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The quantitative analysis of the food system for long-term space missions is a crucial factor for the comparison of different food plans and for the evaluation of the food system as part of the overall mission. Such analysis should include important factors such as nutrition, palatability, diet cycle length, and psychological issues related to food. This paper will give the details of a mathematical model that was developed during the first author's participation as a Summer Faculty Fellow at Johnson Space Center. The model includes nutrition, palatability, diet cycle length, and psychological issues as important components. The model is compatible with the Equivalent System Mass (ESM) metric previously developed as the Advance Life Support (ALS) Research and Technology Metric.