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A maximal covering facility location model for emergency services within an M (t)/M/m/m queuing system

Iman Bahrami (Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran)
Roya M. Ahari (Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran)
Milad Asadpour (Department of Information Systems and Operations Management, Business School, The University of Auckland, Auckland, New Zealand and Young Researchers and Elite Club, Najafabad Branch, Islamic Azad University, Najafabad, Iran)

Journal of Modelling in Management

ISSN: 1746-5664

Article publication date: 28 December 2020

Issue publication date: 20 July 2021

287

Abstract

Purpose

In emergency services, maximizing population coverage with the lowest cost at the peak of the demand is important. In addition, due to the nature of services in emergency centers, including hospitals, the number of servers and beds is actually considered as the capacity of the system. Hence, the purpose of this paper is to propose a multi-objective maximal covering facility location model for emergency service centers within an M (t)/M/m/m queuing system considering different levels of service and periodic demand rate.

Design/methodology/approach

The process of serving patients is modeled according to queuing theory and mathematical programming. To cope with multi-objectiveness of the proposed model, an augmented ε-constraint method has been used within GAMS software. Since the computational time ascends exponentially as the problem size increases, the GAMS software is not able to solve large-scale problems. Thus, a NSGA-II algorithm has been proposed to solve this category of problems and results have been compared with GAMS through random generated sample problems. In addition, the applicability of the proposed model in real situations has been examined within a case study in Iran.

Findings

Results obtained from the random generated sample problems illustrated while both the GAMS software and NSGA-II almost share the same quality of solution, the CPU execution time of the proposed NSGA-II algorithm is lower than GAMS significantly. Furthermore, the results of solving the model for case study approve that the model is able to determine the location of the required facilities and allocate demand areas to them appropriately.

Originality/value

In the most of previous works on emergency services, maximal coverage with the minimum cost were the main objectives. Hereby, it seems that minimizing the number of waiting patients for receiving services have been neglected. To the best of the authors’ knowledge, it is the first time that a maximal covering problem is formulated within an M (t)/M/m/m queuing system. This novel formulation will lead to more satisfaction for injured people by minimizing the average number of injured people who are waiting in the queue for receiving services.

Keywords

Acknowledgements

The authors would like to appreciate dear editor and anonymous reviewers for providing constructive comments which improved the contribution of the present paper significantly.

Citation

Bahrami, I., Ahari, R.M. and Asadpour, M. (2021), "A maximal covering facility location model for emergency services within an M (t)/M/m/m queuing system", Journal of Modelling in Management, Vol. 16 No. 3, pp. 963-986. https://doi.org/10.1108/JM2-06-2020-0152

Publisher

:

Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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