Food, in the form of fresh produce, meat, fish, and/or dairy, is necessary for maintaining life. In this dissertation, I focus on the modeling and analysis of some of the inherent issues in competitive perishable food supply chain networks. I investigate the impacts of trade policies such as tariffs, quotas, and their combination – tariff-rate quotas, as well as the integration of food quality deterioration into food supply chains. The research is especially timely given the prevalence of trade wars and tariffs in todays global political environment. The work is multidisciplinary with constructs from food science integrated into the economics of supply chain networks. The first part of the dissertation overviews the methodological foundations including game theory, network and optimization theory, and variational inequality theory used for the construction and solution of the supply chain network models. In the second part of the dissertation, I first focus on perfectly competitive problems and develop a unified variational inequality framework for spatial price network equilibrium problems with tariff-rate quotas. The accompanying case study on the dairy industry is based on trade between the United States and France. The computational results reveal that tariff-rate quotas may protect domestic producers from foreign competition, but at the expense of higher demand prices for consumers. This work is based on the paper by Nagurney, Besik, and Dong (2019). I then develop an oligopolistic supply chain network equilibrium model with differentiated products consisting of multiple firms, production sites, and demand markets, in which firms compete on product quantities and also quality. I provide a case study on soybeans, an important agricultural product, and investigate different scenarios. Insights as to firm profits and trade volumes, the average product quality, and consumer welfare, are also delineated. Specifically, I find that, although firms may benefit from the imposition of a quota or tariff, the welfare of consumers in the country imposing the quota or tariff declines. This work is based on the paper by Nagurney, Besik, and Li (2019). In the third part of my dissertation, I demonstrate how to incorporate quality deterioration of fresh produce into perishable supply chain network models. I construct an explicit equation for fresh produce quality deterioration based on time and temperature of different pathways in supply chain networks. I first incorporate this feature into local markets in the form of farmers’ markets, which serve as examples of direct to consumer channels and shorter supply chain networks. I also provide a case study of apples in western Massachusetts, under various scenarios, including production disruptions, due to negative weather conditions, resulting in an increase in apple prices at farmers’ markets, a decrease in quality, and a decrease in profits for the apple orchards. These results can be used to inform food firms, policy makers, and regulators. This work is based on the paper by Besik and Nagurney (2017). Subsequently, I develop a competitive food supply chain network model in which the profit-maximizing producers decide not only as to the volume of fresh produce, but they also decide on the initial quality of fresh produce, with associated costs. I incorporate quality deterioration of the fresh produce explicitly with chemical functions depending on time, temperature, and the initial quality of the food product. I then present a case study on peaches, with supply chain disruptions to reveal valuable insights. I find that the disruptions in production result in higher demand prices, and lower initial quality. This is the first such general supply chain network model constructed to include the initial quality of fresh produce. This part of the dissertation is based on the paper by Nagurney, Besik, and Yu (2018).