Optimal pricing in a service-inventory system with delay-sensitive customers and lost sales

We consider a single-server service-inventory system where customers arrive according to a Poisson process and the service times are independent and exponentially distributed. A customer takes exactly one item from the inventory after service if it is available, or the request is lost. A continuous review policy is adopted to replenish the inventory. Upon two different information levels, i.e. the fully unobservable case and the partially observable case, arriving customers decide whether to join or to balk the system. We investigate the customers' individually optimal and socially optimal strategies, and further consider the optimal pricing issue that maximises the server's revenue. Some numerical experiments are carried out to show that the individually optimal joining probability (or threshold) is not always greater than that of socially optimal one. It is observed that, to maximise the server's revenue, concealing some system information to customers may be more profitable. Conversely, to maximise the social welfare, the customers need more system information. Finally, numerical results in the fully unobservable case illustrate a reasonable phenomenon that the revenue maximum is equal to social optimum in most cases.