Optimal Policy for Probabilistic Selling with Three-Way Revenue Sharing Contract under the Perspective of Sustainable Supply Chain

Probabilistic selling (PS) is widely used in the travel industry and marketing practices; how to design a win-win contract using PS in multiple participants’ supply chain to achieve sustainable development has been a worthy concerned issue in the green supply chain development in China. To end this, we consider a three-players supply chain involving two firms and a common retailer in which the firms sell their transparent products via a dual channel, while the retailer sells probabilistic goods by a direct channel. First, the three players’ demand functions are derived using both a Hotelling model and taking account of consumers’ price reference effects. Second, we construct a probabilistic selling model for both decentralized and centralized supply chain systems. The optimal policies for the decentralized system are determined by employing Stackelberg sequential games and an analytical approach. Third, we propose a new three-way revenue sharing contract to deal with channel conflict. Furthermore, we determine the conditions under which the dual-channel supply chain can be coordinated to achieve a win–win situation for all participants. The results indicate that the retailer adopts probabilistic selling depending upon the relative values of the two manufacturers’ production costs in the three-way revenue sharing contract. More interestingly, PS not only can improve the supply chain’s efficiency, but also can coordinate the dual-channel supply chain to achieve a win-win situation for all participants. Finally, we present a numerical analysis to verify our results and a sensitivity analysis of the parameters involved.