Task Assignment in Tree-Like Hierarchical Structures

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.