Joint Assignment, Scheduling, and Routing Models to Home Care Optimization: A Pattern-Based Approach

The design of efficient home care services is a quite recent and challenging field of study. We propose an integrated approach that jointly addresses: (i) the assignment of operators to patients so as to guarantee the compatibility between skills associated with operators and patient visits; (ii) the scheduling of the visits in a given planning horizon; and (iii) the determination of the operator tours in every day of the planning horizon. The main home care problem we investigate refers to providers dedicated to palliative care and terminal patients. In this context, balancing objective functions are particularly relevant. Therefore, two balancing functions are studied, i.e., maxmin, which maximizes the minimum operator utilization factor, and minmax, which minimizes the maximum operator utilization factor. In both cases, the concept of pattern is introduced as a key tool to jointly address assignment, scheduling, and routing decisions, where a pattern specifies a possible schedule for skilled visits. The approach we propose is, however, able to cope with peculiarities from other home care contexts. Model extensions to handle scenarios other than the palliative one are discussed in the paper. Extensive computational results are reported both on palliative home care instances based on real data, and on two real-world data sets from the literature, related to contexts very different from the palliative one. For both data sets the proposed approach is able to find solutions of good quality. In the palliative context, the results show that the selection of the pattern generation policy is crucial to solve large instances efficiently. Furthermore, the maxmin criterion is able to return more balanced solutions; i.e., the difference between the maximum and the minimum operator utilization factors is very small. On the other hand, the minmax criterion is more suitable for minimizing the operating costs, since it computes solutions with smaller total traveled time.