Optimal sequential replenishment of ships during combat

A carrier battle group is operating in an area where it is subject to attack by enemy aircraft. It is anticipated that air raids will occur in large waves. The uncertain time between raids is available for the replenishment of supplies. The authors consider the problem of how best to schedule ammunition replenishment during this period. The theory of Gittins indices provides the technical background to the development of a range of models which yield a hierarchy of index-based heuristics for replenishment. One such heuristic is assessed computationally in a more realistic scenario than is explictly allowed for by the models.