An improved model for large scale inventory routing problem with useful properties

In the previous work, we developed a model for inventory routing problem with split delivery and proposed a hybrid approach based on Lagrangian relaxation to solve the model. Numerical experiments show that the proposed hybrid approach can find a high quality near-optimal solution for the problems with up to 200 customers in a reasonable computation time. In this paper, we further improve and simplify the model by introducing a new parameter - transportation cost that is generated by the vehicle's self-load. We derive some important properties of the optimal solution of the improved model. These properties lay a foundation of the proposed Lagrangian relaxation method. They can be also used as a tool to gauge and improve the quality of solutions.