Benders decomposition for the inventory vehicle routing problem with perishable products and environmental costs

We consider the problem of inventory routing in the context of perishable products and find near-optimal replenishment scheduling and vehicle routes when the objective is to maximize the supplier's profit and minimize the costs due to fuel consumption, inventory holding, and greenhouse gas emissions. Greenhouse gas emissions are calculated as a function of fuel consumed, and fuel consumption levels are accurately calculated as a function of vehicle speed, load and traveled distance. To solve the problem efficiently, we develop an exact method based on Benders decomposition to find high-quality solutions in reasonable time. To enhance the convergence rate of the Benders decomposition algorithm, we present several acceleration strategies, such as addition of valid inequalities to the master problem and warm-up start. The warm-up start acceleration strategy itself is a meta-heuristic based on the greedy random adaptive search procedure (GRASP) and mathematical programming formulations. We present computational results which illustrate the superior performance of the proposed solution methodology in solving large-scale instances with 60 customers and 6 planning periods with 4 vehicles using Benders decomposition. Additionally, we show that utilizing a more comprehensive model to calculate the fuel cost results in fuel savings of 2 to 11% on the tested instances compared to traditional models that assume that the fuel cost is solely a function of the distance traveled during delivery. (C) 2019 Elsevier Ltd. All rights reserved.