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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 globalobjectives, which require coordination using some fair and efficient taskallocation method. In this paper, we review the literature on scalable anddynamic task allocation focusing on deterministic and dynamic two-dimensionallinear assignment problems. We focus on multiagent system representation ofopen vehicle fleets where dynamically appearing vehicles are represented bysoftware agents that should be allocated to a set of dynamically appearingtasks. We give a comparison and critical analysis of recent research resultsfocusing on centralized, distributed, and decentralized solution approaches.Moreover, we propose mathematical models for dynamic versions of the followingassignment problems well known in combinatorial optimization: the assignmentproblem, bottleneck assignment problem, fair matching problem, dynamic minimumdeviation assignment problem, $\sum_{k}$-assignment problem, the semiassignmentproblem, the assignment problem with side constraints, and the assignmentproblem while recognizing agent qualification; all while considering the mainaspect of open vehicle fleets: random arrival of tasks and vehicles (agents)that may become available after assisting previous tasks or by participating inthe fleet at times based on individual interest.

Decentralizing Coordination in Open Vehicle Fleets for Scalable and Dynamic Task Allocation