Police officers conduct routine patrols and perform tasks in response to reported incidents. The importance of each task varies from low (e.g. noise complaint) to high (e.g. murder). The workload associated with each task, indicating the amount of work to be completed for the incident to be processed, may vary as well. Multiple officers with heterogeneous skills may work together on important tasks to share the workload and improve response time. To deal with the underlying law enforcement problem (LEP^H), one needs to allocate police officers to dynamic tasks whose locations, arrival times, and importance levels are unknown a priori. Addressing this challenge and inspired by real police logs, this research aims to solve the LEP^H problem by using and comparing three methods: Fisher market-based FMC_TA^H+, swarm intelligence HDBA, and Simulated Annealing SA algorithms. FMC_TA^H+ is implemented, using agents as buyers and tasks as goods, to compute fair allocations (i.e. envy-free), and efficient (i.e. Pareto-optimal) in a polynomial or pseudo-polynomial time. FMC_TA^H+ allocations are heuristically scheduled, considering inter-agent constraints on shared tasks. HDBA, a probabilistic swarm intelligence algorithm inspired by the emergent behavior of social bees, was previously implemented to allocate agents to tasks based on agent performance, task priorities, and distances between agents and task-execution locations. SA is a meta-heuristic for approximating the global optimums in large optimization problems. The three methods were compared in this study for five different performance measures that are commonly used by law enforcement authorities. The results indicate an advantage for FMC_TA^H+ both in total utility and in the average arrival time to tasks. Also, compared respectively to HDBA and SA, FMC_TA^H+ leads to 34% and 32% higher team utility in the highest shift workload.

警务人员进行例行巡逻，并根据报告的事件执行任务。每个任务的重要性从低（例如噪音投诉）到高（例如谋杀）不等。与每个任务相关联的工作负载（指示要处理的事件要完成的工作量）也可能有所不同。具有不同技能的多个人员可能会共同完成重要任务，以分担工作量并缩短响应时间。为了解决潜在的执法问题（LEP ^H），需要将警官分配给动态任务，这些任务的位置，到达时间和重要性级别事先未知。为应对这一挑战并受到真实警察记录的启发，本研究旨在解决LEP通过使用和比较三种方法来解决^H问题：基于Fisher市场的FMC_TA ^{H +}，群智能HDBA和模拟退火SA算法。FMC_TA ^{H +}是通过使用代理作为买方和将任务作为商品来实现的，以在多项式或伪多项式时间内计算公平分配（即无羡慕）和有效（即Pareto最优）。FMC_TA ^{H +}分配是通过启发式计划的，同时考虑到共享任务的代理间约束。HDBA，是由社交蜜蜂的新兴行为启发而来的一种概率群智能算法，以前已被实现为根据座席性能，任务优先级以及座席与任务执行位置之间的距离将座席分配给任务。SA是一种元启发法，用于在大型优化问题中逼近全局最优值。在本研究中，对三种方法进行了比较，以比较执法机构通常使用的五种不同的绩效指标。结果表明，FMC_TA ^{H +}在总实用性和任务平均到达时间上均具有优势。另外，分别与HDBA和SA相比，FMC_TA ^{H +} 在最高班次工作量下，团队效用分别提高了34％和32％。