The existing literature on make-to-order firms typically supposes that the unit production cost is a constant. In contrast, in this study, this cost is a variable that depends on the lead time. Under this assumption, we investigate the pricing problem for both a monopoly firm and two competing firms. Specifically, we develop a queueing-game-theoretic model to capture the interaction between customers and the firm’s manager and further solve the pricing problem. The results illustrate that, for a monopoly firm, there exists a service rate threshold, and for two homogeneous firms, there is a unique symmetric equilibrium. However, for two heterogeneous firms, the equilibrium may not exist, and if it does, it may not be unique. In this case, the equilibrium is characterized analytically if it is unique and explored numerically if not. Finally, a specific cost function is adopted to analyse the sensitivity of the optimal decisions. When the firms have this variable cost, compared with those with constant unit production cost, customers’ waiting time might be shorter, and the competition between firms might be fiercer. Also, for these firms, increasing the service rate or decreasing the cost parameter does not always help to increase their market share or profit.

中文翻译：

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与交货时间相关的成本在按订单生产的公司中的定价

现有的关于按订单生产的公司的文献通常假设单位生产成本是一个常数。相比之下，在本研究中，此成本是一个取决于交货时间的变量。在这个假设下，我们研究了一个垄断企业和两个竞争企业的定价问题。具体来说，我们开发了一个排队博弈模型来捕捉客户和公司经理之间的互动，并进一步解决定价问题。结果表明，对于垄断企业，存在服务率阈值，对于两个同质企业，存在唯一对称均衡。然而，对于两个异质的公司，均衡可能不存在，即使存在，也可能不是唯一的。在这种情况下，如果平衡是唯一的，则对其进行分析表征，如果不是，则进行数值探索。最后，采用特定的成本函数来分析最优决策的敏感性。当企业具有这种可变成本时，与单位生产成本不变的企业相比，客户的等待时间可能会更短，企业之间的竞争可能会更加激烈。此外，对于这些公司来说，提高服务率或降低成本参数并不总是有助于增加他们的市场份额或利润。