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Batch production is a modern strategy for manufacturing, especially for products unsuitable for continuous assembly lines. This study proposes a method for analysing one such production facility. Here, we characterize a batch production system as a unique sort of quorum feedback retrial queue deployed under Bernoulli working vacation and outfitted with a secondary, stand-by server. The system’s dynamics are thoroughly examined using the supplementary variable technique, providing insights into its behaviour and performance. Key metrics are determined, and the impact of specific parameters is demonstrated through numerical examples. Furthermore, this research aims to achieve the optimal system cost by employing a variety of optimization approaches. Thus, optimizing costs and identifying key metrics are crucial for enhancing efficiency and profitability in batch production systems. This process ensures that resources are used effectively, service quality is maintained, and overall operational costs are reduced, leading to a more sustainable and profitable production system which helps to make informed decisions.

The aim of this paper is to analyze the queuing model entitled to cost optimization in bulk arrival and a batch service retrial queuing system with threshold, server failure, non-disruptive service, and multiple vacations. When bulk arrival of customers find the server is busy, then all customers will join in the orbit. On the other hand, if the server is free, then batch service will be provided according to the general bulk service rule. Batch size varies from a minimum of one and a maximum of ‘b’ number of customers. Customers in the orbit seek service one by one through constant retrial policy whenever the server is in idle state. The server may encounter failure during service. If the server fails, then ‘renewal of service station’ will be considered with probability . If there is no server failure with probability in the service completion or after the renewal process and if the orbit is empty, the server then leaves for multiple vacations. The server stays on vacation until the orbit size reaches the value N. For this proposed queuing model, a probability generating function of the orbit size will be obtained by using the supplementary variable technique and various performance measures will be presented with suitable numerical illustrations. A real time application is also discussed for this system. Additionally, a cost effective model is developed for this queuing model.

Today, with real-life problems, modeling is a primary step in organizing, analyzing and optimizing them. Queueing theory is a particular approach used to model this category of issues. Space constraints, feedback, service dependency, etc. are often inseparable from the issues they create. In light of this objective, this research presents a model and analysis of the steady-state behavior of an M / G / 1 feedback retrial queue with two dependent phases of service under a Bernoulli vacation policy. The service times for the two stages are often independent in normal queueing frameworks. We presume that they are dependent random variables in this case. Indeed, this dependence is one-way (i.e., the service time of the second phase has no effect on the service time of the first phase). Yet, the first phase service time has an impact on the second phase service time. In order to determine the steady-state probabilities and probability-generating functions (PGF) for the different states, the supplementary variable technique (SVT) was utilized. Furthermore, a broad range of performance metrics had been established. The generated metrics are then envisioned and validated with the aid of graphs and tables. Additionally, a nonlinear cost function is constructed, which is subsequently minimized by distinct approaches like particle swarm optimization (PSO), artificial bee colony (ABC) and genetic algorithm (GA). Furthermore, we used certain figures to examine the convergence of these optimization methods. Finally, validation outcomes are compared with neuro-fuzzy results generated with the "adaptive neuro-fuzzy inference system" (ANFIS). [ABSTRACT FROM AUTHOR]

In this article, a working vacation policy-based on bulk arrival feedback retrial queueing system with variable server capacity has been analyzed. The server can serve a minimum of one customer and a maximum of B customers in a batch in accordance with the variable server capacity bulk service rule. As soon as the orbit becomes empty at the time of service completion, the server goes for a working vacation. The server works at a lower speed during a working vacation period. In addition, the steady state probability generating function for system size and orbit size is generated by incorporating the supplementary variables technique (SVT). Further, the conditional decomposition law is shown for this retrial queueing system. Moreover, system performance metrics, and significant special instances are discussed. Finally, the effects of various parameters on the system performance are analyzed numerically. [ABSTRACT FROM AUTHOR]

The suggested queueing model describes a single-server feedback retrial queueing system with starting failure, Bernoulli working vacation and vacation interruptions. The server departs on a working vacation as soon as orbit is empty. During the working vacation period, the server provides a slower level of service. The supplementary variable method was utilized to determine the steady-state probability-generating functions for the system and its orbit. If there are consumers in the system at the end of each vacation, the server becomes idle and ready to serve new customers. The average busy time and the average busy cycle are presented as important system performance indicators. Additionally, the adaptive neuro-fuzzy interface system has compared the numerical results with the neuro-fuzzy results. Finally, particle swarm optimization (PSO) were utilized to obtain the best (optimal) cost for the system in this study. We have examined the convergence of these optimization strategies. [ABSTRACT FROM AUTHOR]

This review article presents an overview of bulk arrival and bulk service with breakdown QM's. The concept of bulk arrivals and bulk service has a new significance in the world of reality. To prevent the problem of traffic congestion, researchers must concentrate their efforts on developing models and processes to address the issue. Numerical methods of QM's are critical in many industries, notably in production lines, to alleviate traffic congestion. This study seeks to give analysts, researchers, and industry professionals enough information to model congestion problems and extract various performance indicators to improve the QS's. [ABSTRACT FROM AUTHOR]

The transient and metaheuristic cost analysis of a MX/G(a, b)/1 retrial queue with random failure during an extended Bernoulli vacation with impatient clients is covered in this study. Any batch that arrives and discovers the server is busy, down, or on vacation joins an orbit. In the alternative, only one new customer from the group joins the service right away, while the others join the orbit. After providing each service, the server either waits to serve the following customer with probability (1 - θ) or goes on vacation with probability θ. It has been found that these systems express steady-state solutions and are dependent on time probability generating functions in consideration of their Laplace transforms. We also discuss a few exceptional and particular instances. After that, the impact of different parameters on the system's effectiveness is evaluated. We are also talking about ANFIS. Additional approaches employed in this study to swiftly determine the system's optimum cost include genetic algorithms (GA), artificial bee colonies (ABC), and particle swarm optimization (PSO). We also examined the graph-based convergence of several optimization algorithms. [ABSTRACT FROM AUTHOR]

In “this paper, first we define the notion direct product of neutrosophic sets in INK-algebras, neutrosophic set, neutrosophic INK-ideals, neutrosophic closed INK-ideals and direct product of neutrosophic INK-ideals in INK-algebras. We prove some theorems which show that there is some relation between these notions. Finally, we define the INK-subalgebra of INK-algebra and then we give related theorem about the relationship between their Images and direct product of neutrosophic INK-ideals. [ABSTRACT FROM AUTHOR]