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Most large organizations, such as corporations, are hierarchicalorganizations. In hierarchical organizations each entity in the organization,except the root entity, is a sub-part of another entity. In this paper we studythe task assignment problem to the entities of tree-like hierarchicalorganizations. The inherent tree structure introduces an interesting andchallenging constraint to the standard assignment problem. When a task isassigned to an entity in a hierarchical organization, the whole entity,including its sub-entities, is responsible from the execution of thatparticular 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 hasalready been employed in an assignment. In the paper, we formally introducethis new version of the assignment problem called Maximum Weight Tree Matching($MWTM$), and show its NP-hardness. We also propose an effective heuristicsolution based on an iterative LP-relaxation to it.

Task Assignment in Tree-Like Hierarchical Structures