A patient assignment algorithm for home care services

We consider the problem of assigning patients to nurses for home care services. The aim is to balance the workload of the nurses while avoiding long travels to visit the patients. We analyse the case of the CSSS Côte-des-Neiges, Métro and Parc Extension for which a previous analysis has shown that demand fluctuations may create work overload for the nursing staff. We propose a mixed integer programming model with some non-linear constraints and a non-linear objective which we solve using a Tabu Search algorithm. A simplification of the workload measure leads to a linear mixed integer program which we optimize using CPLEX.