This research examines a new multiple lot-sizing problem, which is in the context of a two-stage production system with a due-date-based demand and the process yields are both governed by interrupted geometric (IG) distributions. We model this problem as a recursive formula and solve it by dynamic programming. This research also develops lemmas for solving this problem. However, there may still be many computational efforts in solving this DP problem. An efficient algorithm for resolving the computational issue is proposed. This algorithm is designed to reduce the DP network into a much simpler one—through combining a group of DP branches into a single one. Extensive experiments have been carried out. Results indicate that the reduction algorithm is quite helpful to practitioners in dealing with large-scale cases with high-yield.