IMPACT OF QUEUING THEORY MODEL ON PRODUCTIVITY PERFORMANCE IN AN INDUSTRIAL AREA
Lavina Pamnani1 and Varsha Mandwariya2
1Department of Mathematics, Sant Hirdaram Girls College, Bhopal, India
2Department of Mathematics, Sant Hirdaram Girls College, Bhopal, India
Abstract - In this paper we discuss the impact of queueing theory model on the productivity performance in an industry. Queueing theory is an effective process for analyzing and putting limited resources to their optimal use, particularly machine resources in a manufacturing system. Each and every process in production is strictly connected with costs and deadlines which have to be met by the investor/owner and the production company. Equipment usage will give fast and accurate results at a reduced cost.
However, some machine combinations fail to achieve results under the given conditions while other combinations will be optimal in all aspects for the given task. Thus an effective process is required to analyze the conditions carefully and to choose the optimal type, number and combination of equipment. In this paper, we highlight how manufacturing sector can benefit by applying queueing theory models to its production and how ultimately selecting the right level of batch size and output, boosts productivity and utilization of inputs.
Keywords: Queueing theory, Equipment, Utilization, Production, Manufacturing.
1. QUEUING SYSTEM OVERVIEW
Queuing Network is an analytical model used to evaluate manufacturing system. Generally, there are two approaches to model manufacturing system, which are analytical models and simulation models. Analytical models can be categorized into a spreadsheet model and a queuing network model (Marsudi et al., 2009), the latter of which is the focus of this research.
There are many studies by previous researchers that addressed resource utilization in a manufacturing system, but most of these studies are not focused directly on batch size and throughput parameters. Based on that fact, the objective of this study is to evaluate the effect of batch size and throughput in relation to optimizing the resources by using Queuing Network theory.
The manufacturing industry has to strive continually in order to increase efficiency in production process so as to stay competitive and sustainable. Production process is executed at a certain production line which commonly has three types. These are single model line, batch model line and mixed model line (Groover 1987). Each machine in the production line operates at a particular cycle time. The efficiency of a production operation in manufacturing system can be measured based on the utilization of production resource such as machines in a particular cycle time.
For certain operations, resources are not utilized at the optimum level and this will cause the cycle time of production of a commodity to be longer and the throughput is not at the maximum as it is supposed to be. Hence, Queuing Network theory can be applied to determine the ideal batch size and throughput for a particular commodity’s production in order to optimize resource utilization.
Queues can be found in various settings which could either be in the manufacturing or service organization. When we look at the manufacturing sector, taking automotive industry as a case, we have observed in recent times, there has been an increase in variety of products and mix models in order for the manufacturers to effectively compete in the global market. For manufacturers to stay relevant, flexibility in manufacturing is an important concept that must be embraced. However, flexibility has its own cons such as high initial investment, which in turn requires large inventory and this is a non-negligible cost.
Inventory takes different forms like raw material, work in progress, finished products, and goods in the warehouse between customers and suppliers. It is important for all industries to manage inventory properly as it is a detrimental factor in deciding how productive and profitable the business can be. One of the most successful models used to tackle inventory problems in this industry is just-in-time manufacturing that makes use of
the supermarket rule of taking exactly what is needed in the assembly line from the warehouse. This is popularly known as dock management modeling.
If the demand requirement is higher than the capacity, bottlenecks will definitely occur. For the manufacturing industry to remain relevant, sustainable, and compete strongly they must always find a way of improving efficiency in the production process. In a manufacturing system, the efficiency of the production operation is based on how the machines utilize the resource in a particular cycle time. Some operations do not make full use of the resources, this results in an increase in cycle time which also affects the throughput rate at which a product enters and leaves the production line.
Queue management is a smart, efficient way to tackle this issue. It helps to balance costs, minimize loss, and avoid overinvesting in equipment, products, or labour hours you do not actually need—all while maintaining a high level of customer satisfaction.
Similarly, a large amount of project cost is accounted to equipment and machinery.
Advantage of equipment utilization includes increased rate of output, reduction in overall cost, carrying out activities that cannot be carried out manually, maintaining the planned rate of production when there is labor shortage, maintain high quality standard etc. Thus proper choice and use of the equipment contributes to economy, quality, safety, speed and timely completion of the project.
Factors affecting equipment selection include site considerations, economic considerations, equipment specifications, labor consideration, client and project specifications etc. However, delays in project execution may occur due to improper choice of equipment, unavailability of equipment at the required time, increased cycle time and waiting time and also poor technology and wrong mechanization. These problems can be overcome, once again, by applying queuing theory for equipment selection in order to minimize the extent of delays by reducing cycle time and idle time and thus reducing the associated cost.
