  We develop a model for lead-time quotation in a Markovian make-to-order
production or service system with strategic customers who exhibit risk
aversion. Based on a CARA utility function of their net benefit, customers make
individual decisions to join the system or balk by observing the state of the
queue. The decisions of arriving customers result in a symmetric join/balk
game. Regarding the firm's strategy, the provider announces a lead-time
quotation for each state and a respective balking threshold. There is also a
fixed entrance fee and compensation rate for the part of a customer' delay
exceeding the quoted lead-time. Moreover, we consider the problem from the
point of view of a social optimizer who maximizes the total net benefit of the
system.
  We analyze the provider's and social optimizer's maximization problems and we
consider two cases regarding the class of lead-time quotation policies, i.e.,
dynamic and single. We identify the optimal entrance thresholds in each case.
Finally, through computational experiments we quantify the effect of risk
aversion on the profits and the degree of flexibility that the compensation
policy offers. It is shown that the detrimental effects of risk aversion can be
addressed more efficiently for the provider's problem compared to the social
optimizer's one. Furthermore, the profit loss when setting a single lead-time
quote is generally small compared to the optimal dynamic quotation policy.
