We consider a two-echelon production inventory system with a manufacturer having limited production capacity and a distribution center (DC). There is a positive transportation time between the manufacturer and the DC. Customers gain a value by receiving the product and incur a waiting cost when facing a delay. We assume that customers' waiting cost depends on their degree of impatience with respect to delay, which is captured by a convex waiting cost function. Customers are strategic with respect to joining the system and either place an order or balk from the system upon their arrival depending on their expected waiting time. We study the Stackelberg equilibrium assuming that the DC acts as a Stackelberg leader and customers are the followers. We first obtain the total expected revenue and then provide a heuristic to derive the optimal base-stock levels in the warehouse and the DC as well as the optimal price of the product.

中文翻译：

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拥有战略客户的两级生产库存体系

我们考虑一个具有有限生产能力的制造商和配送中心 (DC) 的两级生产库存系统。制造商和 DC 之间存在正传输时间。客户通过收到产品获得价值，并在面临延迟时产生等待成本。我们假设客户的等待成本取决于他们对延迟的不耐烦程度，这是由凸等待成本函数捕获的。客户在加入系统方面具有战略意义，根据他们的预期等待时间，他们要么下订单，要么在他们到达时拒绝系统。我们研究 Stackelberg 均衡假设 DC 充当 Stackelberg 领导者，客户是追随者。