Business Dissertations – Algorithm Production Work

Development of An Algorithm to Arrange Production Work Order For Minimizing Delay Time At An Assembly Line

Abstract

Mixed product assembly lines allow for the assembly of variable products at a time. This fits to one of the customer’s demands for product variability. In order to manufacture and assemble variable products simultaneously, it is therefore important that the work order be designed and balanced at the assembly section so that the production line works as efficiently as possible.

The time standards of different parts vary according to customer preferences. Because of the variation of different time standards, the times that parts arrive at the assembly point vary and thus generate delay at the assembly point. The problem is to how to find a way to optimize the work order so that least delay time is achieved in the line. It accounts for some relevant issues that reflect operating conditions of the real-world assembly lines to make the solution applicable universally for any type of mixed product assembly line.

Methodology includes a step-by-step process of working on how and why to: generate a random data, calculate real-time assembly line calculations, make product patterns, and sort of patterns for the creation of the Universal algorithm. Tools like Microsoft Excel are used for analyzing the generated data. This study is intended to benefit all types of assembly lines in increasing their productivity and reduce lead-time while manufacturing and assembling a variety of products. Examples are presented to illustrate the implementation of methodology.

The delay times of the original random data and the optimized work order data for four data sets with each set consisting of 500 products are compared. Ultimately, the developed algorithm optimizes the work order of products at the assembly section to aid in achieving minimum possible delay time.

Chapter 1

Introduction

Present day competition is pushing for more and more emphasis on product variability based on customer preferences. This can be achieved by installing mixed-model assembly lines which allows making similar model products at a time in a random order. In order to manufacture and assemble a variety of products simultaneously, it is important that the line be optimized and balanced so that it works as effectively and efficiently as possible. Optimization of production order of parts on an assembly line can be achieved by incorporating tools and generation of an algorithm rather than following an infinite list of steps that can be taken in order to solve a specific problem to produce a certain result.

Optimization of the production line or process parameters is an important step to elevate the productivity of a manufacturing company. Minimization of delay time along the production line is one of the optimization techniques. Delay time is a type of “Muda (Waste)” generally occurred in internal and external flows of materials, people and machines. Marc et al (2004) demonstrated that the delay problem is because of unreliable machines, queuing congestion such as starvation and blockage of material on the production line, yield uncertainty and other environmental factors that prevent efficient coordination of a production system.

In addition to these, late delivery of part for the products to be assembled may also cause a longer delay making significant loss of productivity in a production system. To solve the delay problems, most industrial environments follow mathematical calculations involving infinite set of instructions, or loops to get a desired result and process the parts based on those results while others focus on the use of finite set of instructions or list of steps and simple statistical tools to arrange these parts on an assembly line.

Thus, creating an algorithm which uses a finite list of steps using tools like Microsoft excel, visual basic helps arrange variety of products on assembly lines thus reducing the total delay time which ultimately leads to the goal of accelerating development cycle and reduce development cost. Sofia Simaria & Pedro Vilarinho (2004) demonstrated that single model assembly lines are designed to carry out a single homogenous product while a set of similar models are manufactured and assembled on mixed-model assembly lines.

Industries use numerous techniques to minimize the delay time among and between various work stations such as linear programming methods while for a large number of work stations, this becomes cumbersome and time consuming. However, using a simulation model, we can achieve far better results in a short span of time when compared to generalized models.

This study is designed to explore the application of manufacturing and production systems through a simulation mode to optimize the work order. Tools like Microsoft Excel can speed up the problem by analyzing randomly generated data with a view to improve any existing processes. The algorithm created for arranging the order of assembly lines can satisfy the needs of problem solving and process design optimization objects. Optimization of the work order will give the least delay time among sub lines at the assembly point for a variety of products.

Statement of Problem

A product has three parts (say A and B) and they are made separately in three branch production lines and are put together at the end of the three lines. Times needed to accomplish these three parts are different from product to product. For example, product 1 part A (P1A) needs 3.4 minutes, P1B 2.6, P2A 4.2, P2B4.4, and P3A 2.1, etc. As we can imagine in this circumstances, that delay at the join point is unavoidable.

For example, sample production lines with three sub lines are here. The time standards of some work stations vary according to the customer demands in a range as you can find in the chart. The researcher also generated specific time standard for a couple sample products in the table. Because of the variation of these work stations, the time that sub products A and B arrive at the assembly point, station C6 is in that station. The researcher goal is to find a way to optimize the work order so that least delay time is achieved in the line.

