Gittins-index heuristics for research planning

The classical work of Gittins, which resulted in the celebrated index result, had applications to research planning as an important part of its motivation. However, research planning problems often have features that are not accommodated within Gittins’s original framework. These include precedence constraints on the task set, influence between tasks, stopping or investment options and routes to success in which some tasks do not feature. The authors consider three classes of Markovian decision models for research planning, each of which has all of these features. Gittins-index heuristics are proposed and are assessed both analytically and computationally. They perform impressively.