  Robots performing tasks in warehouses provide the first example of
wide-spread adoption of autonomous vehicles in transportation and logistics.
The efficiency of these operations, which can vary widely in practice, are a
key factor in the success of supply chains. In this work we consider the
problem of coordinating a fleet of robots performing picking operations in a
warehouse so as to maximize the net profit achieved within a time period while
respecting problem- and robot-specific constraints. We formulate the problem as
a weighted set packing problem where the elements in consideration are items on
the warehouse floor that can be picked up and delivered within specified time
windows. We enforce the constraint that robots must not collide, that each item
is picked up and delivered by at most one robot, and that the number of robots
active at any time does not exceed the total number available. Since the set of
routes is exponential in the size of the input, we attack optimization of the
resulting integer linear program using column generation, where pricing amounts
to solving an elementary resource-constrained shortest-path problem. We propose
an efficient optimization scheme that avoids consideration of every increment
within the time windows. We also propose a heuristic pricing algorithm that can
efficiently solve the pricing subproblem. While this itself is an important
problem, the insights gained from solving these problems effectively can lead
to new advances in other time-widow constrained vehicle routing problems.
