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 problem motivated by the ever increasing age of population and the consequent need to reduce hospitalization costs. We are given a weekly planning horizon, a set of operators each characterized by a skill and a set of patients each requiring a set of visits also characterized by a skill. We propose an integrated model that jointly addresses the following problems: (i) the assignment of operators to patients guaranteeing the appropriate levels of skill; (ii) the scheduling of visits in the planning horizon; and (iii) the determination of a set of tours indicating the sequence of patients each operator must visit in every day of the week. Several variants of this model are investigated. All of them use the pattern as a key tool to formulate the problem. A pattern is an a priori given profile specifying a possible schedule for a given set of visits possibly characterized by differnt skills. Computational results on a set of real instances are analysed. They show that the selection of the pattern generation policy is crucial to solve large instances efficiently.