2. LITERATURE SURVEY
Some previous studies to improve the resource utilization of manufacturing system was conducted by Taylor et al. (1994), Hopp and Spearman (2004), Seraj (2008),Walid (2006), Gamberi et al. (2008), and Hajji, et al. (2011). Great effort was taken to study a batch size and scheduling model for production lines such as that by Marchet et al. (2011) who presented an innovation model that can be used in initial phase of ―pick-and-sort‖ OPS design. Hussain and Drake (2011) said that previous similar studies have used control theoretic techniques and it has been pointed out that control theorists are unable to solve the batch size problem. Therefore, they applied system dynamic simulation to investigate the impact of various batch sizes on bullwhip effect.
Stadtler and Sahling (2013) presented a new model formulation for batch size and scheduling of multi-stage flow lines which works without a fixed lead-time offset and still guarantees a feasible material flow. Gamberia et al. (2008) presented a new approach to evaluating the suitability of implementing a batchproduction-oriented manufacturing line.
Hong et al. (2012) proposed an integrated batching and sequencing procedure called the indexed batching model (IBM), with the objective of minimizing the total retrieval time (the sum of travel time, pick time and congestion delays).
Mengfei Yu, et al. (2013) proposed an approximation model based on queuing network theory to analyze the impact of order batching and picking area zoning on the mean order throughput time in a pick-and-pass order picking system. Pazoura and Meller (2013) analyzed the impact batch retrieval processing has on throughput performance for horizontal carousel systems that use automated storage and retrieval machines as robotic pickers. The analysis is conducted on a set of product that consists of existing products mixed with the detail design of new product. In the case where maximum production quantity is not enough, the design of the new product should be changed in order to avoid production process at critical or bottleneck resources utilization.
Gamberi et al. (2008) presented the evaluation of the implementation of a manufacturing line by comparing different layouts. His studied was focused on analytical model for multi-stage multiproduct production line without buffer. In particular, the proposed approach involves both a preliminary choice considering the production capacity utilization rate. Hajji, et al. (2011)described the analytical approach with an experimental
approach based on simulation modeling, design of experiment and response surface methodology, to control manufacturing systems including to control utilization parameter.
Walid (2006) addressed the issue of capacity estimation and improvement in a multi-product unreliable production line with finite buffers. The procedure allowed for the enumeration of the defined states that a station may have while processing the mix of products. Durations of service interruptions or downtimes were taken into account as the mean time to repair the failed. This approach complements a linear programming model by altering the production sequence and inserting fictive product at appropriate positions in the sequence. The modified model provided the expected cycle time of the unreliable production line. Chincholkar et al. (2004) presented the analytical model for estimating the total manufacturing cycle time and throughput of the manufacturing system.
Herrmann et al. (2000) presented a manufacturing system model based on queuing network approximations for estimating the manufacturing cycle time and throughput of such systems. In particular, the model can be used to evaluate the placement of inspection stations in a process flow. This analytical model can provide insights into how the manufacturing system parameters (including processing times, arrival rate, and placement of an inspection station) affect manufacturing system performance (including total manufacturing cycle time and throughput). The important result of their study was that the increasing manufacturing cycle time at one workstation can reduce both total manufacturing cycle time and throughput. Johnson (2003) concluded that the utilization of a workstation in a production line can be increased by reducing production batch size.
The supply chain of industry is characterized for a properly organized structure, where the partial exchange of forecasting amongst manufacturers and their first-tier suppliers are requirement demand; this means that suppliers in most cases must be ready to handle a variety of potential requirements. In order to handle such varieties, it important to consider technological tools for efficiently managing the decision-making in this area.
In order to reduce the time spent in waiting systems, one solution would be to supplement the checkout clerks, but this is not always the most economical strategy to improve services. One of the factors influencing consumers' perception on service quality is the efficiency of waiting systems. The waiting time is inevitable in the case of random requests. Thus, providing the capacity for a sufficient service is needed, but it is involving high costs. This is the premise from which the queuing theory starts in designing service systems (Alecu, F., 2004).
As presented by Cooper (2000), Hoover and Bartlett have also applied the results of queuing theory to show how the cycle time is related to large and small production. In large production, cycle time is important to determine the amount of work in progress, and it can be determined by using queuing models. However, their study had limitation which it can be applied only in large production. Their simulation has showed greater fluctuations in cycle time compared to the value predicated by queuing theory.
Queuing theory is applied in mining operations for haul routes in multi-channel queuing models by assuming finite customers, closed system that serves customers in FIFO concept. The model developed calculates several outputs like loader utilization, time spent in system, number of trucks/customers in the system etc. which are used to measure the efficiency of haulage operations. However in this model if any changes are made to the mining haul system then new service rate and inter arrival times have to be calculated and also the scope of the project is limited to truck and shovel behavior in open pit mining operations.
