Multi-objective Fractional Interval Programming for Sustainable Waste Management

This study presents a novel multi-objective linear fractional interval programming model for sustainable waste management under uncertainty, with a focus on the Melbourne metropolitan region. The model integrates three conflicting objectives: minimizing the cost per recycled ton, minimizing emissions per processed ton, and minimizing the energy-related carbon footprint. In the existing literature, most traditional models rely on fixed decision variables, which often fail to capture the inherent uncertainty present in real-world, data-driven problems. Thus, in this study, all key parameters, including transport costs, recycling efficiencies, emissions, and facility capacities, are represented as interval values to account for parameter variability. The optimal solution allocates waste primarily to residential and green streams, yielding a cost per recycled ton in the range [21.01, 37.44] AUD, emissions per processed ton of [8.88, 20.75] kg CO $$_2$$ , and an energy-related carbon footprint of [4.44, 9.00] kg CO $$_2$$ . All solutions satisfy the prescribed budget and emission caps, demonstrating operational feasibility. The results further indicate that environmental objectives exhibit greater robustness to parameter uncertainty than economic costs, highlighting the effectiveness of the proposed interval-based framework for supporting sustainable municipal waste management decisions.