Figure 1: Diagrammatic representation of statement of problem

Table 1: Example for statement of problem

	product 1	product 2	product 3
station A1	1.23	3.03
station A2	3.65	2.54
station A3	6.78	5.98
station A4	4.32	3.76
station B1	2.02	1.89
station B2	5.74	2.43
station B3	3.65	4.32
station C1	1.87	3.67
station C2	4.56	2.68
station C3	2.34	4.45
station C4	1.29	5.36
station C5	6.66	3.08
station C6	4.43	4.43
station C7	1.08	1.08
station C8	2.33	2.33

In this study, a product has three parts (say A, B and C) and they are made separately in three branch production lines and are put together at the end of the three lines. Times needed to accomplish these three parts are different from product to product. As we can imagine in this circumstances, that delay at the join point is unavoidable. The problem is how to put a total of 500 or so such products in an order so that there is least delay time when these three parts are assembled together. The researcher goal is to find a way to optimize the work order so that least delay time is achieved in the line.

Guiding Research Questions

The main research question for this study is: How can a universal algorithm are created to the work orders so that the least delay time is achieved in a production line? There are several additional questions that are included in the research.

Additional questions:

• How to calculate the time taken by each part on an assembly line?

• How to find out the total time taken by each product individually?

• How do you group products to which similar operation are to be performed?

• How do you prioritize each group?

• What are the tools necessary to optimize the work order?

Once these questions are answered, a random data is generated and the generated data is treated, interpreted and shared with large-scale and small-scale industries to improve the productivity. Through out the rest of study, the researcher describe how this study was conducted, how the data was collected and interpreted, and why these data is important to this study and to small scale and mid scale industries in a real time situation.

Assumptions

The assumptions of the study are:

• The time for a certain operation on a part is constant.

• Demand of the products is known in advance.

• No additional products’ data is added during the study or the analysis.

• All the machines are in running condition without any problems. Sufficient raw material is available to feed the machines.

• All the operators are ready to work at all times.

• Number of machines on each assembly line is fixed. No other sub-assembly lines are arranged to move the machined part.

Limitations

The limitations of the study are:

• This study will be limited to only manufacture, assemble parts and make variety of products which vary slightly in their design and time-related processes such as hospital services, supply chain services.

• This study will not determine or evaluate the number of combinations for optimizing the production line as there will be millions of the combinations possible for 500 parts, as the created algorithm will use a minimum number of combinations or a finite list of steps.

• The study is limited to a number of patterns, as with the increasing in the number of patterns, dividing all the products into patterns becomes cumbersome thereby algorithm becomes complicate for creating a finite list of steps.

• The algorithm is limited to minimum variation in the patterns containing number of products, other wise there may be a situation of improper fit among the patterns.

• The algorithm is limited to the processing times in a particular range.

Justification of Study

The optimization concept is mostly introduced to traditional manufacturing systems. To my knowledge, developing an algorithm with the help of an algorithm using Microsoft Excel has not been explored. One can speed up the optimization process rather than using the traditional mathematical calculations.

Importance of the Study

In the present fast growing technology and market, a customer expects to have a right product at the right time and right location based on his requirement. In order to satisfy customer’s needs, a manufacturer (supplier) needs to make a product by altering the existing product design slightly, and introduce in the market in a bulk quantity in shortest possible time. This study helps manufacturers choose exact work order so as to make the products minimizing the delay time. This potentially brings to maximize the productivity which in turn maximizes the sales, profits etc.

Benefits of Research

This study will be beneficial for manufacturing industries to use the Manufacturing and Production Systems concepts using modern tools in the corporate world. Since it can be introduced in a simulation mode, it is especially beneficial for smaller companies who can not afford to implement the software that costs thousands of dollars for their production lines.

In addition to this, it benefits all manufacturing industries in increasing their productivity and reduces lead-time while manufacturing and assembling a variety of products. The intended audiences for the study are juniors, seniors, researchers, educators and industrialists who are interested in learning and implementing the application of various technologies.

Audience will gain knowledge on how to use and integrate various tools for optimization of work order on any mixed model assembly line. Based on the examples presented to illustrate the implementation of algorithm, there is a huge scope for the intended audience to implement it in real world.

This particular issue is important to several groups of small scale industries, work shops, retail stores, government offices, fast food centers. The findings of this research will aid industries, retails stores by demonstrating how the algorithm is currently used, and how retail stores can assist customers to implement universal algorithm. Industries may benefit from models of evaluating arrangement of parts of a product on an assembly line.

Furthermore, Industries can benefit from identifying the pitfalls for their productivity. Ultimately, the industries will benefit because the purpose of universal algorithm will aid in improving the process. This research may benefit these industries by providing a better understanding of how universal algorithm is used in real-time situations, and what can be done to help integrate current technology into more industries.

