We devise models and algorithms to estimate the impact of current and future patient demand for examinations on Magnetic Resonance Imaging (MRI) machines at a hospital radiology department. Our work helps improve scheduling decisions and supports MRI machine personnel and equipment planning decisions. Of particular novelty is our use of scheduling algorithms to compute the competing objectives of maximizing examination throughput and patient-magnet utilization. Using our algorithms retrospectively can help (1) assess prior scheduling decisions, (2) identify potential areas of efficiency improvement and (3) identify difficult examination types. Using a year of patient data and several years of MRI utilization data, we construct a simulation model to forecast MRI machine demand under a variety of scenarios. Under our predicted demand model, the throughput calculated by our algorithms acts as an estimate of the overtime MRI time required, and thus, can be used to help predict the impact of different trends in examination demand and to support MRI machine staffing and equipment planning.