A Mass-flow based MILP Formulation for the Inventory Routing with Explicit Energy Consumption

In this paper, we present a new mass-flow based Mixed Integer Linear Programming (MILP) formulation for the Inventory Routing Problem (IRP) with explicit energy consumption. The problem is based on a multiperiod single-vehicle IRP with one depot and several customers. Instead of minimizing the distance or inventory cost, the problem takes energy minimization as an objective. In this formulation, flow variables describing the transported mass serve as a link between the inventory control and the energy estimation. Based on physical laws of motion, a new energy estimation model is proposed using parameters like vehicle speed, average acceleration rate and number of stops. The solution process contains two phases with different objectives: one with inventory and transportation cost minimization as in traditional IRP, the other with energy minimization. Using benchmark instances for inventory routing with parameters for energy estimation, experiments have been conducted. Finally, the results of these two solution phases are compared to analyse the influence of energy consumption to the inventory routing systems.