Stackelberg-game solution of seller-buyer supply chain with random uncertainty

Under the assumption that the product demand was composed of the dominant theoretical demand and the non-dominant random demand, this paper investigated the problem of Stackelberg-game of a single-seller single-buyer supply chain. Based on the criterion to maximize the expected individual profits, we got the explicit expressions of Stackelberg-game´s optimal solutions via assuming the non-dominant random demand is uniformly distributed. Moreover, the optimal solutions of the centralized control and the Stackelberg-game without random disturbance were also given, which served as a benchmark for the random disturbance situation. The results show that the supply chain performs best under the centralized control. Compared with the Stackelberg game having deterministic demand-response function, the optimal wholesale price is higher but the optimal retail price is lower in random disturbance situation. On the other hand, as the fluctuation extent of random demand increases, the expected profits of the supply chain and the buyer become gradually less, however, the expected profit of the seller becomes larger. The given numerical results further illustrate the above results.