Task assignment in tree-like hierarchical structures

Cem Evrendilek (), Ismail Hakki Toroslu () and Seyedsasan Hashemikhabir ()
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Cem Evrendilek: Izmir University of Economics
Ismail Hakki Toroslu: Middle East Technical University
Seyedsasan Hashemikhabir: Middle East Technical University

Journal of Combinatorial Optimization, 2017, vol. 34, issue 2, No 23, 655 pages

Abstract: Abstract Many large organizations, such as corporations, are hierarchical by nature. In hierarchical organizations, each entity, except the root, is a sub-part of another entity. In this paper, we study the task assignment problem to the entities of a tree-like hierarchical organization. The inherent tree structure introduces an interesting and challenging constraint to the standard assignment problem. Given a tree rooted at a designated node, a set of tasks, and a real-valued function denoting the weight of assigning a node to a task, the Maximum Weight Tree Matching (MWTM) problem aims at finding a maximum weight matching in such a way that no tasks are left unassigned, and none of the ancestors of an already assigned node is allowed to engage in an assignment. When a task is assigned to an entity in a hierarchical organization, the whole entity including its children becomes 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 any task. In the paper, we formally introduce MWTM, and prove its NP-hardness. We also propose and experimentally validate an effective heuristic solution based on iterative rounding of a linear programming relaxation for MWTM.

Keywords: Task assignment; Integer programming; Linear programming relaxation; Heuristics; NP-hardness (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0097-6

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