Sequential pattern mining has been a popular data mining technique for extracting useful information from large databases and has successfully been used for numerous industrial and commercial problems. This paper presents a new mathematical modelling application to healthcare, providing important information to health service managers and policy makers to help them identify sequential patterns which require attention for efficiently managing scarce healthcare resources and developing effective healthcare management policies. In healthcare, these sequential patterns are analogous to the patient pathways. We present a non-homogeneous Markov model for identifying not only patient pathways which have high probability but also for identifying pathways which incur high cost or time. In order to have a more realistic model, we also consider time-dependent covariates and their impact on the pathways. An algorithm based on branch and bound global optimization is presented which can efficiently extract a required number of such patient pathways of interest. The approach is illustrated using historical data on geriatric patients from an administrative database of a London hospital.