in production must contain in order to meet customer requirements. The total number of chips per wafer is constant, and any mix of chip types is allowed on a wafer. Two levels of failure may arise during the manufacturing process, namely 1) the ones that result in rejecting a wafer and, as a consequence, all the chips contained in this wafer, and 2) the failures that result in rejecting chips individually. We know the probability of a wafer to fail, as well as the probability of a chip of any type to be rejected. The goal is to minimize the number of wafers to launch in production in order to meet the customer requirements with a given probability. In this paper, we propose an efficient heuristic algorithm that leads to a near-optimal solution. Several numerical examples illustrate this algorithm