Regarding the fact that getting a suitable combination of the human resources and service stations is one of the important issues in the most service and manufacturing environments, In this paper, we have studied the two models of planning Queuing systems and its effect on the cost of the each system by using two fuzzy Queuing models of M/M/1 and M/E2/1. In the first section, we have compared two different fuzzy Queuing models based on the costs of each model and fuzzy ranking methods are used to select optimal model due to the resulted complexity. This paper results in a new approach for comparing different Queuing models in the fuzzy environment (regarding the obtained data from the real conditions) that it can be more effective than deterministic Queuing models. Also a sensitivity analysis is carried out to help the decision maker in selecting the optimal model.

The probability of losing a customer in M/G/n/0 and GI/M/n/0 loss Queuing systems with heterogeneous servers is minimized. The first system uses a queue discipline in which a customer who arrives when there are free servers chooses any one of them with equal probability, but is lost otherwise. Provided that the sum of the servers rates are fixed, loss probability in this system attains minimum value when all the service rates are equal. The second system uses queue discipline, in which a customer who enters into the system is assigned to the server with the lowest number. Loss probability in this system takes the minimum value in the case when the fastest server rule is used in which an incoming customer is served by the free server with the shortest mean service time. If the mean of the arrival distribution is fixed, then loss probability is minimized by deterministic arrival distribution.

This paper presents a new cell formation and cell layout problem considering multiple process routings and subcontracting using the principles of Queuing theory. It is assumed that each machine operates as an M/M/1 Queuing system and a Queuing network is used to obtain in-process inventories and machine utilization. The problem is formulated as a mixed-integer nonlinear program with the objective of minimizing the total costs, including the production, subcontracting, material handling, machine idleness, and holding costs. Due to the computational complexity of the problem, a heuristic method is suggested to effectively solve the problem. A numerical example is given to clarify the proposed approach, and finally, further instances are solved to verify the performance of the solution method and to accomplish comparisons. The computational results show that the proposed heuristic is both effective and efficient.

Considering the competition in today’s business environment, tactical planning of a supply chain becomes more complex than before. In many multi-product inventory systems, substitution flexibility can improve profits. This paper aims to prepare a comprehensive substitution inventory model, where an inventory system with two substitute products with ignorable lead time has been considered, and effects of simultaneous ordering have been examined. In this paper, demands of customers for both of the products have been regarded as stochastic parameters, and Queuing theory has been used to construct a mathematical model. The model has been coded by C++, and it has been analyzed due to a real example, where the results indicate efficiency of proposed model.

Clustering parts and machines into part families and machine cells is a major decision in the design of cellular manufacturing systems which is defined as cell formation. This paper presents a non-linear mixed integer programming model to design cellular manufacturing systems which assumes that the arrival rate of parts into cells and machine service rate are stochastic parameters and described by exponential distribution. Uncertain situations may create a queue behind each machine; therefore, we will consider the average waiting time of parts behind each machine in order to have an efficient system. The objective function will minimize summation of idleness cost of machines, sub-contracting cost for exceptional parts, non-utilizing machine cost, and holding cost of parts in the cells. Finally, the linearized model will be solved by the Cplex solver of GAMS, and sensitivity analysis will be performed to illustrate the effectiveness of the parameters.

This paper applies the Markov models, optimal control theory, eigen vectors and eigen values concepts to propose a methodology to analyze the transient behavior of Exponential Queuing systems. We propose a procedure to calculate the transient probability, the average queue length and the duration of the system to reach the steady state. The method is implemented through an algorithm which is developed and tested in MATLAB software environment. The new method enjoys a stronger mathematical foundation and more flexibility to analyze the transient behavior of Exponential Queuing systems.

The importance of reliable supply is increasing with supply chain network extension and just-in-time (JIT) production. Just in time implications motivate manufacturers towards single sourcing, which often involves problems with unreliable suppliers. If a single and reliable vendor is not available, manufacturer can split the order among the vendors in order to simultaneously decrease the supply chain uncertainty and increase supply reliability. In this paper we discuss with the aim of minimizing the shortage cost how we can split orders among suppliers with different lead times. The (s, S) policy is the basis of our inventory control system and for analyzing the system performance we use the fuzzy Queuing methodology. After applying the model for the case study (SAPCO), the result of the developed model will be compared in the single and multiple cases and finally we will find that order splitting in optimized condition will conclude in the least supply risk and minimized shortage cost in comparison to other cases.

Nowadays, with the advent of new satellite services, the need for resource management in the emerging fifth generation satellite systems (5G-satellite) is inevitable. Thus, to solve this problem, the Bandwidth Manager for resource reservation in satellite link is mandatory. On the other hand, due to limited resources, their resource management¬ is essential. In order to resource management in 5G-satellite systems, can be applied in one phase or many phases. In this paper, resource management for 5G-satellite services is evaluated. The proposed optimization problem is to maximize mean response time under the propagation delay constraints in satellite links. We solve the considered optimization problem via the single phase and two phase algorithms. Finally, through simulation, the proposed algorithms are investigated and confirmed. In our scenarios, satellite is a Central node in call flows and ground stations are End nodes in 5G-satellite based on Internet protocol. So we simulated all of scenarios in matlab software for this reason.

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