Planar 3D Assignment For Sensor Resource Allocation

We consider the problem of assigning n
1
targets to be illuminated by n
2
radars over n
3
time slots with n
1
≤ n
2
≤ n
3
, whereby no two radars illuminate the same target in the same time slot, as many targets are illuminated each time as possible, and all radars illuminate all targets over the span of all time slots. The problem is formulated as a planar three-index assignment problem. A branch-and-bound algorithm as well as an approximate Lagrangian relaxation algorithm are presented. The Lagrangian relaxation algorithm can efficiently approximate solutions to very large optimization problems.