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The locomotive assignment problem involves assigning a set of locomotives to each train in a pre-planned train schedule so as to provide sufficient power to pull them from their origins to their destinations. An integrated model that determines the set of active and deadheaded locomotives for each train, light travelling locomotives and train-to-train connections is presented. The model explicitly considers consist-busting and consistency. A Mixed Integer Programming (MIP) formulation of the problem that contains about 92 integer variables and 56 constraints is presented in the study. Three models are discussed for assigning locomotives to wagons and coaches and the results are compared amongst the models themselves and compared to the existing scenario at National Railways of Zimbabwe (NRZ). The models generally improve the number of saved locomotives and number of used locomotives. The Locomotive Assignment Model(LAM) solution obtained showed savings of over 70 locomotives, which translates into savings of over one-hundred thousand dollars weekly.