Scheduling target illuminators in naval battle-group anti-air warfare

The authors schedule a set of illuminators (homing devices) to strike a set of targets using surface-to-air missiles in a naval battle. The task is viewed as a production floor shop scheduling problem of minimizing the total weighted flow time, subject to time-window job availability and machine downtime side constraints. A simple algorithm based on solving assignment problems is developed for the case when all the job processing times are equal and the data are all integer. For the general case of scheduling jobs with unequal processing times, the authors develop two alternate formulations and analyze their relative strengths by comparing their respective linear programming relaxations. They select the better formulation in this comparison and exploit its special structures to develop several effective heuristic algorithms that provide good-quality solutions in real time; this is an essential element for use by the Navy.