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Combining Fairness and Efficiency in Dynamic Task Allocation with Spatial and Temporal Constraints

Realistic multiagent team applications often feature distributed dynamic environments with soft deadlines that penalize late execution of tasks. This puts a premium on quickly allocating tasks to agents, but finding the optimal allocation is NP-hard due to temporal and spatial constraints that require tasks to be executed sequentially by agents. We propose a novel task allocation algorithm that allows tasks to be easily sequenced to yield high quality solutions by finding allocations that are fair (envyfree), balancing the load and sharing important tasks between agents, and efficient (Pareto optimal). We compute such allocations in polynomial time using a Fisher market with agents as buyers and tasks as goods, then sequence the allocations by maximizing utility at each step. We empirically compare our algorithm to two state-of-the-art incomplete methods on synthetic problems and on realistic law enforcement problems inspired by real police logs. The results show a clear advantage for our algorithm in measures commonly used by law enforcement authorities.