The Optimal Number of Hospital Beds Under Uncertainty: A Costs Management Approach

Document Type : Original Manuscript


1, Department of Industrial Engineering, Yazd University, Yazd, Iran

2 Faculty member, Department of Industrial Engineering, University of Torbat Heydarieh, Torbat Heydarieh, Iran.

3 Faculty member, Department of Industrial Engineering, quchan university advanced technologyUniversity, quchan, Iran


Equipping hospital beds uses a great deal of a hospital''''s resources. Therefore, it is essential to consider the hospital beds'''' efficiency. To increase its efficiency, a fuzzy unrestricted model for managing hospital expenses is presented in this paper. The lack of beds in hospitals leads to patients’ admission loss and consecutively profit loss. On the other hand, increasing the bed count leads to an increase in equipment expenses. Therefore, in order to determine optimal bed capacity, it is of utmost importance to consider these two costs simultaneously. In our paper, hospital admission system is modeled with a multi-server queuing system (M/M/K). Therefore, to calculate the total cost function, limiting probabilities of multi-server queueing model is used. Furthermore, due to uncertain nature of parameters, such as interest rate and hospitalization profit in various future time periods, these uncertainties are covered by fuzzy logic. Finally, to determine the optimal bed count, Lee and Li''''s fuzzy ranking method is used. This model is implemented ona case study. Its goal is to determine the optimal bed count for emergency unit of Razi hospital in Torbat Heydarieh. Considering the high capability of Markovian chains in modeling different circumstances and the various queueing models, the proposed model can be extended for various hospital units.

Graphical Abstract

The Optimal Number of Hospital Beds Under Uncertainty: A Costs Management Approach


  • Unrestricted fuzzy non-linear model. This model is used in addition to fuzzy ranking. Together, this approach reduces execution time. Furthermore, compared to the corresponding restricted fuzzy non-linear model, this approach is understood more easily by humans.
  • The use of Markovian chains and queueing theory. The high flexibility of Markov chains in modeling would lead to a suitable model for various hospitals and conditions. Therefore, the resulting model will have a high level of flexibility.
  • Integration of fuzzy logic and queuing theory. This integration leads to the coverage of uncertain conditions which is an inherent condition of servicing environments and especially hospitals.
  • A novel cost function with the consideration of time value of money


Main Subjects

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