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

Abstract

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 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 while 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, while the capacitated model can be approximated by using decision rules. Finally, numerical experiments demonstrate the attractiveness and competitiveness of our proposed model.

Keywords: hub location, financial budget, time series, robust optimization, Wasserstein distance.