A study of staff scheduling with the aim of maintaining the quality of nursing

1.家务助理人员的排班（1）为了掌握这一排班问题，我们在2004年进行了一项调查。我们向在“东京福利导航”网站上注册的所有2380个家庭帮助组织发送了关于其工作人员安排的问卷。387个组织回答了调查问卷（回收率为17%）。我们根据这一调查结果对“家务助理人员调度”进行了建模，如下所示：当用户要求提供有时间限制的服务时，必须将工作时间有时间窗限制的助手分配到这些服务，以确保提供服务，同时考虑到提供限制，行程时间及路线质素，以及在一个调度期间内“佣工的工作量及每个使用者的佣工平衡”均须考虑在内。(2)我们展示了一个数学规划制定的家庭帮助人员调度问题，并在制定中，介绍了两种类型的下界在特定的一天需要的帮手的数量。然后，我们使用一个简单的启发式算法来计算助手的数量，以确定数量的上限。结合确定界限时所获得的信息的界限是有用的，为每一天安排适当的助手，然后再作出详细的时间表。(3)我们在Microsoft Excel上开发了一个“家务助理人员日程安排支持系统”的原型，该系统可以生成每天的日程表。该算法是简单的，是基于子问题为中心的方法。在此基础上，我们在Microsoft Excel上开发了一个“护士排班支持系统”的原型，该原型采用基于子问题中心法的护士排班算法来解决该问题。

1. Home help staff scheduling(1) In order to grasp this scheduling problem, we conducted a survey in 2004. We sent a Questionnaire about their staff scheduling to all of the 2380 home help organizations registered on "Tokyo Welfare Navigation" website. 387 organizations responded the questionnaire (the collection percentage was 17%). We modeled "home help staff scheduling" based on this survey results, as follows : When services with time constraints are requested by users, helpers with time window constraints for their working hours must be assigned to these services in order to make sure that the services are provided, while considering provision constraints, traveling time and quality of routes as well as "helper's workloads and helper balance for each user" in a scheduling period have to be taken into consideration.(2) We show a mathematical programming formulation of the home help staff scheduling problem, and, in the formulation, introduce two types of lower bounds for the number of helpers needed on a specific day. We then calculate the number of helpers using a simple heuristic algorithm in order to determine the upper bound for the number. Combining the bounds with the information obtained when determining the bounds is shown to be useful for arranging the appropriate helpers for each day before making a detailed schedule.(3) We developed, on Microsoft Excel, a prototype of "home help staff scheduling support system" which can produce a schedule for each day. The algorithm for this is simple and is based on the Subproblem-centric approach.2. Nurse schedulingWe also developed, on Microsoft Excel, a prototype of "nurse scheduling support system" which solves the problem by our nurse scheduling algorithm based on the Subproblem-centric approach.