This paper considers a two-echelon channel in which a monopolistic manufacturer supplies a single product to multiple heterogeneous retailers who are in separate markets. The present paper studies the problem of how the manufacturer in a manufacturer-Stackelberg game designs a unified quantity-discount pricing scheme to improve the whole channel's profit as well as each partner's profit. Considered in the paper are two types of unified quantity-discount pricing schemes: the regular quantity-discount pricing scheme and the incremental volume discount pricing scheme. Each of the two types of schemes includes a single pricebreak discount policy and a non-linear quantity discount policy. Optimal solutions are derived and numerical examples presented to illustrate the efficiency of each discount policy.

This paper considers the pricing and quantity decisions of a two-echelon system with a manufacturer who supplies a single product to two competitive retailers. A Stackelberg structure is assumed between two echelons in the two-echelon chain, in which the manufacturer who acts as a leader declares her wholesale price to both retailers and the duopolistic retailers who act as followers set their sale prices and associated order quantities independently under the manufacturer's pricing scheme. The paper analyzes the effects of the duopolistic retailers' different competitive behaviors-Cournot, Collusion and Stackelberg-on the optimal decisions of the manufacturer and the duopolistic retailers themselves. The results indicate that: (i) among the three scenarios, the duopolistic retailers' action in collusion makes the retailers charge the highest sale price while the duopolistic retailers' Cournot behavior results in the lowest pricing of the retailers; (ii) the more drastic the duopolistic retail market competes, the higher the manufacturer's and the duopolistic retailers' pricing should be; and (iii) the total profit of the duopolistic retailers who act as the followers will exceed the more powerful manufacturer's profit as long as the degree of dissimilarity between the duopolistic retailers' market demands is large enough.

In the integrated production-shipment models for the single vendor-single-buyer system presented hitherto, the demand rate of items is treated as a constant. However, many researchers have observed that the presence of more quantities of the same product tends to attract more customers. This suggests that the demand rate should depend on the stock level. This paper presents a single-vendor-single-buyer production-shipment model with the stock dependent demand rate, based on the demand rate linearly depending upon the stock level at any instant of time.