Carbon-aware hybrid replenishment under uncertainty

Abstract

Inventory policies influence not only holding and shortage costs but also the transport emissions associated with replenishment frequency, shipment size, and the use of expedited delivery. Existing carbon-aware inventory models typically represent emissions as a cost term or regulatory constraint, while adaptive inventory approaches mainly respond to changes in demand and lead time. This study proposes a carbon-aware adaptive replenishment policy that extends a conventional adaptive (s, S) model by incorporating the anticipated environmental consequence of delayed ordering. Three policies—a static (s, S) policy, a conventional adaptive policy, and the proposed carbon-aware policy—were evaluated through Monte Carlo simulation under stable conditions, demand uncertainty, and combined demand and lead-time uncertainty. The results show that the additional value of carbon-aware adjustment is negligible in a stable environment but becomes more visible as uncertainty increases. Under combined uncertainty, the proposed policy reduced total logistics cost by 3.61%, expedited shipments by 28.48%, and transport-related emissions by 6.73% relative to the static benchmark, while improving the fill rate by 1.69 percentage points. These benefits were accompanied by a 15.97% increase in average inventory. Compared with the conventional adaptive policy, the additional gains were smaller, indicating that adaptive parameter updating remains the primary source of improvement. Carbon awareness therefore acts as a targeted refinement that is most useful when emergency replenishment is frequent and substantially more emission-intensive than regular supply.