  One of the major challenges in the coordination of large, open,
collaborative, and commercial vehicle fleets is dynamic task allocation.
Self-concerned individually rational vehicle drivers have both local and global
objectives, which require coordination using some fair and efficient task
allocation method. In this paper, we review the literature on scalable and
dynamic task allocation focusing on deterministic and dynamic two-dimensional
linear assignment problems. We focus on multiagent system representation of
open vehicle fleets where dynamically appearing vehicles are represented by
software agents that should be allocated to a set of dynamically appearing
tasks. We give a comparison and critical analysis of recent research results
focusing on centralized, distributed, and decentralized solution approaches.
Moreover, we propose mathematical models for dynamic versions of the following
assignment problems well known in combinatorial optimization: the assignment
problem, bottleneck assignment problem, fair matching problem, dynamic minimum
deviation assignment problem, $\sum_{k}$-assignment problem, the semiassignment
problem, the assignment problem with side constraints, and the assignment
problem while recognizing agent qualification; all while considering the main
aspect of open vehicle fleets: random arrival of tasks and vehicles (agents)
that may become available after assisting previous tasks or by participating in
the fleet at times based on individual interest.
