Single versus dynamic lead-time quotations in make-to-order systems with delay-averse customers

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, customers make individual decisions to join the system or balk after observing the state of the queue. The decisions of arriving customers result in a symmetric join/balk game. The provider announces a lead-time quotation for each state and a respective balking threshold. There is a fixed entrance fee and compensation rate for the part of a customer’ delay exceeding the quoted lead-time. We also consider the problem from the point of view of a social optimizer who maximizes the total system utility. We analyze the provider’s and social optimizer’s optimization problems and consider two classes of lead-time quotation policies, dynamic and single. We identify the optimal entrance thresholds in each case. Through computational experiments we quantify the effect of risk aversion on the profits and the flexibility the compensation policy offers. We show 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.