A statistical Markov chain approximation of transient hospital inpatient inventory

doi:10.1016/j.ejor.2010.06.021

European Journal of Operational Research

Volume 207, Issue 3, 16 December 2010, Pages 1645-1657

https://doi.org/10.1016/j.ejor.2010.06.021 Get rights and content

Abstract

Inventory levels are critical to the operations, management, and capacity decisions of inventory systems but can be difficult to model in heterogeneous, non-stationary throughput systems. The inpatient hospital is a complicated throughput system and, like most inventory systems, hospitals dynamically make managerial decisions based on short term subjective demand predictions. Specifically, short term hospital staffing, resource capacity, and finance decisions are made according to hospital inpatient inventory predictions. Inpatient inventory systems have non-stationary patient arrival and service processes. Previously developed models present poor inventory predictions due to model subjectivity, high model complexity, solely expected value predictions, and assumed stationary arrival and service processes. Also, no models present statistical testing for model significance and quality-of-fit. This paper presents a Markov chain probability model that uses maximum likelihood regression to predict the expectations and discrete distributions of transient inpatient inventories. The approach has a foundation in throughput theory, has low model complexity, and provides statistical significance and quality-of-fit tests unique to this Markov chain. The Markov chain is shown to have superior predictability over Seasonal ARIMA models.

Section snippets

Introduction and motivation

Inventory predictions are critical to the operations, management, and capacity of throughput systems. Throughput system complexities including heterogeneous entity types, non-stationary arrival and service processes, and limited production visibility inhibit the application of historical inventory prediction models. Examples of such systems include complex manufacturing systems, organ banks, and blood banks. Hospital inpatient (IP) units are prime examples of very complex throughput systems as

Literature review

The review of the literature generally categorizes relevant transient inventory prediction literature as either a throughput model (e.g. Markov chains, queuing theory, computer simulation) or an empirical statistical model (e.g. time series, regression, summary statistics). Some throughput models include non-stationary arrival and service processes. All throughput models require explicit prior knowledge of the arrival and service process, rates, and non-stationary behavior. No empirical

DTCM model formulation and statistical fitting

This section presents a DTMC probability formulation that captures the short term effects of inventory fluctuations in an IP throughput system. The formulation incorporates hourly seasonality (non-stationarity) in both the arrival and service rate. Because the service rate is assumed unknown by hour of the day, the probability model is combined with maximum likelihood regression to best estimate hourly service rates. Statistical significance and model validation tests specific to this

DTMC validation and model performance in an IP unit

In this section, we explore the validation and performance of the DTMC described in Section 3 using data from two IP units. We consider an intensive care unit (ICU) and a telemetry unit (TELE) from one of Banner Health’s hospitals in Arizona. In this particular hospital, the TELE is significantly larger, receives higher patient volume, and typically has longer treatment times than the ICU. Descriptions of the hospital’s ICU and TELE units are presented in Table 3.

The data used are the IP hourly

Conclusion and future work

This paper presents a DTMC for generically predicting transient inventory in complex, non-stationary, heterogeneous inventory systems. The system is motivated by the hospital IP unit. Unlike much of the IP inventory modeling literature, this formulation has a throughput theory foundation (not strictly empirical) and does not have high complexity. Unlike much of the throughput modeling literature, this research captures the transient inventory in a non-stationary arrival and service process

Acknowledgements

This research is support by Banner Health, Phoenix, AZ. The authors would like to thank Twila Burdick, VP of Organizational Performance, and Management Engineering at Banner Health.

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Innovative Applications of O.R.A statistical Markov chain approximation of transient hospital inpatient inventory☆

Abstract

Section snippets

Introduction and motivation

Literature review

DTCM model formulation and statistical fitting

DTMC validation and model performance in an IP unit

Conclusion and future work

Acknowledgements

European Journal of Operations Research

Socio-Economic Planning Sciences

Annals of Emergency Medicine

International Journal of Production Economics

Introduction to Probability and Mathematical Statistics

Deducing queuing from transactional data: The queue inference engine, revisited

Operations Research

Extension of Palm’s theorem: A review

Management Science

A decision support system for hospital bed assignment

Hospital Health Services Administration

Analysis of a retrial queue with two-phase service and server vacations

Queueing Systems

Management control of blood through a short-term supply-demand forecast

Management Science

A framework for operational modeling of hospital resources

Health Care Management Science

Modelling for the planning and management of bed capacities in hospitals

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Transient solutions for denumerable-state Markov processes

Applied Probability Trust

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Incorporating exogenous factors in adaptive forecasting of hospital census

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Innovative Applications of O.R.
A statistical Markov chain approximation of transient hospital inpatient inventory☆