Economic and environmental considerations in a continuous review inventory control system with integrated transportation decisions

•A sustainable continuous review inventory control system with transportation decisions is analyzed.•A bi-objective (Q,R)(Q,R) model is formulated for each transportation mode.•A method to approximate the Pareto Front of each model is proposed.•Sensitivity analyses on demand variance, lead time, and sustainability are provided.•Examples are discussed to illustrate the practical use of the models.

Sustainability throughout supply chains is gaining more importance and re-planning inventory operations can help companies curb emissions. In this study, we present two bi-objective integrated continuous review inventory control and transportation models with less-than-truckload and truckload carriers. Solution methods to approximate the Pareto Frontiers are proposed. Numerical studies illustrate the effects of demand variance and lead time on expected costs and carbon emissions as well as the changes in expected costs and carbon emissions due to sustainability considerations. Sample examples illustrate the use of the methods to compare different carriers in terms of not only economic but also environmental considerations.