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Modelling and analysis of healthcare inventory management systems

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Abstract

The core competency of the healthcare system is to provide treatment and care to the patient. The prime focus has always been towards appointing specialized physicians, well-trained nurses and medical staffs, well-established infrastructure with advanced medical equipment, and good quality pharmacy items. But, of late, the focus is driven towards management side of healthcare systems which include proper capacity planning, optimal resource allocation, and utilization, effective and efficient inventory management, accurate demand forecasting, proper scheduling, etc. and may be dealt with a number of operations research tools and techniques. In this paper, a Markov decision process inventory model is developed for a hospital pharmacy considering the information of bed occupancy in the hospital. One of the major findings of this research is the significant reduction in the inventory level and total inventory cost of pharmacy items when the demand for the items is considered to be correlated with the number of beds of each type occupied by the patients in the healthcare system. It is observed that around 53.8% of inventory cost is reduced when the bed occupancy state is acute care, 63.9% when it is rehabilitative care, and 55.4% when long-term care. This may help and support the healthcare managers in better functioning of the overall healthcare system.

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Acknowledgements

The authors would like to thank the case study hospital authority for their support and cooperation during data collection.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Indian Institute of Technology Kharagpur, Kharagpur, 721 302, India

    Esha Saha & Pradip Kumar Ray

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  1. Esha Saha
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  2. Pradip Kumar Ray
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Correspondence to Esha Saha.

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Appendix

Appendix

1.1 Testing markovian property

To prove that the states hold the Markov assumption, a higher-order Markov model is designed (Chen and Hong [22]). It is because if the Markov assumption holds then building memory into the model via higher order models should have no effect on the transition probabilities.

1.2 Hypotheses of interest and test statistics

Suppose bed states, \(\left\{ {S_{t} } \right\}\) is a strictly stationary time series process. It follows a Markov process if the conditional probability distribution of \(S_{t + 1}\) given the information set \(Z_{t} = \left\{ {S_{t} , S_{t - 1} , \ldots } \right\}\) is the same as the conditional probability distribution of \(S_{t + 1}\) given \(S_{t}\) only.

This can be expressed by the null hypothesis,

$$H_{0} :P (S_{t + 1} \le i|Z_{t} ) = P (S_{t + 1} \le i|S_{t} )$$

for all \(i\) and for all \(t \ge 1\). Under \(H_{0}\), the past information set \(Z_{t - 1}\) is redundant i.e. the current state variable or vector \(S_{t}\) will contain all information about the future behaviour of the process that is in the current information set \(Z_{t}\).

The alternative hypothesis is when

$$H_{A} :P(S_{t + 1} \le i|Z_{t} ) \ne P(S_{t + 1} \le i|S_{t} )$$

for some \(t \ge 1\), then \(S_{t}\) is not a Markov process. The Chapman–Kolmogorov equation is able to detect Markovian property.

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Saha, E., Ray, P.K. Modelling and analysis of healthcare inventory management systems. OPSEARCH 56, 1179–1198 (2019). https://doi.org/10.1007/s12597-019-00415-x

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