  The multi-vehicle covering tour problem with time windows (MCTPTW) aims to
construct a set of maximal coverage routes for a fleet of vehicles that serve
(observe) a secondary set of sites given a fixed time schedule, coverage
requirements, and energy restrictions. The problem is formulated as a
mixed-integer second-order cone programming (MISOCP) model and is an extension
of both the multi-covering tour problem and the vehicle routing problem with
time windows under energy constraints. Further, we study a special case of the
proposed model and develop a labeling algorithm to solve its Lagrangian
relaxation problem, which exploits the combinatorial structure exhibited by an
optimal solution to the Lagrangian relaxation.
