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Lot sizing is important in production planning. It consists of determining a production plan that meets the orders and other constraints while minimizing the production cost. Here, we consider a Discrete Lot Sizing and Scheduling Problem (DLSP), specifically the Pigment Sequencing Problem (PSP). We have developed a solution that uses Genetic Algorithms to tackle the PSP. Our approach introduces adaptive techniques for each step of the genetic algorithm, including initialization, selection, crossover, and mutation. We conducted a series of experiments to assess the performance of our approach across some multiple trials using publicly available instances of the PSP. Our experimental results demonstrate that Genetic Algorithms are practical and effective approaches for solving DLSP.