The present study investigates a two-echelon supply chain including a usual retailer and two competing manufacturers. The objective function of our model is the maximization of the whole profit of the supply chain, which consists of the stochastic demand, shortage cost, and holding costs. This paper aims to analyze a single period with two products to define the optimum retail prices and wholesales under different game theory approaches (e.g., Bertrand, cooperation, and Stackelberg competitions) based on Double Interval Grey Numbers (DIGN). The other aim of this paper is to specify the price using the manufacturers and the common retailer and considering the stochastic different channel power structures and demand function. In this paper, it is considered that different power structures of channel members may affect the optimal pricing decisions. In this paper, two pricing policies of manufacturers, eight pricing models and various structures of distribution channel members are utilized. In these pricing models, the impacts of retail substitutability are evaluated on the decisions of the chain members and the equilibrium profits. In this paper, the products are substitutable and the demand is stochastic. In this model, the demand is not certain then, we may have shortages or unsold products. Finally, sensitivity analysis is provided for illustrating the theoretical outcomes established in each case.

中文翻译：

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基于双间隔灰数的可替代产品两级供应链定价模型

本研究调查了一个包括二级零售商和两个竞争制造商的两级供应链。我们模型的目标函数是使供应链的整体利润最大化，其中包括随机需求，短缺成本和持有成本。本文旨在分析两种产品的单一时期，以基于双间隔灰色数字（DIGN）的不同博弈论方法（例如Bertrand，合作和Stackelberg竞争）定义最佳零售价格和批发量。本文的另一个目的是使用制造商和通用零售商并考虑随机不同的渠道权力结构和需求函数来指定价格。本文认为渠道成员的不同权力结构可能会影响最优定价决策。本文利用制造商的两种定价策略，八种定价模型和分销渠道成员的各种结构。在这些定价模型中，评估了零售可替代性对连锁店成员的决策和均衡利润的影响。在本文中，产品是可替代的，需求是随机的。在这种模式下，需求不确定，那么我们可能会出现短缺或未售出的产品。最后，提供敏感性分析以说明每种情况下建立的理论结果。在本文中，产品是可替代的，需求是随机的。在这种模式下，需求不确定，那么我们可能会出现短缺或未售出的产品。最后，提供敏感性分析以说明每种情况下建立的理论结果。在本文中，产品是可替代的，需求是随机的。在这种模式下，需求不确定，那么我们可能会出现短缺或未售出的产品。最后，提供敏感性分析以说明每种情况下建立的理论结果。