A statistical Markov chain approximation of transient hospital inpatient inventory

James R. Broyles, Jeffery K. Cochran, Douglas Montgomery

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1645-1657
Number of pages13
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - Dec 16 2010


  • Markov chain
  • Regression
  • Statistical inference
  • Transient inpatient inventory

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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