The researcher believes that small-scale industries may receive an immediate benefit. With this study, the industries may be able to determine what and how to minimize delay time to improve productivity. Helping industries more with algorithms, industries ultimately become the beneficiaries of the research.

Definitions

The terms “assembly line” or “work stations” are often misunderstood as a physical form of an object. In this section, definitions are provided for those terms and other terms that are often used in manufacturing and production systems.

Assembly plant & Assembly line

A physical plant housing assembly lines, where production-line assembly work is performed. Assembly lines consist of several work stations at which products are processed (Agpak and Gokcen, 2005). All the material handling from the work station or storage area to the assembly line is done with the help of standard containers (Mauricio et al 2008). It is a production method requiring workers to perform a repetitive task on a product as it moves along on a conveyor belt or track. Assembly line has advantages of part standardization and rationalization of work.

Work station

Work stations are places where some tasks (operations) on products are performed. Products stay at each work station of a cycle time which corresponds to the time interval between successively completed units (Agpak & Gokcen 2005).

Assembly line balancing

Assembly line balancing is the assignment of various tasks to the work stations while optimizing one or more objectives with out violating restrictions imposed on the line. Some objectives include minimization of cycle time and work load smoothness (Kim 1996). Amen (2001) defined assembly line balancing as the assignment of a given number of tasks (I) with different time durations (dt,max/dt,min) at workstations to a not yet known number of stations under certain restrictions.

Time standard

It is the time taken by the machine to perform a process on a particular part or the product. These time standards are taken randomly for this study with the help of Microsoft Excel tool.

Random data

Data is picked randomly with out any reference level. The range of data under study was from 1 to 10 where 1 represents the time taken by the machine to process is 1 second and 10 represents the time taken by the machine to process the part in 10 seconds.

Simulation

According to Schriber (1987),”simulation is the modeling of a process or system in such a way that the model mimics the response of the actual system to events that take place over time.” It is a mathematical representation of interaction of real-world objects.

Basic Formulae

Lead-time calculation (general) Lead-time = Processing time + delays

Processing time is the time taken by a machine to perform a task on a particular part.

Delay time is the waiting time of a part at the machine for the operation to perform on it. Summary

In this chapter, the problem has been stated followed by a set of guiding research questions to analyze and proceed to think over the problem. Then, the study assumptions, limitations are noted stated in order the study to be valid and it follows various important definitions for the terms used in the study. In the next chapter, the researcher discusses the literature review related to the study.

Chapter II Literature Review

Introduction

To research on what algorithm will arrange the order of parts to minimize the delay time on the production line I conducted a review of literature. At this stage of my investigation primary focus is to provide basic information about lean manufacturing concepts; the different tools used in lean manufacturing are presented. Other parts included in this chapter are about assembly line, lead time, delay time, algorithm and tools used to generate algorithm. This investigation begins with a review of mixed model assembly lines in the first part followed by lead time in the second part.

Lean Manufacturing

After World War II, there was a continuous improvement in the manufacturing industries. Development in production technology helped people to improve efficiency at their work. Much impact took place when these technologies were come into existence. Invention of the computer and usage of the information technology has also helped industries to produce more and more using less and less resources. There are many developments in manufacturing and production of products like lean manufacturing, Toyota production system, and Kaizen.

Japanese manufacturers Taiichi Ohno (1940) and his technical collaborators focused on the continuous flow in small-lot production and developed a disciplined, process-focused production system known as the “Toyota Production System” or “Lean Production”. And Ohno is regarded as the founder of the Toyota Production System (TPS). The ultimate goal of Lean manufacturing is to find and eliminate muda so as to make value added products, processes and systems. Lean manufacturing is defined as “an operational strategy oriented toward achieving the shortest possible cycle time by eliminating waste” (Retrieved from Web, 2008).

Lean Tools

Chu (1996) stated that 5S concept is from the Japanese words Seiri, Seiton, Seison, Seiketsu, and Shitsuke, are simple but effective methods to organize the work place” (p.1). Dennis (2002) stated that 5S is used to create a safe, clean, well organized, and efficient work environment. 5S audits are done regularly. The audit contains checklist and it varies depending on the area to be audits.

Dennis (2002) defined all 5S’s in the following way.

Sort The first S focuses on eliminating unnecessary items from the work place.

Set The second S focuses on efficient and effective storage methods. Some questions to ask are: What resources do I need to do y job? Where should the resources be located? How should the resources be identified?

Shine The third S focuses on cleaning after clutter and waste has been eliminated. Workers take ride to clean; organized work area and this step can also foster employee ownership in their work areas. They also become aware of surroundings and equipment they operate and begin to notice changes and potential problems. Oil and coolant leaks, vibration, misalignment ad loose parts are some of the symptoms of future problems they may recognize while keeping their work areas clean and organized.

