Joint pricing and inventory control in a make-to-stock queue with delay-sensitive customers

We consider price and inventory decisions in a make-to-stock system from the perspectives of a profit-maximizing server and a social planner in which customers are delay-sensitive. Under two information cases (i.e. an almost unobservable case and a fully observable case), customers decide whether to purchase the product based on their utility. The utility is closely related to whether the inventory of the product is available, the product’s price, and the waiting time. We first investigate the optimal decision in the almost unobservable case. In this case, the server’s inventory strategy depends on the relationship between the unit holding cost of the product and the unit waiting cost of the customer. Additionally, the system utilization factor also affects the inventory strategy. Then, we analyse the corresponding results in the fully observable case. The results illustrate that, in both cases, profit maximization and welfare maximization lead to different pricing and inventory strategies. Finally, the numerical results show that the optimal price is sensitive to delay information, whereas the optimal stock level is not.