  Most large organizations, such as corporations, are hierarchical
organizations. In hierarchical organizations each entity in the organization,
except the root entity, is a sub-part of another entity. In this paper we study
the task assignment problem to the entities of tree-like hierarchical
organizations. The inherent tree structure introduces an interesting and
challenging constraint to the standard assignment problem. When a task is
assigned to an entity in a hierarchical organization, the whole entity,
including its sub-entities, is responsible from the execution of that
particular task. In other words, if an entity has been assigned to a task,
neither its descendants nor its ancestors can be assigned to a task.
Sub-entities cannot be assigned as they have an ancestor already occupied.
Ancestor entities cannot be assigned since one of their sub-entities has
already been employed in an assignment. In the paper, we formally introduce
this new version of the assignment problem called Maximum Weight Tree Matching
($MWTM$), and show its NP-hardness. We also propose an effective heuristic
solution based on an iterative LP-relaxation to it.
