A Improved Subgradient Lagrangian Relaxation Algorithm for Solving the Stochastic Demand Inventory Routing Problem

In order to improve the coordination efficiency of vehicle routing problem, a multi-level stochastic demand in ventory routing problem was established in this paper, which minimizes the total cost of the system by determining the relation among inventory of distribution center, fleets, and customer needs. Solving the Lagrangian dual problem by the traditional subgradient Lagrangian relaxation algorithm may easily cause oscillation and then slow down the solving speed. To tackle the problem, an improved subgradient Lagrangian relaxation algorithm was proposed. Compared with the traditional subgradient algorithm , the proposed method is faster and improves the quality of the approximate solution.