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.

中文翻译：

---

M (t) / M / m / m 排队系统内紧急服务的最大覆盖设施位置模型

目的

在紧急服务中，在需求高峰期以最低成本实现人口覆盖最大化非常重要。此外，由于急诊中心包括医院的服务性质，服务器和床位的数量实际上被认为是系统的容量。因此，本文的目的是提出一个最大程度覆盖设施位置的多目标M _(t) / M / m / m 排队系统内的紧急服务中心模型，考虑了不同的服务水平和周期性需求率。

设计/方法论/方法

服务病人的过程是根据排队理论和数学规划建模的。为了应对所提出模型的多目标性，GAMS 软件中使用了增强的 ε 约束方法。由于计算时间随着问题规模的增加呈指数增长，因此 GAMS 软件无法解决大规模问题。因此，提出了一种 NSGA-II 算法来解决此类问题，并通过随机生成的样本问题将结果与 GAMS 进行比较。此外，在伊朗的一个案例研究中，研究了所提议模型在实际情况中的适用性。

发现

从随机生成的样本问题中获得的结果表明，虽然 GAMS 软件和 NSGA-II 几乎共享相同的解决方案质量，但所提出的 NSGA-II 算法的 CPU 执行时间明显低于 GAMS。此外，案例研究模型的求解结果表明，该模型能够确定所需设施的位置，并适当地为其分配需求区域。

创意/价值

在以往的大多数应急服务工作中，以最低成本实现最大覆盖是主要目标。因此，似乎忽略了尽量减少等待接受服务的患者人数。据作者所知，这是第一次在 M _(t) / M / m / m 排队系统中制定最大覆盖问题。排队等候接受服务的受伤人员的平均数量。