Iterated local search and simulated annealing algorithms for the inventory routing problem

This paper addresses the inventory routing problem (IRP), which consists in defining the customer visit schedule, the delivery quantities, and the vehicle routing plan to meet the demands of a set of customers over a given time horizon. We consider the variant with a single item, a single supplier, multiple vehicles, and a finite multiperiod planning horizon, minimizing the sum of inventory and travel costs. In addition, we address an alternative objective function that minimizes the logistic ratio, defined as the total travel cost divided by the total quantity delivered to customers. This second objective function, while more realistic in some logistics settings, poses a challenge for integer programming models and exact methods because of its nonlinearity. To our knowledge, no heuristic method has been proposed to address this objective in the IRP variant addressed in this paper. To solve this problem with each of these objective functions, we propose effective metaheuristic algorithms based on iterated local search and simulated annealing. Computational experiments show that these algorithms provide reasonably high-quality solutions in relatively short running times for both objective functions when compared to other methods for well-known instances from the literature. Moreover, the algorithms produce new best solutions for some of these instances.