Optimal pricing and capacity management in service systems with delay-sensitive mixed-risk customers

In service systems with delay-sensitive customers, customer decisions to join the queue or balk influence demand, impacting service provider profits. Studies show that customers can be risk-seeking for short waits and risk-averse when waits exceed expectations. Prior research on this mixed-risk attitude is limited, focussing on optimal pricing policies from a social welfare perspective. This study fills this gap by investigating the impact of this behaviour on customer joining strategies and the provider's pricing and capacity policies. We analyse a profit-maximising firm managing an unobservable queue where customers display mixed-risk behaviour towards delay parameterised by a risk-switching point and a degree of risk propensity. Customers join or balk based on expected utility, while the firm determines the service price and rate to maximise expected profit. We derive optimal strategies for both customers and the firm under scenarios with concave or convex capacity costs. Computational experiments show that optimal pricing, capacity, and profit peak at intermediate risk-switching points. For smaller points, optimal price and capacity rise with the customers' degree of risk propensity, while larger points have minimal impact. Numerical exploration emphasises the significance of capacity cost and the effectiveness of leveraging price over controlling capacity for maximising firm profitability.