This thesis presents the development of a model for parallel replacement and improvement for a fleet of assets to minimize both the economic costs and greenhouse gas (GHG) emissions where the emissions are limited by cap-and-trade. The firm which owns the assets has the options of using the assets, putting them in inventory, improving them, or salvaging them. Different technological types and their performances have been considered for assets. The firm has the option of purchasing new assets from varying technologies and/or improving its existing assets to a higher-performance type. Moreover, the model considers the possibility of both banking the emission allowances and trading them in the market. The model was later used with data of a fleet of excavators in Ontario, Canada. The use of this model could help emitter firms to simultaneously manage the emissions and costs of their fleet of assets in a jurisdiction regulated by cap-and-trade.I would like to thank my dear friend, Mr. Markus W. Jesswein, as he made the hardships of starting a new life and being far away from family and friends while facing challenges of graduate life, much easier by his valuable company and support. I dedicate this thesis to his sincere friendship.I thank Mr. Christopher Brierly, a wonderful and dedicated teacher, and a great mentor. I thank him for all the things I learned from him and dedicate this thesis to his tireless efforts to help international students achieve their goals. Lastly, I would like to acknowledge the Natural Sciences and Engineering Research Council (NSERC) for continuing to fund quality research generally, and for funding my research dreams, specifically. v