Multi-Period Hub Location with Time Series

This chapter discusses the application of distributionally robust optimization to an uncapacitated multi-period hub location. Uncertain periodic demand is assumed. A nested ambiguity set is constructed, incorporating a general multivariate time series model for uncertain periodic demands. To ensure stable cost flows, each expected periodic cost is limited by a budget while maximizing the robustness level in terms of the size of the ambiguity set. It is shown that the budget-driven uncapacitated model constructed optimizes a “Sharpe Ratio” type criterion over the worst case among all periods. The influence of the budgets on the optimal robustness level is also discussed. To efficiently solve the resulting model, a bisection search algorithm is presented that solves (in each iteration) a mixed-integer conic program. Numerical experiments support the attractiveness of the model.