Uncapacitated \(p\)-hub location problem with fixed costs and uncertain flows

Hub location problem is an important problem and has many applications in various areas, such as transportation and telecommunication. Since the problem involves long-term strategic decision, the future flows will change with time. However, it is difficult or costly to obtain the data of flows, which implies that it is necessary to consider hub location problems in the absence of data. A commonly used way is to estimate future flows by experts’ subjective information. As a result, this paper presents a new uncapacitated \(p\)-hub location problem, in which the flows are described by uncertain variables. Two uncertain programming models are formulated to respectively minimize the expected cost and the \(\alpha \)-cost with the corresponding constraints. Equivalent forms are given when the information about uncertainty distributions of flows is further provided. A genetic algorithm is designed to solve the proposed models and its effectiveness is illustrated by numerical examples.