Flexible Hub Assignment of Flows for the Air Express Shipment Service Network Design
(2016) ORBEL 30 — Location: Louvain-la-Neuve, Belgium (28.January.2016)
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- Abstract
- The Service Network Design problem arises for carriers that need to determine which routes to operate at the minimal possible cost, offering a high quality service in terms of speed, flexibility and reliability. The express integrators are one of the carriers that face such a problem. They offer overnight, door-to-door delivery of shipments, within regions as large as the US, Europe or the Middle East. Changes in the design of their operative network are expensive and limited to the availability of resources, e.g., airport slots, number of aircrafts, handling capacity of the facilities. As a result, they design networks that repeat the same schedules every day during months. For connecting all the origins with all the destinations, they have three processes. The \textit{pickup process} consolidates the shipments, in stages, by transporting them from the origin customers to ground stations, then to airport facilities called gateways, and then to hubs. The hubs are large airport facilities that perform the \textit{sorting process}, i.e. they receive the shipments ordered by origin and sort them by destination. The \textit{delivery process} deconsolidates the shipments by transporting them from hubs to gateways, to stations, and to the final customer. Typically for both the pickup and delivery processes, the movements are performed with vans between customers and stations, with trucks between stations and gateways, and with aircrafts between gateways and hubs. From all the operative costs, the most important by far are those related with the aircrafts. Thus, it is a critical task for the express companies to design an efficient network of flights that enables the overnight flow of shipments from their origin gateways to their destination gateways. Such task is known as the Air Express Shipment Service Network Design (AESSND). It forms a sub-class of the service network design problem since the express carriers must also consider specific behaviors for the routes and hubs. The routes have four main characteristics. First, they have to respect the windows of times for loading and unloading the shipments at hubs and gateways. Second, they have to observe the curfew and slot constraints imposed by the airports. Third, for each aircraft type, the number of equipments used in the network cannot surpass the number available. Finally, for ensuring the operations repeatability each day, routes must be selected such that each gateway and each hub start and end with the same number of aircrafts, of the same types. For the hubs there are two elements to consider. First, their sorting capacity per unit of time has to be respected. Second, if there is more than one hub within a region, the allocation of shipments to hubs becomes a critical decision, known as the \textit{hub assignment}. When the hub assignment is provided as an input to the AESSND, it is referred as a \textit{fixed hub assignment}. If the hub assignment is an explicit decision of the AESSND, then it is called a \textit{flexible hub assignment}. In this research, we develop an optimization model for addressing the Air Express Shipment Service Network Design problem, for the next day deliveries within a region, with two hubs and flexible hub assignment. We provide a reformulation of this multi-commodity network design problem that improves the LP relaxation and reduces the number of variables and constraints. We also strengthen the LP relaxation with three families of valid inequalities: strong linking inequalities, strong cutset inequalities, and commodity connectivity constraints. Then, our model is tested using extensive numerical experiments to show the value added in terms of efficiency and effectiveness. First, a comparison of our approach to the different formulations in the literature is presented on reduced size instances (20 gateways). Then, the performance of our model is presented for variations of these same instances, were the demand, the sorting capacity, the number of equipments, the distance between hubs, and the number of gateways are varied. Finally, the performance of our model is analyzed on realistic instances in the European region.
- Affiliations
Louvain School of Management Operations and Information
Citations
Quesada Perez, J. M., Lange, J.-C., & Tancrez, J.-S. (2016). Flexible Hub Assignment of Flows for the Air Express Shipment Service Network Design. ORBEL 30, Louvain-la-Neuve, Belgium. https://hdl.handle.net/2078.5/186248