Realistic multi-agent team applications often feature dynamic environments with soft deadlines that penalize late execution of tasks. This puts a premium on quickly allocating tasks to agents. However, when such problems include temporal and spatial constraints that require tasks to be executed sequentially by agents, they are NP-hard, and thus are commonly solved using general and specifically designed incomplete heuristic algorithms. We propose FMC_TA, a novel such incomplete task allocation algorithm that allows tasks to be easily sequenced to yield high-quality solutions. FMC_TA first finds allocations that are fair (envy-free), balancing the load and sharing important tasks among agents, and efficient (Pareto optimal) in a simplified version of the problem. It computes such allocations in polynomial or pseudo-polynomial time (centrally or distributedly, respectively) using a Fisher market with agents as buyers and tasks as goods. It then heuristically schedules the allocations, taking into account inter-agent constraints on shared tasks. We empirically compare our algorithm to state-of-the-art incomplete methods, both centralized and distributed, on law enforcement problems inspired by real police logs. We present a novel formalization of the law enforcement problem, which we use to perform our empirical study. The results show a clear advantage for FMC_TA in total utility and in measures in which law enforcement authorities measure their own performance. Besides problems with realistic properties, the algorithms were compared on synthetic problems in which we increased the size of different elements of the problem to investigate the algorithm’s behavior when the problem scales. The domination of the proposed algorithm was found to be consistent.
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