This paper presents a novel two-stage distributionally robust optimization model of the two-allocation p-hub median problem with different hub link scales. With the objective of minimizing overall costs of building and operating the hub network, the choices of hub locations and hub link scales are decided in the first stage, while the optimal flows are determined in the second stage once the uncertain demands have been realized. Before establishing the hub network, we just have partial distribution information about the uncertain flow demands, which can be described by a given perturbation set based on the historical information. Due to the ambiguous distributions leading to a computationally intractable model, we reformulate the proposed model into the tractable robust counterpart forms under two types of uncertainty sets (Box[Formula: see text]ellipsoidal perturbation set and Generalized ellipsoidal perturbation set). Finally, to demonstrate the effectiveness and applicability for our model, we conduct a case study for the express network system in the Beijing–Tianjin–Hebei region.
A distributionally robust optimization approach for two-stage facility location problems
