# A non-homogeneous discrete time Markov model for admission scheduling and resource planning in a cost or capacity constrained healthcare system

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## Abstract

Healthcare resource planners need to develop policies that ensure optimal allocation of scarce healthcare resources. This goal can be achieved by forecasting daily resource requirements for a given admission policy. If resources are limited, admission should be scheduled according to the resource availability. Such resource availability or demand can change with time. We here model patient flow through the care system as a discrete time Markov chain. In order to have a more realistic representation, a non-homogeneous model is developed which incorporates time-dependent covariates, namely a patient’s present age and the present calendar year. The model presented in this paper can be used for admission scheduling, resource requirement forecasting and resource allocation, so as to satisfy the demand or resource constraints or to meet the expansion or contraction plans in a hospital and community based integrated care system. Such a model can be used with both fixed and variable numbers of admissions per day and should prove to be a useful tool for care managers and policy makers who require to make strategic management decisions. We also describe an application of the model to an elderly care system, using a historical dataset from the geriatric department of a London hospital.

### Keywords

Resource management Admission scheduling Non-homogeneous Markov model Stochastic optimal control## Notes

### Acknowledgements

The authors acknowledge support for this work from the Engineering and Physical Sciences Research Council funded RIGHT and MATCH projects (Grant References EP/E019900/1 and GR/S29874/01). Any views or opinions presented herein are those of the authors and do not necessarily represent those of RIGHT or MATCH, their associates or their sponsors.

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