No abstract

We study a robust model of the multi-armed bandit (MAB) problem in which the transition probabilities are ambiguous and belong to subsets of the probability simplex. We first show that for each arm there exists a robust counterpart of the Gittins index that is the solution to a robust optimal stopping-time problem and can be computed effectively with an equivalent restart problem. We then characterize the optimal policy of the robust MAB as a project-by-project retirement policy but we show that arms become dependent so the policy based on the robust Gittins index is not optimal. For a project selection problem, we show that the robust Gittins index policy is near optimal but its implementation requires more computational effort than solving a non-robust MAB problem. Hence, we propose a Lagrangian index policy that requires the same computational effort as evaluating the indices of a non-robust MAB and is within 1% of the optimum in the robust project selection problem.

For many consumer-intensive (B2C) services, delivering memorable customer experiences is a source of competitive advantage. Yet, there are few guidelines available for designing service encounters with a focus on customer satisfaction. In this paper, we show how experiential services should be sequenced and timed to maximize satisfaction of customers who are subject to memory decay and acclimation. We find that memory decay favors positioning the highest service level near the end, whereas acclimation favors maximizing the gradient of service level. Together, they maximize the gradient of service level near the end. Although memory decay and acclimation lead to the same design individually, they can act as opposing forces when considered jointly. Overall, our analysis suggests that short experiences should have activities scheduled as a crescendo and duration allocated primarily to the activities with the highest service levels, whereas long experiences should have activities scheduled in a U-shaped fashion and duration allocated primarily to activities with the lowest service level so as to ensure a steep gradient at the end.

We study a robust model of the multi-armed bandit (MAB) problem in which the transition probabilities are ambiguous and belong to subsets of the probability simplex. We first show that for each arm there exists a robust counterpart of the Gittins index that is the solution to a robust optimal stopping-time problem and can be computed effectively with an equivalent restart problem. We then characterize the optimal policy of the robust MAB as a project-by-project retirement policy but we show that arms become dependent so the policy based on the robust Gittins index is not optimal. For a project selection problem, we show that the robust Gittins index policy is near optimal but its implementation requires more computational effort than solving a non-robust MAB problem. Hence, we propose a Lagrangian index policy that requires the same computational effort as evaluating the indices of a non-robust MAB and is within 1% of the optimum in the robust project selection problem.

No abstract