Commission production contracts with revenue sharing for a capacitated manufacturer and multiple retailers

In this paper, we consider a manufacturer with limited production capacity producing multiple kinds of independent products, such that each kind of product is sold by a distinct retailer who is offered a commission production contract with revenue sharing by the manufacturer. We study the contract in the centralised and decentralised systems respectively. Under certain conditions of price elasticities and cost fractions, we show the uniqueness of optimal revenue share for all products. Moreover, by comparing both systems with same capacity constraint, we find that at least one retailer's price in the centralised system is higher than that of the decentralised system, and the order quantity for that retailer is lower under some conditions. As a consequence, the decentralised system's profit is always higher than the centralised system's profit under that condition. Also, the retailers' optimal prices (resp. order quantities) are increasing (resp. decreasing) in production capacity of the manufacturer, whereas the manufacturer's expected profit is increasing in its production capacity in both systems. Finally, we conduct numerical study to justify our theoretical results, and examine the effect of processing cost on both systems' profits, and the effect of demand uncertainty on the optimal prices and order quantities. [Received 22 May 2018; Accepted 28 October 2019]