Effective resource allocation in the agri-food sector is pivotal in reducing environmental impacts and moving towards circular food supply chains. Recent studies highlight the potential of integrating the established life cycle assessment (LCA) with machine learning (ML), a subset of artificial neural networks. This hybrid approach is beneficial not only for evaluating food supply chains but also for optimizing them towards a more sustainable system. However, a crucial step in the optimization process is defining the bounds, or minimum and maximum values, for the variables. Typically, the bounds for optimization variables in these studies are derived from the minimum and maximum values obtained through interviews and questionnaires. A discrepancy in these ranges can influence the final optimization outcomes. To tackle this issue, this study introduces a novel method for determining optimization bounds using the Delphi methodology. An integrated environmental assessment approach combining LCA, multilayer perceptron artificial neural network, Delphi methodology, and genetic algorithm was applied to optimize a pomegranate case study in a food supply chain context. The findings reveal that the proposed approach holds promise for achieving significant reductions in environmental impacts (potential reduction of global warming by 46%) within the investigated case study. The inclusion of the Delphi methodology for variable bound determination adds novelty to the resource allocation optimization process in the agri-food sector. This research contributes to the broader understanding of sustainable practices and offers practical insights for enhancing environmental performance in the agri-food industry.