关键词: 多产品库存；交叉销售；数据驱动；鲁棒优化；支持向量聚类

Abstract: The data-driven robust optimization model for a single-period multi-product inventory problem with cross-selling effect and budget constraint is established under the uncertain market demand. Cross-selling, as an important mutual relationship between items, is rarely introduced into the problem of inventory management. Cross-selling means that when a particular product has been purchased, other related products may also be purchased together due to their unknown interior associations. At the same time, if one of the set of jointly demanded items is out of stock, the sales pattern for the associated items will be altered and demands for the other items in this set may decrease as a result. The key to data-driven robust optimization is the choice of an appropriate uncertainty set which should flexibly adapt to the intrinsic structure of the data, thereby well characterizes the demand probability distributions and ameliorates the suboptimality of solutions. In this study, a support vector clustering (SVC) approach is used to construct the data-driven uncertainty set to which the uncertain demands belong with a certain confidence level. Furthermore, the proposed robust optimization model is transformed into a tractable linear programming model by Lagrange dual method. At last, numerical studies are conducted to compare and analyze the retailer's profit under the SVC-based uncertainty set and the traditional uncertainty sets. Besides, the performance loss caused by the SVC-based data-driven robust optimization method is evaluated, and then the impacts of budget and cross-selling coefficient on the retailer’s profit performance are analyzed. The results show that the SVC-based data-driven robust optimization approach is robust and can effectively restrain the impact of demand uncertainties on the retailer’s profit performance. In particular, although the lack of demand distribution information can incur a certain loss of inventory performance, the loss is very small, which indicates that the proposed SVC-based data-driven robust optimization method can provide effective support for managers to make inventory strategy under demand uncertainties. Some recommendations for performance improvement are proposed. For example, the inventory managers should adjust the regularization parameter appropriately to control the conservatism as well as the complexity of the induced robust optimization problems and should keep a good record of the daily sales data to improve the effectiveness of inventory decisions.

Key words: multi-product inventory; cross selling; data-driven; robust optimization; support vector clustering