Bounds for staff size in home help staff scheduling

Home help organizations provide services at respective users' homes at a time that is convenient for the user. Helpers with time window constraints for their working hours must be assigned to these services to ensure that the services are provided. Producing adequate schedules usually takes the schedulers a considerable amount of time due to many types of constraints and requirements. It is difficult even to estimate the number of helpers needed. In this paper, we introduce a mathematical programming formulation of the home help staff scheduling problem, and propose two types of lower bounds for the number of helpers needed on a specific day. We then also calculate the number of helpers using a simple heuristic algorithm in order to determine the upper bound. Combining the bounds with the information obtained when determining the bounds was shown to be useful for arranging the appropriate helpers for each day before making a detailed schedule, even though each of the algorithms that obtains the bounds is very simple.