Proof. When (1 − r) p = v, i.e., rp = p − v, from Eq. (6), we get (p − v + s)F (Q ∗ ) = p − c + s and F (Q ∗ ) = F (Qc∗ ), and the result in Eq. (7) holds. Corollary 1 implies that the classical newsvendor model is a special case of our model, and when the net value of the product on the barter platform is equal to the salvage value, then our model reduces to the classical newsvendor model. Q