In this paper, we construct a competitive food supply chain network model in which the profit-maximizing producers decide not only as to the volume of fresh produce produced and distributed using various supply chain network pathways, but they also decide, with the associated costs, on the initial quality of the fresh produce. Consumers, in turn, respond to the various producers' product outputs through the prices that they are willing to pay, given also the average quality associated with each producer or brand at the retail outlets. The quality of the fresh produce is captured through explicit formulae that incorporate time, temperature, and other link characteristics with links associated with processing, shipment, storage, etc. Capacities on links are also incorporated as well as upper bounds on the initial product quality of the firms at their production/harvesting sites. The governing concept of the competitive supply chain network model is that of Nash Equilibrium, for which alternative variational inequality formulations are derived, along with existence results. An algorithmic procedure, which can be interpreted as a discrete-time tatonnement process, is then described and applied to compute the equilibrium produce flow patterns and accompanying link Lagrange multipliers in a realistic case study, focusing on peaches, which includes disruptions. Food, and especially fresh produce, in the form of fruits and vegetables, is essential to the well-being and health of consumers. In this paper we construct a supply chain network game theory model which captures competition among food firms, along with the quality associated with their fresh produce products as they move along the pathways from production/harvesting, through storage and distribution, to the retail outlets. The food firms are profit-maximizers whereas the consumers reflect their preferences for the fresh produce by taking quality into consideration. Qualitative properties of the model are established and illustrative examples provide along with a case study on peaches, under both status quo and disruption scenarios. This is the first such general supply chain network model constructed, analyzed, and solved and has great relevance to this important industry.
