This paper explores the Price of Anarchy in a single-server queueing-inventory system with delay-sensitive customers. The arrival follows the Poisson process, and the service time follows an exponential distribution. Upon arrival, the customers strategically decide whether to join or to balk the system based on the available information. Our study delves into equilibrium and socially optimal behaviours in fully unobservable and partially observable contexts. The Price of Anarchy measures the system’s inefficiency resulting from customers’ selfish behaviour, providing insights into decentralized system efficiency. We derive this inefficiency for these scenarios to highlight how customers’ self-interested actions affect the system’s overall performance, supported by a detailed numerical analysis. This research provides deeper insight into the dynamics of customer behaviour and their effects on system optimization.