3. FACTORS AFFECTING EQUIPMENT SELECTION
For the efficient selection of equipment the factors affecting equipment use and efficiency have to be carefully analysed. From critical literature review it is found that the following factors have to be taken into consideration while choosing equipment:
3.1 Suitability for Job Conditions
The equipment must meet the requirement of the work, climate and working conditions.
3.2 Size of the Equipment
Size of equipment should be such that it must be able to be used with other matching units. If the equipment selected is of larger size that will remain idle for most of the time or shall work on part loads, which means production cost will be more. On other side, if the equipment is of smaller size than desired, the equipment will not be able to work with the matching equipment and hence other equipment will have to remain idle or to be allowed to work on part loads, which shall again be uneconomical.
3.3 Standardization
It is better to have same type and size of equipment in the project. It means lesser spare parts reserve, more inter changeability of parts, easy for the operators to understand, mechanics will be able to maintain and repair better as. They become expert by handling similar type of equipment.
3.4 Availability of Equipment
The equipment which is easily available in the market should be purchased. It should also be ensured that the equipment is of repute and is likely to be continued manufactured in future also. This is necessary for future standardization and ensuring spare parts supply. It is easy to dispose of equipment after completion of project.
3.5 Availability of Spare Parts
While selecting a particular type or make of equipment, it should be ensured that the spare parts will be available at reasonable price throughout the working life of the equipment. It should also be ensured that the downtime of the equipment for want of spare parts may not be more. This is all the more necessary in case of imported equipment.
3.6 Multipurpose Equipment
There are certain types of equipment which are not utilized fully. Therefore if possible, they should be capable of performing more than one function. For example, take the case of an excavator with wheel loader bucket arrangement or with rock breaker attachment.
3.7 Use in Future Projects
When equipment completes only a part of their useful life in a project, it should be kept in view that the equipment can be used in future projects and may not become obsolete.
3.8 Service Support
Service support should be available in the area of project where the equipment shall be used. Service after sales is a major criterion for selection of equipment.
3.9 Versatility
Versatilityof the equipment should be given due priority. This means a machine which can be used for many jobs. The versatility promises extra profit from two directions ; (i) allows one machine to do the job of several machines and thus cutting into ownership and operating costs associated with additional plant and labour, (ii) it increases equipment utilization, which means a machine earns money when it might other-wise be idle. Now-a- days attachments can be fitted or changed quickly with the help of couplers. A balance should be maintained between reliability, operating cost, and investment cost, since selecting the lowest priced equipment can often lead to overall higher costs.
4. MANUFACTURING
Manufacture is defined as to make something from raw materials by hand or using machines. An example of to manufacture is to make clothing from cotton, automobiles in factories. It is the production of goods through the use of labour, machinery, tools and biological or chemical processing or formulation. In manufacturing, queuing is a necessary element of flexible systems in which factors of production may be continually adjusted to handle periodic increases in demand for manufacturing capacity.
It has close connections to the engineering and industrial process design sectors.
There are three main type of manufacture: - 4.1 Make-To-Stock (MTS)
In this system a factory produces goods that are held in stock at stores and showrooms.
This means that a market for the goods needs to be predicted so that the items can be produced in advance ready for the consumer. However, producing too much can mean that surplus stock needs to be sold at a loss while producing too little may mean the market is missed and costs aren’t covered by sales.
4.2 Make-To-Order (MTO)
The make to order method allows the manufacturer to wait until orders are received before production begins. This makes it much easier to manage inventories and react to market demand. However, customers will need to wait for their products to be produced and the manufacturer will need a steady stream of orders to keep the factory in production and profitable.
4.3 Make-To-Assemble (MTA)
This method is similar to make to stock, except the factory will produce component parts in a chance of orders for assembly. This means that the manufacturer is ready to fulfil customer orders as they arrive but can leave the manufacturer with a stock of unwanted parts if there is no demand.
Quality control is also an important aspect of any manufacturing process in order to protect the image of your brand and products. A successful manufacturing business requires a good mix of sales management, stock management, quality control and production costing.
5. MECHANISM OF SERVICE SYSTEM
The service mechanism describes how the customer is served. The service facility may consist of one or several situations or channels. They may operate either in parallel, in which case an arrival has to go through one channel only before being discharged from the system, or they may operate in series, in which case an arrival has to go through several channels in sequence before being discharged. Decision on the structure and nature of queues would be incomplete and remain an arm chair academic exercise without considering the probability distribution describing the service times (Griffin, 1978). The service times at each channel may be constant or random with a known service time distribution.
