Pricing in make-to-order firms with a lead time-dependent cost

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.