Demands for cost-efficient and just-in-time service systems have rapidly increased due to the present-day competitive resource allocation. We focus on optimizing policies for highly efficient service systems because customer congestion often arises from suboptimal policies rather than flawed arrangements. Quasi and metaheuristic optimization techniques are widely employed to establish cost-optimal service policies, mitigating customer congestion, primarily caused by unplanned policies or inadequate facilities. This article initially introduces a notion of unreliable service and the F-policy for stochastic modeling of finite capacity customer service systems. Next, we utilize the recently-developed and proficient Grey Wolf Optimizer, a metaheuristic approach, along with the Quasi-Newton method, to determine the optimal values of decision parameters for a cost-efficient service systems. This is achieved through extensive numerical experiments that encompass diverse service characteristics, customer behavior, and performability measures. The results emphasizes the importance of both preventive and corrective actions for enhancing service system efficiency. Our findings also highlight the practicality of the Grey Wolf Optimization approach and stochastic modeling in achieving efficient policies and optimizing performance for the studied service model. In general, the F-policy is widely adopted for controlling queueing systems across various industries such as telecommunications, transportation, and healthcare, where maintaining reasonable wait times, service levels, and system stability is crucial. This article contributes to the mathematical modeling of this approach. Nonetheless, further research is needed to validate and simulate these findings in industrial settings.

由于当今竞争激烈的资源分配，对具有成本效益和及时服务系统的需求迅速增加。我们专注于优化高效服务系统的政策，因为客户拥堵通常是由于政策不理想而不是有缺陷的安排引起的。准和元启发式优化技术被广泛用于建立成本最优的服务政策，缓解主要由计划外政策或设施不足引起的客户拥堵。本文首先介绍了不可靠服务的概念和有限容量客户服务系统随机建模的F策略。接下来，我们利用最近开发的成熟的灰狼优化器（一种元启发式方法）以及拟牛顿法来确定具有成本效益的服务系统的决策参数的最佳值。这是通过广泛的数值实验来实现的，这些实验涵盖了不同的服务特征、客户行为和性能指标。结果强调了预防和纠正措施对于提高服务系统效率的重要性。我们的研究结果还强调了灰狼优化方法和随机建模在实现有效策略和优化所研究服务模型性能方面的实用性。一般来说，F策略广泛用于控制电信、交通和医疗等各个行业的排队系统，在这些行业中，保持合理的等待时间、服务水平和系统稳定性至关重要。本文致力于对这种方法进行数学建模。尽管如此，还需要进一步的研究来在工业环境中验证和模拟这些发现。