Towards Sustainable Inventory Systems: Multi-Objective Optimisation of Economic Cost and CO 2 Emissions in Multi-Echelon Supply Chains

Effective supply chain planning increasingly requires balancing cost-efficiency with environmental responsibility, particularly as organisations face growing pressure to reduce the carbon footprint of logistics operations. This study develops a mixed-integer linear programming model to optimise inventory and transportation decisions in a multi-echelon distribution network comprising a central warehouse, regional warehouses, and retailers. The model integrates a continuous-review (r,Q) replenishment policy, stochastic demand, safety stock requirements, transportation lead times, and stockout behaviour, enabling a detailed representation of operational dynamics under uncertainty and environmental concerns. Unlike most sustainable inventory models—which typically treat environmental impacts and replenishment control separately or rely on simplified service assumptions—this study provides an integrated framework that jointly embeds (r,Q) policies, stochastic demand, stockouts and distance-based CO 2 metrics within a unified optimisation structure. The model advances prior work by explicitly integrating continuous-review (r,Q) replenishment policies with distance-based CO 2 metrics under stochastic demand, a combination rarely addressed in sustainable multi-echelon inventory models. A multi-objective formulation captures the trade-off between economic performance and CO 2 emissions, allowing the identification of Pareto-efficient strategies that reconcile financial and environmental goals. Reducing emissions by over 90% requires an additional cost of only about 4%, demonstrating that substantial emission reductions can be achieved at relatively low additional cost. The findings offer practical insights for managers seeking to design more sustainable and cost-effective distribution policies, highlighting the value of integrated optimisation approaches in contemporary logistics systems.