Joint pricing and inventory decisions for substitutable and perishable products under demand uncertainty

A new data-driven robust optimization approach to multi-item newsboy problems

“…Remark 4. By Proposition 2, it is seen that there exist a number of differences between the classical newsboy model (see Model (32) in Section 5.1) and the proposed data-driven robust optimization model (13) in this paper. For example, when the unit selling price decreases, the optimal order quantity derived from Model (32) decreases, which contradicts the first result in Proposition 2.…”

“…Denote ∆α = α 1 − α. Then, the changes of the two intercepts are 1, the intersection points of l 1 and l 2 is exactly the optimal solution of Model (13), where the horizontal ordinate of the intersection point is the optimal order quantity and its vertical ordinate is the maximal profit. Thus, with regard to impacts of the confidence level on the optimal solution and the maximal profit, we conclude that:…”

“…As done in [7], if both of the shortage loss and the salvage value are not taken into consideration, then x = µ 0 + F −1 KDE (α) solves Model (13). Otherwise, the following inner optimization problem:…”

“…Remark 5. Comparison between the proposed Model ( 13) and the absolute robust optimization model based on an interval demand (see Model (33) in Section 5.1) demonstrates that the optimal order quantity and the maximal profit from either Model (13) or Model (33) have the same monotonicity with respect to the fixed parameters of items (for example, the unit shortage loss). However, in the multiitem situation, we need to use the principal component analysis method to handle the correlation between items such that Model (5) can provide a more realistic and valuable solution than that with assumption of interval demands ( also see Figure 2(a) in Section 5.2).…”

“…Owing to its wide applications, a great number of extended models have been presented under assumption of given demand distribution in the past seven decades [8,19,34,40]. Especially, for the recent research works on the newsboy problems, one can see [13,17,39] and the references therein.…”