Sustainable supply chain management is a topical area which is continuing to grow and evolve. Within supply chains, downstream distribution from producers to customers plays a significant role in the environmental performance of production supply chains. With consumer consciousness growing in the area of sustainable food supply, food distribution needs to embrace and adapt to improve its environmental performance, while still remaining economically competitive. With a particular focus on the dairy industry, a robust solution approach is presented for the design of a capacitated distribution network for a two-layer supply chain involved in the distribution of milk in Ireland. In particular the green multi-objective optimisation model minimises CO2 emissions from transportation and total costs in the distribution chain. These distribution channels are analysed to ensure the non-dominated solutions are distributed along the Pareto fronts. A multi-attribute decision-making approach, TOPSIS, has been used to rank the realistic feasible transportation routes resulting from the trade-offs between total costs and CO2 emissions. The refined realistic solution space allows the decision-makers to geographically locate the sustainable transportation routes. In addition to geographical mapping the decision maker is also presented with a number of alternative analysed scenarios which forcibly open closed distribution routes to build resiliency into the solution approach. In terms of model performance, three separate GA based optimisers have been evaluated and reported upon. In the case presented NSGA-II was found to outperform its counterparts of MOGA-II and HYBRID.