The Economic Lot Scheduling Problem (ELSP) is a pivotal challenge in the field of manufacturing, characterized by the quest for optimal batch sizes to produce multiple products efficiently on a single machine. This problem entails the development of diverse strategies, encompassing independent solutions, adjustments to production parameters, setup times, and responses to varying demand characteristics. Central to the lot scheduling and sizing decisions is the critical trade-off between inventory holding costs and setup costs. This thesis embarks on an extensive journey through the historical evolution of lot sizing models, tracing its roots from the foundational Economic Order Quantity (EOQ) model introduced by Ford W.