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.
Similar content being viewed by others
References
World Health Statistics: Monitoring Health for the SDGs. World Health Organization, Geneva (2018)
Nicholson, L., Vakharia, A.J., Erenguc, S.S.: Outsourcing inventory management decisions in healthcare: models and application. Eur. J. Oper. Res. 154, 271–290 (2004)
Saedi, S., Kundakcioglu, O.E., Henry, A.C.: Mitigating the impact of drug shortages for a healthcare facility: an inventory management approach. Eur. J. Oper. Res. 251, 107–123 (2015)
McClean, S., Millard, P., Garg, L.: Using Markov models for decision support in management of high occupancy hospital care. In: Chountas, P., Petrounias, I., Kacprzyk, J. (eds.) Intelligent techniques and tools for novel system architectures, vol. 109, pp. 187–200. Springer, Berlin (2008)
Volland, J., Fügener, A., Schoenfelder, J., Brunner, J.: Material logistics in hospitals: a literature review. Omega 69, 82–101 (2017)
Vila-Parrish, A., Ivy, J., King, R., Abel, S.: Patient-based pharmaceutical inventory management: a two-stage inventory and production model for perishable products with Markovian demand. Health Syst 1, 69–83 (2012)
Roni, M., Eksioglu, S., Jin, M., Mamun, S.: A hybrid inventory policy with split delivery under regular and surge demand. Int. J. Prod. Econ. 172, 126–136 (2016)
Gebicki, M., Mooney, E., Chen, S., Mazur, L.: Evaluation of hospital medication inventory policies. Health Care Manag. Sci. 17, 215–229 (2014)
Guerrero, W., Yeung, T., Guéret, C.: Joint-optimization of inventory policies on a multi-product multi-echelon pharmaceutical system with batching and ordering constraints. Eur. J. Oper. Res. 231, 98–108 (2013)
Uthayakumar, R., Priyan, S.: Pharmaceutical supply chain and inventory management strategies: optimization for a pharmaceutical company and a hospital. Oper. Res. Health Care 2, 52–64 (2013)
Bijvank, M., Vis, I.: Inventory control for point-of-use locations in hospitals. J. Oper. Res. Soc. 63, 497–510 (2012)
Little, J., Coughlan, B.: Optimal inventory policy within hospital space constraints. Health Care Manag. Sci. 11, 177–183 (2008)
Kelle, P., Woosley, J., Schneider, H.: Pharmaceutical supply chain specifics and inventory solutions for a hospital case. Oper. Res. Health Care 1, 54–63 (2012)
Rosales, C., Magazine, M., Rao, U.: The 2Bin system for controlling medical supplies at point-of-use. Eur. J. Oper. Res. 243, 271–280 (2015)
Haijema, R.: Optimal ordering, issuance and disposal policies for inventory management of perishable products. Int. J. Prod. Econ. 157, 158–169 (2014)
Hovav, S., Tsadikovich, D.: A network flow model for inventory management and distribution of influenza vaccines through a healthcare supply chain. Oper. Res. Health Care 5, 49–62 (2015)
Wu, D., Rossetti, M., Tepper, J.: Possibility of inventory pooling in China’s public hospital and appraisal about its performance. Appl. Math. Model. 39, 7277–7290 (2015)
Wang, L., Cheng, C., Tseng, Y., Liu, Y.: Demand-pull replenishment model for hospital inventory management: a dynamic buffer-adjustment approach. Int. J. Prod. Res. 53, 7533–7546 (2015)
Attanayake, N., Kashef, R. F., Andrea, T., Carolina, N.: A simulation model for a continuous review inventory policy for healthcare systems. In: Canadian Conference on Electrical and Computer Engineering, pp. 1–6 (2014)
Hillier, F., Lieberman, G.: Introduction to Operations Research. Tata McGraw-Hill, New York (2010)
Puterman, M.: Markov Decision Processes. Wiley, New York (1994)
Chen, B., Hong, Y.: Testing for the Markov property in time series. Econom. Theory 28, 130–178 (2012)
Malik, A.I., Sarkar, B.: Optimizing a multi-product continuous-review inventory model with uncertain demand, quality improvement, setup cost reduction, and variation control in lead time. IEEE Access 6, 36176–36187 (2018)
Sarkar, B., Mahapatra, A.S.: Periodic review fuzzy inventory models with variable lead time and fuzzy demand. Int. Trans. Oper. Res. 24(5), 1197–1227 (2017)
Cheikhrouhou, N., Sarkar, B., Ganguly, B., et al.: Optimization of sample size and order size in an inventory model with quality inspection and return of defective items. Ann. Oper. Res. 271, 445–467 (2018)
Pal, S., Mahapatra, G.S., Samanta, G.P.J.: A three-layer supply chain EPQ model for price- and stock-dependent stochastic demand with imperfect item under rework. Uncertain. Anal. Appl. 4, 10 (2016)
Pal, S., Mahapatra, G.S., Samanta, G.P.: An inventory model of price and stock dependent demand rate with deterioration under inflation and delay in payment. Int. J. Syst. Assur. Eng. Manag. 5(4), 591–601 (2014)
Dey, B.K., Sarkar, B., Sarkar, M., Pareek, S.: An integrated inventory model involving discrete setup cost reduction, variable safety factor, selling-price dependent demand, and investment. RAIRO Oper. Res. 53, 39–57 (2019)
Sarkar, B., Ahmed, W., Choi, S., Tayyab, M.: Sustainable inventory management for environmental impact through partial backordering and multi-trade-credit-period. Sustainability 10, 4761 (2018)
Acknowledgements
The authors would like to thank the case study hospital authority for their support and cooperation during data collection.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
None.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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,
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
for some \(t \ge 1\), then \(S_{t}\) is not a Markov process. The Chapman–Kolmogorov equation is able to detect Markovian property.
Rights and permissions
About this article
Cite this article
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
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12597-019-00415-x