According to Vohra (2007), there are two aspects of a service system which the entrepreneur must consider:
(i) The structure of the service system, and (ii) The speed of service.
The structure of the service system means how the service facilities exist. There may be a single service facility, a multiple, parallel facilities with single queue, multiple parallel facilities with multiple queues and services facilities in a series. In a queuing system, the speed with which service is provided can be expressed in either of two ways - as service rate and service time. The service rate describes the number of customers served during a particular time, while the service time indicates the amount of time needed to service customers. Service rates and service times are reciprocals of each other and either of them is sufficient to indicate the capacity of the facility. In determining a particular capacity level of operation, it is incumbent on the entrepreneur to identify the cost of either increase the service rate or reduce the service time. There is also sojourn time. This is waiting time plus the service time.
The cost structure specifies the payment made by the customer and the various operating costs of the system. The goal of waiting line management is essentially to minimize total cost involved in operating the system. The entrepreneur while trying to remove idle time needs to balance the cost of offering an acceptable level of service capacity with the cost of customers waiting, and even refusing to wait for service due to delay.
According to Sharma (2009), the more the capacity increases, the less the waiting customers, time and of course, cost. It is important for the entrepreneur to identify a level
of service capacity at which cost will be minimized. The optimum service capacity level is identified by Sharma (2009) as the one that minimizes the sum of the two costs. Thus,
TC = Customer waiting cost + Capacity cost
It is essential that cost of waiting and cost of service should be such as to minimize total expected cost, and while experience and mathematical formulae may be used for simple waiting line situations, complex situations can be solved by simulation methods (Olaitan, Bojerenu and Onyebuchi, 2015).
The optimum service facility that minimizes costs, according to Griffin (1978) is also given as:
𝜇 = 𝜆 + 𝐶𝑤𝜆 𝐶𝑠 Where
𝜇 = Average service rate 𝜆= Average arrival rate
𝐶𝑤 = Cost of waiting in the queue.
𝐶𝑠 = Cost of service per unit of time
The cost structure analysis involves the use of both explicit and implicit costs elements (Aremu, 2005). Queuing models that restrict analysis of waiting line situations to the use of explicit cost are not comprehensive enough and less satisfactory. Implicit cost elements such as frustrations, boredom, irritation, man-hour loss and associated hazard arising from waiting in line are therefore essential elements to be taken into consideration (Olaitan, Bojerenu and Onyebuchi, 2015).
6. CONCLUSION
This paper presented the effect of batch size and throughput to optimize the resource utilization of a manufacturing system by using Queueing Network theory. In particular, the manufacturing system studied here is of a multiple production line nature that produces a single product. This study also found that cycle time of each station can affect the resource utilization in a particular workstation, where the higher the cycle time of a workstation, the higher is the resource utilization and this sometimes can cause bottleneck when the capacity is not enough to meet the demand requirement. To solve this problem, the quantity of the workstation having high cycle time can be increased to reduce the cycle time of the entire process so as to ensure that the utilization level of each line in the manufacturing system is balanced. Based on this study, it can be concluded that the batch size is proportional to the throughput in terms of optimizing the resource utilization of a manufacturing system.
Advantages of equipment utilization includes increased rate of output, reduction in overall cost, carrying out activities that cannot be carried out manually, maintaining the planned rate of production when there is labor shortage, maintaining high quality standard etc. Thus proper choice and use of the equipment contributes to economy, quality, safety, speed and timely completion of the project. However, delays in project execution may occur due to improper choice of equipment, unavailability of equipment at the required time, increased cycle time and waiting time and also poor technology and wrong mechanization.
These problems can be overcome by applying queuing theory for equipment selection in order to minimize the extent of delays by reducing cycle time and idle time and thus reducing the associated cost. The key to solve queuing problem is on the modeling of customers and servers. This method when formulated appropriately can be used in managing a wide variety of equipment combinations.
The study will however be incomplete without some recommendations on the possible means of improving the quality of services to make it effective and efficient. Based on the findings, the queuing problem in an automobile assembly plant can be tackled by the proper implementation of the following recommendations.
The floor space should be effectively utilized.
The management should acquire modern and appropriate handling equipment to aid the movement of parts or subassemblies from one workstation to another.
The operations at the plant should be properly designed and automated.
Increasing the number of human workers and putting in mind the cost implications.
The optimum number of workers should be selected for each station such that the overall production cost and the assembly time is minimized.
Motivating and training of staff on the use of modern equipment used in the plant.
This study is very valuable for the industry, because by knowing all information related to the performance of its assembly line, it is more effective and easier for the management of industry to plan their production in future.
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