Robust Strategic Route Planning in Logistics

Abstract

Listen

Translate article

Logistics is a cost sensitive industry with large and fast growing routing networks. In this paper we devise a computational, robust optimization method for the strategic routing decisions of a logistics’ customer, i.e., a company that uses the services of different freight forwarders to meet its transportation demands between several sources, sinks, and hubs. The costs of such transports are determined by tariff systems that typically show economies of scale and reward the consolidation of goods that complement each other in properties relevant for transport, such as weight and volume. In the strategic planning phase, routes and hubs have to be chosen roughly one year ahead, in particular, before the actual demand is known. Our method anticipates the fluctuation of demands by minimizing the worst-case cost over a restricted scenario set. The combination of a realistic cost function, a robust modeling of uncertainty, and large-scale networks leads to highly intractable models. We show that the corresponding adversary problem is NP-hard. To nevertheless find solutions for real instances with very good worst-case cost we derive a carefully relaxed and simplified mixed-integer linear program that solves well for large instances because of its powerful linear programming relaxation. We test the method for real-world instances. The results show that robust optimization can significantly reduce worst-case cost. Furthermore, we derive from our method two heuristic techniques to solve even larger networks and report on the corresponding computational results. Neglecting the typical uncertainty about demand values can cause significant cost in logistic routing problems. This paper provides for a practical method to avoid such costs.