The capacitated newsboy problem with revenue sharing

In this paper we consider a single inventory (newsboy) problem in which the vendor has a limited amount of funds to purchase items to sell. We assume that the manufacturer will either sell the items to the vendor outright or offer the items to the vendor on a revenue sharing (consignment) basis. In the latter case, that amount of money the vendor pays per unit is less than if the items are purchased from the vendor, but the vendor must share some of the revenue with the manufacturer. The purpose of our analysis is to investigate under what circumstances, it would pay for the vendor to only purchase the items from the manufacturer, only take the items on consignment from the manufacturer, or both purchase and take consignment shipments form the manufacturer.