Hub-and-spoke network design problem under uncertainty considering financial and service issues: A two-phase approach

This paper proposes a bi-objective hub-and-spoke (H&S) network design problem with type-2 (T2) fuzzy transportation cost and travel time described by parametric secondary possibility distributions, which are obtained using three types of mean value (MV) reduction methods. The considered objectives jointly minimize the generalized expectation of the total transportation costs and the maximum travel time requirement in terms of generalized value-at-risk (VaR). To solve the fuzzy bi-objective H&S network design problem, we develop a two-phase approach, where in the first phase we convert the proposed model into its equivalent parametric mixed-integer programming problems by applying an equivalent transformation method. This is followed by the second phase using a fuzzy linear programming approach implemented with an augmented max-min operator to obtain a non-dominated solution that has an equal satisfactory degree on both objectives. Finally, a case study based on the Civil Aeronautics Board (CAB) data set is conducted to demonstrate the effectiveness of the proposed model and solution approach.