This paper reviews the literature on quantitatively-oriented approaches for determining lot sizes when production or procurement yields are random. It discusses issues related to the modeling of costs, yield uncertainty, and performance in systems with random yields. A taxonomy of lot-sizing problems with random yields is presented, providing a framework for the review. The paper also gives a brief analysis of the existing literature and suggests directions for future research. The problem of determining production and procurement quantities and their timing, known as lot-sizing, is central to inventory and production-inventory systems. Much research has focused on solving these problems when demands and production rates are known. However, less research has considered random yields in production or procurement. The goals of this paper are to classify and describe the research on lot-sizing in the presence of random yields. The paper focuses on analytical models for pure inventory and production/inventory systems, and within those areas, on those that consider lot-sizing decisions. Three important issues in modeling systems with random yields are: (1) the modeling of costs affected by random yields, (2) the modeling of yield uncertainty, and (3) measures of performance. The paper discusses each of these issues in turn. Yield uncertainty has been modeled in several different ways in the literature. The simplest model assumes that the creation of good units is a Bernoulli process. Other models involve specifying the distribution of the fraction of good units or the time until a process becomes out of control. These models have different assumptions and applications. The paper also discusses the modeling of costs affected by random yields, including setup costs, variable unit costs, inventory holding costs, and shortage costs. It highlights the importance of considering the timing and nature of inspection processes in both production and procurement situations. The paper concludes with a brief analysis of the existing literature and a discussion of research directions. It suggests that future research should focus on robustness, the impact of yield variability, and the application of these models to real-world scenarios. The paper also discusses the use of different models for continuous and discrete time frameworks, and the implications of random yields on inventory management and production planning.This paper reviews the literature on quantitatively-oriented approaches for determining lot sizes when production or procurement yields are random. It discusses issues related to the modeling of costs, yield uncertainty, and performance in systems with random yields. A taxonomy of lot-sizing problems with random yields is presented, providing a framework for the review. The paper also gives a brief analysis of the existing literature and suggests directions for future research. The problem of determining production and procurement quantities and their timing, known as lot-sizing, is central to inventory and production-inventory systems. Much research has focused on solving these problems when demands and production rates are known. However, less research has considered random yields in production or procurement. The goals of this paper are to classify and describe the research on lot-sizing in the presence of random yields. The paper focuses on analytical models for pure inventory and production/inventory systems, and within those areas, on those that consider lot-sizing decisions. Three important issues in modeling systems with random yields are: (1) the modeling of costs affected by random yields, (2) the modeling of yield uncertainty, and (3) measures of performance. The paper discusses each of these issues in turn. Yield uncertainty has been modeled in several different ways in the literature. The simplest model assumes that the creation of good units is a Bernoulli process. Other models involve specifying the distribution of the fraction of good units or the time until a process becomes out of control. These models have different assumptions and applications. The paper also discusses the modeling of costs affected by random yields, including setup costs, variable unit costs, inventory holding costs, and shortage costs. It highlights the importance of considering the timing and nature of inspection processes in both production and procurement situations. The paper concludes with a brief analysis of the existing literature and a discussion of research directions. It suggests that future research should focus on robustness, the impact of yield variability, and the application of these models to real-world scenarios. The paper also discusses the use of different models for continuous and discrete time frameworks, and the implications of random yields on inventory management and production planning.