An IRP model to improve the sustainability of cold food supply chains under stochastic demand

There has been limited progress in addressing the demand uncertainty inherent over time and the sustainability impact on food logistics. This paper aims to fill this gap, addresses the sustainability of cold food supply chains, and proposes a mixed-integer programming model to solve a multi-period inventory routing problem (IRP) under non-stationary stochastic demand, route -dependent costs, and environmental concerns. The study investigates the replenishment and routing plans to minimise the total expected cost while producing a minimum amount of CO 2 emission. Due to the uncertainty of demand, we apply the static-dynamic strategy and propose a mathematical model under the ( R, S ) replenishment policy to maintain flexibility in ordering decisions under a pre-determined replenishment schedule. Our numerical experiments suggest that the ( R, S ) policy reduces inventory costs significantly, since it solves the excess inventory issue caused by the higher buffer stock levels due to the pre-determined order quantities in the ( R, Q ) policy. However, the resulting CO 2 emission levels and routing costs remain similar in both models. Due to the reduced inventory costs, the ( R, S ) policy makes a significant improvement on the total cost. Moreover, our numerical experiments show that the difference between the cumulative ending inventory levels for the ( R, Q ) and ( R, S ) policies increasingly grows as the time horizon gets longer, and it results in increasingly larger differences in the total cost values for both policies.