A Sustainable Order Quantity Model under Uncertain Product Demand

Abstract

The Economic Order Quantity (EOQ) model is one of the most known classical continuous review inventory model based on the trade-off between holding and order costs. In actual logistic systems, transport costs play a key role, and in case of stochastic variability of product demand and/or supply lead time, a safety stock is required. Transport and safety stock costs affect the solution of the lot size problem. Recently, wide attention is being paid to sustainable manufacturing and in particular on negative effects of transport. Transports are the main source of air pollutant emissions in EU and are expected to increase in magnitude in the future. Costs evaluations of transport emissions are defined in EU documents based on Kyoto protocol. When transport environmental costs are considered in the logistic cost function a new lot-sizing problem can be defined. In (Digiesi, Mossa and Mummolo 2012), the Sustainable Order Quantity (SOQ) analytical model is proposed aiming at identifying optimal lot-size and transport means which minimize the logistic and environmental costs in case of a deterministic product demand. In this paper, the authors propose an SOQ model in case of stochastic variability of product demand. Analytical model solutions rely on sustainable (in terms of both logistic and environmental costs) order size, transport means and safety stocks. Results obtained in a full case study from automotive supply chain case study are presented.