Manufacturer-buyer coordination for newsvendor-type-products with two ordering opportunities and partial backorders

In a recent paper [Weng, Z.K., 2004. Coordinating order quantities between the manufacturer and the buyer: A generalized newsvendor model. European Journal of Operational Research 156, 148-161], a newsvendor-type coordination model was developed for a single-manufacturer single-buyer channel with two ordering opportunities. This paper further extends the model to the case where the excess demand after the first order is partially backlogged and both parties share the manufacturing setup cost of the second order (if happened). We show that the decentralized system would perform best if the manufacturer covers utterly the second production setup cost, which is opposite to that obtained in Weng (2004). Another extension in the present paper is that in the centralized system, the second order decision is made by the buyer based on the channel's benefit rather than based on the buyer's benefit as in Weng (2004). It is proved that the expected profit of the system in our paper is always larger than that in Weng (2004). In order to maximize the expected profit of the channel, two coordinated policies are proposed to achieve perfect coordination: a two-part-tariff policy for the special case that the buyer pays all the manufacturing setup cost, and a revised revenue-sharing contract for the case that two parties share the manufacturing setup cost.