Canned tuna is consumed around the world and is popular in Australia as an affordable, convenient and protein-rich food. However, the environmental and social cost of canned tuna can vary depending on where and how the fish is caught, processed and transported. Although Australia has an active tuna fishing industry and export high-value tuna species, most canned tuna consumed domestically is imported. Australia’s last large-scale tuna cannery in Port Lincoln closed in 2010 due to high processing and labour costs and competition from lower-cost overseas production. Recently, few Australian businesses have shown renewed interest in shorter and more traceable canned tuna supply chains. Compared with imported canned tuna, Australian local canned tuna supply chains may offer advantages through lower transport emissions, stronger traceability, local employment creation, and broader social value. This makes canned tuna a useful case for examining how agrifood supply chains can be optimised not only for economic benefits, but also for environmental sustainability and social outcomes. This study develops a linear programming model and applies weighted sum method, using the Australian canned tuna supply chain as a case study, to maximise net profit by integrating economic profit, emissions cost, and social value. The environmental impacts were assessed using a multi-regional input-output framework, while social performance represented through indicators such as employment, local value creation and nutrition contribution. By testing alternative economic, environmental and social weights, the model identifies the trade-offs among profitability, emissions reduction and social value. The results are expected to provide a decision-support framework for evaluating whether shorter and more traceable Australian canned tuna supply chains can become competitive when broader sustainability benefits are considered.