A multiple channel queueing model under an uncertain environment with multiclass arrivals for supplying demands in a cement industry

In recent years, cement consumption has increased in most Asian countries, including Malaysia. There are many factors which affect the supply of the increasing order demands in the cement industry, such as traffic congestion, logistics, weather and machine breakdowns. These factors hinder smooth and efficient supply, especially during periods of peak congestion at the main gate of the industry where queues occur as a result of inability to keep to the order deadlines. Basic elements, such as arrival and service rates, that cannot be predetermined must be considered under an uncertain environment. Solution approaches including conventional queueing techniques, scheduling models and simulations were unable to formulate the performance measures of the cement queueing system. Hence, a new procedure of fuzzy subset intervals is designed and embedded in a queuing model with the consideration of arrival and service rates. As a result, a multiple channel queueing model with multiclass arrivals, (M1, M2)/G/C/2Pr, under an uncertain environment is developed. The model is able to estimate the performance measures of arrival rates of bulk products for Class One and bag products for Class Two in the cement manufacturing queueing system. For the (M1, M2)/G/C/2Pr fuzzy queueing model, two defuzzification techniques, namely the Parametric Nonlinear Programming and Robust Ranking are used to convert fuzzy queues into crisp queues. This led to three proposed sub-models, which are sub-model 1, MCFQ-2Pr, sub-model 2, MCCQESR-2Pr and sub-model 3, MCCQ-GSR-2Pr. These models provide optimal crisp values for the performance measures. To estimate the performance of the whole system, an additional step is introduced through the TrMF-UF model utilizing a utility factor based on fuzzy subset intervals and the α-cut approach. Consequently, these models help decision-makers deal with order demands under an uncertain environment for the cement manufacturing industry and address the increasing quantities needed in future

Analysis of Performance Measures with Single Channel Fuzzy Queues under Two Class by Ranking Method

In this paper, we propose a procedure to find different performance measures in terms of crisp value for new single fuzzy queues FM/F(H1,H2)/1 with two classes of arrival. The arrival and service rate are fuzzy numbers which represented by triangular, trapezoidal and hexagonal membership functions. The main idea is to obtain the exact crisp values from the fuzzy values, which is more realistic and practical in queueing system. The left and right ranking method is adopted to remove the fuzziness before the performance measures are computed by using conventional queueing theory. The main advantage of this approach, that it is simplicity in application and capability in discovering exact real data around fuzzy values. Numerical example is presented to illustrate the validity application of the procedur

Analysis of performance measures with single channel fuzzy queues under two class by using ranking method

In this paper, we propose a procedure to find different performance measurements under crisp value terms for new single fuzzy queue FM/F(H1,H2)/1 with two classes, where arrival rate and service rates are all fuzzy numbers which are represented by triangular and trapezoidal fuzzy numbers.The basic idea is to obtain exact crisp values from the fuzzy value, which is more realistic in the practical queueing system.This is done by adopting left and right ranking method to remove the fuzziness before computing the performance measurements using conventional queueing theory.The main advantage of this approach is its simplicity in application, giving exact real data around fuzzy values.This approach can also be used in all types of queueing systems by taking two types of symmetrical linear membership functions. Numerical illustration is solved in this article to obtain two groups of crisp values in the queueing system under consideration

Minimizing waiting times using multiple fuzzy queueing model with supply priorities

This paper proposes to construct the membership function of the system characteristics of a multiple channel queueing model with two classes of priority in which arrival rates and service rates of customers are all fuzzy numbers.A crisp multiple channel with two classes of priority queueing system generalized to a fuzzy environment has been seen to adopted widely in previous literature, hence the motivation to transform a fuzzy queue with multiple channel and two class of priority into a family of conventional crisp queues with the application of alpha cut approach. A set of parametric nonlinear programs is developed to describe the family of crisp queues with multiple channels priority and a numerical example is solved successfully to demonstrate the validity of the proposed procedure.The developed mathematical formula in this article is expressed by membership functions rather than by crisp values and more focus is placed on queueing systems encountered in real life with the aim of reducing the expected waiting time of customers in the queue for each priority class

Designing Basic Variables as Linguistic States with Multiple Channel Queueing Models and Supply Priorities In Uncertainty Environment

This paper develops a new contribution for constructing an architecture that describes the linguistic states as intervals with two basic variables; arrival rates and service rates, while increasing the supplying order of demands in the manufacturing production line under uncertainty environment. The basic idea for this paper considers classifying these basic values as linguistic values represented by three ranges for each value, in a multiple channel queueing model with two class of priority having ranges in each interval. Trapezoidal fuzzy numbers are considered as they are efficient to build these intervals. Adopting robust ranking index and a-cut confidence interval are suitable approaches for converting the fuzzy arrival and service values into crisp values. Numerical application is shown for the application of this new approach in evaluating the exact real waiting time of customers in the queue for each interval, which further contributes to evaluation of the whole system in uncertainty environment. Hence, an easy way for dealing with fuzzy numbers in decision-making problems is develope

Performance measurements of single server fuzzy queues with unreliable server using left and right method

There are a number of real life systems that can be described as a queuing system, and this paper presents a queuing system model applied in a manufacturing system example.The queuing model considered is depicted in a fuzzy environment with retrial queues and unreliable server.The stability condition state of this model is investigated and the performance measurement is obtained by adopting the left and right method.The new approach adopted in this study merges the existing α-cut interval and nonlinear programming techniques and a numerical example was considered to explain the methodology of this technique.From the numerical example, the flexibility of the method was shown graphically showing the exact real mean value of customers in the system and also the expected waiting times

Performance measure of multiple-channel queueing systems with imprecise data using graded mean integration for trapezoidal and hexagonal fuzzy numbers

In this paper, a procedure to establish the different performance measures in terms of crisp value is proposed for two classes of arrivals and multiple channel queueing models, where both arrival and service rate are fuzzy numbers. The main idea is to convert the arrival rates and service rates under fuzzy queues into crisp queues by using graded mean integration approach, which can be represented as median rule number. Hence, we apply the crisp values obtained to establish the performance measure of conventional multiple queueing models. This procedure has shown its effectiveness when incorporated with many types of membership functions in solving queuing problems. Two numerical illustrations are presented to determine the validity of the procedure in this queueing model, which involved using trapezoidal and hexagonal fuzzy numbers. It can be concluded that graded mean integration approach is efficient with fuzzy queueing models to convert fuzzy queues into crisp queues. This finding has contributed to the body of knowledge by suggesting a new procedure of defuzzification as another efficient alternative

A Single Server Fuzzy Queues with Priority and Unequal Service Rates

This article presents to develop a new mathematical model to construct membership functions of the fuzzy single channel queueing model F(M1, M2)/F(M1, M2)/1/PR-NP with two class of non-preemptive priority with unequal service rates. The main idea of this article is to merge between mathematical programming technique and Yager’s ranking method by using α-cut approach and Zadeh extension principle to transform fuzzy queues into a family of conventional crisp (distinct) queues in this context. A numerical example is given to explain the validity of this new approach to obtain real exact values under different levels of α in the syste