Robust multi-product inventory optimization under support vector clustering-based data-driven demand uncertainty set

A robust multi-product inventory optimization approach is developed with an uncertainty set constructed from the available data using support vector clustering (SVC). The multi-product inventory problem is subject to demand uncertainties in a newsvendor setting with the historical demand data as the only available information. By using SVC, the uncertainty set to which the uncertain demands belong is constructed with a certain confidence in a data-driven approach. The associated robust counterpart model is then developed using the absolute robustness criterion. Through mathematical deduction, the proposed counterpart model is transformed into a tractable linear programming model which can be solved efficiently. The transformed and the original models are proved to be mathematically equivalent. Numerical studies are conducted to illustrate the effectiveness and practicality of the proposed SVC-based data-driven robust optimization approach for dealing with demand uncertainties. The results show that the robust optimization approach under the proposed SVC-based uncertainty set outperforms those under the traditional, i.e., the box and the ellipsoid, uncertainty sets. These results provide evidences that the proposed data-driven robust optimization approach can better hedge against demand uncertainties in multi-product inventory problems.