Optimal pricing in a service-inventory system with delay-sensitive customers and lost sales
研究了一个单服务器库存服务系统，顾客对延迟敏感，服务后取走一件库存。分析了顾客在完全不可见和部分可见信息下的最优加入策略，以及服务器如何定价以最大化收入，发现隐藏信息可能更有利可图。
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.