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

Jie Hu (), Zhi Chen () and Shuming Wang ()
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Jie Hu: School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China; and School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China
Zhi Chen: Department of Decisions, Operations and Technology, CUHK Business School, The Chinese University of Hong Kong, Hong Kong
Shuming Wang: School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China; and MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation, Beijing 100190, China

Operations Research, 2025, vol. 73, issue 2, 613-631

Abstract: 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.

Keywords: Transportation; hub location; financial budget; time series; robust optimization; Wasserstein distance (search for similar items in EconPapers)
Date: 2025
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