Weekly scheduling models for traveling therapists

This paper presents a series of models that can be used to find weekly schedules for therapists who provide ongoing treatment to patients throughout a geographical region. In all cases, patient-appointment times and visit days are known prior to the beginning of the planning horizon. Variations in the models include single vs. multiple home bases, homogeneous vs. heterogeneous therapists, lunch break requirements, and a nonlinear cost structure for mileage reimbursement and overtime. The single home base and homogeneous therapist cases proved to be easy to solve and so were not thoroughly investigated. This left two cases of interest: the first included only lunch breaks while the second added nonlinear overtime and mileage reimbursement costs. For the first case, 40 data sets were solved, each consisting of either 15 or 20 therapists and between roughly 300 and 540 patient visits over five days. For each instance, we were able to obtain the minimum cost of providing residential healthcare services using a commercial solver. The results showed that CPU time increases more rapidly than total cost as the total number of visits grows. For the second case, which was much more difficult, it was necessary to develop heuristics to find good solutions quickly. Results for 5- through 20-therapist instances are presented and compared to the linear programming relaxation lower bounds. In the first of two parametric analyses, the tradeoff between the number of therapists on staff and the cost of providing service was examined. In the second, a similar tradeoff was explored between cost can the number of home bases used by the therapists.