Economic and environmental considerations in a stochastic inventory control model with order splitting under different delivery schedules among suppliers

This study analyzes an integrated inventory control and delivery scheduling problem in a stochastic demand environment with economic and environmental considerations. In particular, we examine a bi-objective continuous review inventory control model with order splitting among multiple suppliers, where both expected costs and carbon emissions per unit time are minimized. For this problem, two different delivery scheduling policies are considered for the split orders: sequential splitting and sequential delivery. First, we formulate the problem under each delivery scheduling policy as bi-objective mixed-integer nonlinear models. Then, an adaptive ϵ-constraint algorithm and an evolutionary search algorithm are proposed to approximate the Pareto front of these models. A numerical study is conducted to compare the two approximation algorithms. Another numerical study demonstrates the effects of the demand variance on the expected costs and carbon emissions per unit time under each delivery scheduling policy. Finally, examples are presented to show how the tools provided in this study can be used to compare different scheduling policies. Our results show that the delivery policy and supplier selection both have strong effects on the economic and environmental performance, and also that a good approximation of the Pareto front is crucial to accurately compare delivery scheduling policies.