This thesis primarily focuses on investigating existing literature regarding dynamic programming approaches for various equipment replacement problems, with the overarching goal of identifying optimal replacement policies that effectively optimize specified criteria. Through an extensive literature review, the study systematically explores fundamental dynamic programming models, including Bellman's classical model, Wagner's economic life models, and age replacement policies. Additionally, the research extends its scope to dynamic programming methods addressing equipment replacement problems influenced by the stochastic arrival of new technology, considering both single and multiple challengers and drawing insights from Hartman's study. Furthermore, the investigation broadens to encompass capacity scheduling problems, providing a nuanced understanding of the complexities inherent in strategic planning and operational efficiency. By examining a diverse array of equipment replacement models and other relevant models, our goal is to uncover their respective strengths and weaknesses, offering a comprehensive understanding of the landscape surrounding equipment replacement models.

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