Abstract In this paper, we study a new Workforce Scheduling and Routing Problem, denoted Multiperiod Workforce Scheduling and Routing Problem with Dependent Tasks. In this problem, customers request services from a company. Each service is composed of dependent tasks, which are executed by teams of varying skills along one or more days. Tasks belonging to a service may be executed by different teams, and customers may be visited more than once a day, as long as precedences are not violated. The objective is to schedule and route teams so that the makespan is minimized, i.e., all services are completed in the minimum number of days. In order to solve this problem, we propose a Mixed-Integer Programming model, a constructive algorithm and heuristic algorithms based on the Ant Colony Optimization (ACO) metaheuristic. The presence of precedence constraints makes it difficult to develop efficient local search algorithms. This motivates the choice of the ACO metaheuristic, which is effective in guiding the construction process towards good solutions. Computational results show that the model is capable of consistently solving problems with up to about 20 customers and 60 tasks. In most cases, the best performing ACO algorithm was able to match the best solution provided by the model in a fraction of its computational time.

中文翻译：

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具有相关任务的多周期劳动力调度和路由问题

摘要 在本文中，我们研究了一个新的劳动力调度和路由问题，称为具有相关任务的多周期劳动力调度和路由问题。在这个问题中，客户向公司请求服务。每项服务都由依赖任务组成，这些任务由不同技能的团队在一天或几天内执行。属于一个服务的任务可以由不同的团队执行，并且只要不违反优先级，客户每天可以访问一次以上。目标是安排和安排团队，以便最小化完工时间，即所有服务在最短的天数内完成。为了解决这个问题，我们提出了混合整数规划模型、构造算法和基于蚁群优化（ACO）元启发式的启发式算法。优先约束的存在使得开发高效的局部搜索算法变得困难。这激发了 ACO 元启发式的选择，它可以有效地引导构建过程走向良好的解决方案。计算结果表明，该模型能够一致地解决多达约 20 个客户和 60 个任务的问题。在大多数情况下，性能最好的 ACO 算法能够在其计算时间的一小部分内匹配模型提供的最佳解决方案。