This thesis is outlined in six chapters. Chapter One describes the background of the research, in terms of the consumption of cement material, specifically in a cement manufacturing industry in Malaysia as well as the challenges faced when conducting this research. The research problem is described and the objectives that need to be achieved are highlighted.
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Chapter Two presents three main subjects: firstly, the introduction of queueing concepts; secondly, it explains the details of the elements affecting queue congestion; and thirdly, attention is given to the list of approaches that has been used to solve the issues that have risen in queueing under an uncertain environment, beginning from the history of this problem (Prade, 1980). The gaps in the queueing formulation problem identified from previous studies are also addressed in this chapter.
Chapter Three is classified into three main sections. Firstly, an explanation on the overview of the priority queueing concept is given, followed by the discussion on some preliminaries of fuzzy set theory. The last section presents two defuzzification approaches, i.e., the PNLP and RR techniques. These techniques are used to convert fuzzy queues into crisp queues specifically reaching to the optimal crisp values. Consequently, the aim of this chapter is to show the relationship of these techniques and the multiple channel queueing model with multiclass arrivals under an uncertain environment in the cement industry.
Chapter Four describes the research methodology to achieve the objectives as described in this chapter. The first step in the methodology is the research design and problem definition in the cement Malaysian industry. This is then followed by data collection, fuzzification of data with steps for design of the basic elements, i.e., the arrival rates Class One and Class Two, and service rates based on intervals and fuzzy subsets; and development of the mathematical multiple channel queueing model with multiclass arrivals (M1,M2)/G/C/2Pr, model under an uncertain environment. This
model is developed by using the PNLP and RR techniques which lead to three sub- models: sub-model 1, MCFQ-2Pr, sub-model 2, MCCQ-ESR-2Pr and sub-model 3,
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MCCQ-GSR-2Pr. In addition, a new TrMF-UF model under an uncertain environment is developed by using fuzzy subset of intervals and the α-cut approach. Validation and evaluation of the developed sub-models and model rely on existing mathematical models.
Chapter Five shows the results and discussions of the new alternative sub-models which contribute to the fuzzy queueing model. This includes the effectiveness of designing the basic elements, i.e., the arrival rates Class One and Class Two, and service rates based on fuzzy subsets of intervals. The multiple channel queueing model with multiclass arrivals under an uncertain environment in the cement industry is developed using the PNLP and RR techniques. Furthermore, another proposed model is utilized with respect to the UF in fuzzy queueing systems. Several experiments are done for testing the validation, evaluation and verification of the efficiency of the new sub-models against the existing mathematical models.
Finally, Chapter Six presents a conclusion of the thesis. A summary of the methodology and the successful accomplishment of the research objectives are described. Some recommendations for future work are proposed in this chapter.
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CHAPTER TWO
LITERATURE REVIEW OF QUEUEING SYSTEMS
Based on the discussions in Chapter One on the investigation of queueing problems with different approaches to solving them, this chapter begins with the introduction to the factors that influence the growth of queues. One important element of this growth is the type of environment. Hence, a few queueing techniques and approaches that have been previously applied in this field of queueing are reviewed. These approaches or techniques include the mathematical approach under fixed values, schedule models, simulation approach and some mathematical techniques under approximated values, such as the parametric nonlinear programming (PNLP) technique, robust ranking (RR) technique, Dong Shah and Wong (DSW) algorithm, left-right (LR) technique, and other techniques. Based on the mathematical approach under an uncertain environment, a review of certain fuzzy priority models is offered. This chapter ends with a summary.
2.1 Introduction to Queueing Concept
A queue is a line of people or things waiting to be handled, usually in the sequential order, starting at the beginning or top of the line or sequence (Cooper, 2004; Hillier, & Lieberman, 2010; Bhat, 2015). In general, a queueing problem is a common problem which is encountered by humans or objects inside a congested service system and this leads to an increase in the waiting time of customers to receive a service. Queues are seen to occur in our day-to-day activities, such as, demand for supplies in logistical loading operations and making payment at the checkout counter of a supermarket or bank, amongst others (Taha, 2007; Gross, 2008; Bhat, 2015). It
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is one of the branches in the field of operations research because the results from analyzing the queueing system are often used when making business decisions about the waiting lines to provide the best services or reduce the queueing congestion problem as a whole (Taha, 2007).
The term, „queueing‟ was coined by Erlang who first mathematically analyzed queues, and as a result of his further research and analysis in the field, the concept of queueing theory came to light in his first paper published over a century ago (Erlang, 1909). His work studied telephone traffic congestion problems in the first decade of the 20th century in the research work titled, “The Theory of Probabilities and Telephone Conversations”. Based on his work, which he adopted for the Danish Copenhagen Telephone Company from 1909 to 1920, several studies to date have explored various areas where a queueing problem can exist or where a waiting line is expected to occur. Some of these fields include analyzing hospital patients during peak congestion (Bastani, 2009; Madelbaum, Momcilovic, & Tseytlin, 2012); and adoption of the queueing concept in emergency departments (Izady, 2010; Brahma, 2013). In the area of manufacturing industries, specifically for supply and demand and production level, queue problems are most times experienced in the supply and demand through logistical loading operations (Groover, 2007; White, Schmidt, & Bennett, 2012; Newell, 2013). This manufacturing inventory sector has been seen to be a good area for the application of queueing techniques for solving congestion problems as demonstrated in the work of Buzacott & Shanthikumar (1992), which gave a review of queueing models that can be used for the design of manufacturing systems; and Dallery and Gershwin (1992) which presented an extensive review of models with some analytical results for manufacturing flow line systems.
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Furthermore, Papadopoulos and Heavey (1996); and Altiok (2012) considered the actual design of production lines, setting inventory management issues and master production plans with policies of switching from one product to another, procurement plans, product and customer priorities, work-flow under batch size and maintenance plans, daily or weekly production distribution, repair management and routing due to failures (Anderson, Sweeney, Williams, Camm, & Cochran, 2015).
Therefore, it can be concluded that the problem encountered in queues is one that needs to be solved with the aim of reducing the waiting time of units or customers in the whole system. The understanding of how to reduce or eliminate queues will help industry managers towards better decision-making and better estimation of their organizations.There are certain elements that contribute to the increase or congestion in queues, and some major ones are discussed in the next section.