关键词: 多产品库存, 数据驱动, 鲁棒优化, ø, -散度, (s, S)库存策略

Abstract: The robust optimization model for a multi-product joint inventory problem with joint setup cost is established under the uncertain market demand. A series of discrete scenarios with unknown probabilities are used to describe the uncertain market demand and the corresponding robust counterpart model is developed based on min-max criteria. In particular, the optimality of an (s,S) inventory strategy is proved. Furthermore, a data-driven approach based on ø-divergence is used to construct the uncertainty set which the uncertain demand probability belongs to with a certain confidence level when only the historical demand data of the market demand is known. On that basis, to obtain the relevant parameters' values of the (s,S) inventory policy, a robust optimization model of multi-product inventory problem is transformed into a tractable programming by Lagrange dual method. At last, some numerical examples are conducted to analyze the multi-product inventory performances under the Kullback-Leibler divergence, Cressie-Read divergence and different confidence levels. Moreover, the robust inventory performance is also compared with that derived by applying robust inventory strategy to the real distribution. The results show that the proposed data-driven robust optimization approach based on ø-divergence is robust and can effectively restrain the impact of demand uncertainties on the retailer's cost 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 ø-divergence based data-driven robust optimization approach can provide effective support for managers to make inventory policy under demand uncertainties.

Key words: multi-product inventory, data-driven, robust optimization, ø-divergence, inventory policy