Budget-Driven Multi-Period Hub Location: A Robust Time Series Approach

We study the (un)capacitated multi-period hub location problem with uncertain periodic demands. With a distributionally robust approach that considers time series, we build a model that is driven by budgets on periodic costs. In particular, we construct a nested ambiguity set that incorporates a general multivariate time series model for uncertain periodic demands, and to ensure stable periodic cost flows, we propose to constrain each expected periodic cost within a budget while maximizing the robustness level (\textit{i.e.}, the size) of the ambiguity set. Statistically, the proposed ambiguity set ensures the model's solution to enjoy finite-sample performance guarantees under certain regularity conditions on the underlying VAR($p$) or VARMA($p,q$) process of the stochastic demand. Operationally, for the uncapacitated case we show that our budget-driven model essentially optimizes a ``Sharpe Ratio''-type criterion over the worst case among all periods, and we discuss how the 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, while the capacitated model can be well approximated by an extended linear decision rule approach. Numerical experiments demonstrate the attractiveness and competitiveness of our proposed modeling and solution approaches.