The two-echelon production-routing problem

This paper introduces the Two-Echelon Production-Routing Problem. This problem is motivated from the petrochemical industry, enlarging the supply chain integration by taking into account production, inventory, and routing decisions in a two-echelon vendor-managed inventory system. We describe, model, and design a branch-and-cut (B&C) to solve the problem under different inventory policies. We also propose a novel exact algorithm, by employing parallel computing techniques, in order to combine local search procedures within a traditional B&C scheme. We evaluate the performance of our methods through extensive computational experiments, both by comparing the algorithms, the effectiveness of the different inventory policies, and the impact of these policies on the partial costs. We derive many managerial insights based on the results. We also validate our new exact algorithm by solving similar problems from the literature, such as the two-echelon multi-depot inventory-routing (2E-MDIRP) and the classical multi-vehicle production-routing problem (MV-PRP). Computational experiments show that our method is very competitive. Based on 512 experiments for the 2E-MDIRP, our algorithm was able to find 111 new best known solutions (BKS), besides proving 412 optimal solutions, against 298 from the literature. For 336 experiments over small and medium size MV-PRP instances, we proved 242 optimal solutions, 11 more than the exact methods from the literature, besides providing 95 new BKS. Moreover, we were the first to tackle large MV-PRP instances exactly, and in this case, our algorithm provides all BKS for instances up to 50 customers, 20 periods and 5 vehicles, outperforming all meta/matheuristics procedures from the literature.