Online algorithms for the multi-vehicle inventory-routing problem with real-time demands

The increasing availability of sophisticated information and communication technology has stimulated new research within the distribution logistics area in the last few decades. Real-time information is crucial to ensure not only the competitiveness of a company but also its survival in the e-commerce era. Companies try to offer delivery to their customers within a few hours of receiving a request. In addition, real-time information can be exploited in systems that operate under emergencies, where response time is critical. We model and solve a multi-vehicle inventory-routing problem in which new service requests are revealed dynamically over time, in real-time or online. For this problem, we propose a class of online algorithms based on iteratively solving integer programming models. These models are solved through a tailored branch-and-cut method, in which several families of valid inequalities are separated and dynamically introduced in the model or through a matheuristic to speed up the solution process. We carry out a competitive analysis that allows us to prove the competitive ratio of the online algorithms we propose and, therefore, to evaluate their performance with respect to the optimal solution of the offline problem, in the worst case. An extensive computational experience on benchmark instances shows that these algorithms are also effective on average and require short computational time when the matheuristic is applied to solve the integer programming models. Additional tests on large real-world instances indicate that the proposed solution methods achieve performance that remains reasonable for the size of these instances.