Budget-Driven Multiperiod Hub Location: A Robust Time-Series Approach

We study the (un)capacitated multiperiod hub location problem with uncertain periodic demands. With a distributionally robust approach that considers time series, we build a model driven by budgets on periodic costs. In particular, we construct a nested ambiguity set that characterizes uncertain periodic demands via a general multivariate time-series model, and to ensure stable periodic costs, we propose to constrain each expected periodic cost within a budget whereas optimizing the robustness level by maximizing the size of the nested ambiguity set. Statistically, the nested ambiguity set ensures that the model’s solution enjoys finite-sample performance guarantees under certain regularity conditions on the underlying VAR( p ) or VARMA( p , q ) process of the stochastic demand. Operationally, we show that our budget-driven model in the uncapacitated case essentially optimizes a “Sharpe ratio”–type criterion over the worst case among all periods, and we discuss how cost budgets would affect the optimal robustness level. Computationally, the uncapacitated model can be efficiently solved via a bisection search algorithm that solves (in each iteration) a mixed-integer conic program, whereas the capacitated model can be approximated by using decision rules. Finally, numerical experiments demonstrate the attractiveness and competitiveness of our proposed model.