Two-stage stochastic programming for the inventory routing problem with stochastic demands in fuel delivery

The inventory routing problem (IRP) arises in the joint practices of vendor-managed inventory (VMI) and vehicle routing problem (VRP), aiming to simultaneously optimize the distribution, inventory and vehicle routes. This paper studies the multi-vehicle multi-compartment inventory routing problem with stochastic demands (MCIRPSD) in the context of fuel delivery. The problem with maximum-to-level (ML) replenishment policy is modeled as a two-stage stochastic programming model with the purpose of minimizing the total cost, in which the inventory management and routing decisions are made in the first stage while the corresponding resource actions are implemented in the second stage. An acceleration strategy is incorporated into the exact single-cut Benders decomposition algorithm and its multi-cut version respectively to solve the MCIRPSD on the small instances. Two-phase heuristic approaches based on the single-cut decomposition algorithm and its multi-cut version are developed to deal with the MCIRPSD on the medium and large-scale instances. Comparing the performance of the proposed algorithms with the Gurobi solver within limited time, the average objective value obtained by the proposed algorithm has decreased more than 7.30% for the medium and large instances, which demonstrates the effectiveness of our algorithms. The impacts of the instance features on the results are further analyzed, and some managerial insights are concluded for the manager.