This paper reviews the literature on lot-sizing problems when production or procurement yields are random. It discusses issues related to cost modeling, yield uncertainty, and performance measures in systems with random yields. The authors present a taxonomy of lot-sizing problems with random yields and provide a brief analysis of existing literature, suggesting future research directions. The review covers both continuous and discrete time models, focusing on analytical models for pure inventory and production/inventory systems. Key topics include the impact of random yields on setup costs, variable unit costs, inventory holding costs, and shortage costs. The paper also explores different methods for modeling yield uncertainty, such as Bernoulli processes, yield rate distributions, and time-to-failure distributions. Additionally, it discusses measures of performance, including cost minimization and robustness, and reviews general papers, continuous time models, and discrete time models. The review highlights the importance of considering yield variability in lot-sizing decisions and the need for more research in this area.This paper reviews the literature on lot-sizing problems when production or procurement yields are random. It discusses issues related to cost modeling, yield uncertainty, and performance measures in systems with random yields. The authors present a taxonomy of lot-sizing problems with random yields and provide a brief analysis of existing literature, suggesting future research directions. The review covers both continuous and discrete time models, focusing on analytical models for pure inventory and production/inventory systems. Key topics include the impact of random yields on setup costs, variable unit costs, inventory holding costs, and shortage costs. The paper also explores different methods for modeling yield uncertainty, such as Bernoulli processes, yield rate distributions, and time-to-failure distributions. Additionally, it discusses measures of performance, including cost minimization and robustness, and reviews general papers, continuous time models, and discrete time models. The review highlights the importance of considering yield variability in lot-sizing decisions and the need for more research in this area.