Standardize This S involves establishing and applying standards to the first three S’s. These standards should be clear, simple and visual. Schedules and methods of performing the first three S’s are established to aid workers in maintaining the program. Inspections involving the effected workers of an area can be implemented to measure performance and promote employee involvement.

Sustain The last S is by far the most difficult to achieve and implement. Workers are human and tend to resist change. Sustain focuses on defining a new status quo and standards of organization.

Lean Manufacturing Principles

Womack and Jones (1996) describe the business environment within which they saw Lean techniques being successful. Five key principles emerged:

• Value

• Value Stream

• Flow

• Pull

• Perfection

Value

Rich (2001) defined the definition of ‘value’ from the customer perspective which is the only reason why businesses exist; therefore an understanding of what the customer actually requires is an essential element of the strategy of a lean organization. Ikovenko and Bradley (2004) stated that the value, defined from a customer’s perspective, is then aligned within the organization and value-adding activities can be recognized as any activity that the customer is happy and prepared to pay for.

Womack and Jones (1996) estimated that for a typical manufacturing firm, value-adding accounts for less than 5% of the total time a material is at the factory. Womack and Jones (1996) horrified to think that remaining 95% of the time is spent adding costs (storage, delaying at queues within the factory, transportation between the stages of the process, etc.).

Even more frightening still is the knowledge that such wastes are present at every supplier; customer and distribution point as the product moves towards the actual consumer and that many other types of “Muda” (wastes) have actually been “designed into” the internal and external material flow process. The principles of Lean manufacturing and thinking provide a method to specify and add "Value" while combating "waste", referred to as “Muda “(The Japanese word). Waste is the result of the over use of any resource required to produce a product or deliver a service. Waste is also identified as idle time where no value is being added to a product or service.

There are eight types of muda proposed by Taiichi Ohno:

Motion

Motion waste occurs when there is unnecessary walking, reaching, or twisting for a material to process.

Delay

Waiting waste occurs when a worker has to wait for a material, part, or product to be delivered for an assembly.

Lead time = Processing time + Retention time

As delay increases retention time increases, which far exceeds processing time in more manufacturing operations.

Conveyance

Conveyance waste occurs when a large-scale waste is caused by an inefficient work place layout, overly large equipment. This waste occurs when large batches are to be removed from process to process. It can be eliminated by making smaller batches and moving processes closer together.

Correction

Correction waste occurs when there are defective parts in made products. These defective parts will consume all material, time, and energy involved in making and repairing defects.

Over processing

Over processing waste occurs, making parts more than what customer is required. This type of muda often exists in companies by engineering departments.

Over production: Over production waste is a combination of all the six types of muda.

Inventory

Inventory waste occurs when keeping unnecessary raw materials, parts, and work in progress (WIP).

Knowledge disconnection

Lack of exploiting the knowledge and talent of employees

Value Stream

Garnett, Jones and Murray (1998) pointed that once value has been specified, the next step is to make the value stream so as to make the entire production process. The value stream identifies all those steps required to make a product. Ikovenko and Bradley (2004) stated that the traditional key technique behind the value stream is process mapping.

Process mapping is a work flow diagram to better understand a process or a series of parallel processes. It is to understand how value is built in the product from the client point of view. The value stream map is used to both illustrate the “current state” and the desired “future state” of the process. The map highlights the seven types of Muda mentioned above and is used to provide a basis for developing plans to implement lean tools and techniques.

Flow

Flow in this study is to ensure materials flow within a factory and derive value rather than cost, involving elimination all types of Muda. Ikovenko and Bradley (2004) defined flow as producing a product from raw material to completion without unnecessary interruption or delay (that is, Muda). Rich (2001) states that the goal is to achieve single-piece flow in each process, ensuring work flows smoothly from one stage to the next, one at a time. As a result, we will get reduction in work in progress, part movement, parts handling, quality defects and therefore, the lead time.

The key objective of material flow is to align the processes to suit the customer requirements, thus reducing waste in the system. The key tools for implementing Flow are:

• “Takt Time”

• Standardized Work

• 5S

• Work Balancing

• Leveled Production

Pull

At a strategic level, Pull really identifies the need to be able to deliver the product to the customer as soon as the needs it. This principle derives from Toyota’s innovation, Kanban. Kanban is a tool that communicates specific production/withdrawal of parts information to the upstream process. The Kanban applies for the lean approach where the flow of materials in not organized between departments or processes. At these points it is important to have materials available when required and these key buffers effectively disconnect the internal (or external) customer and supplier operations.

Perfection

Once an improvement is made, it must become the standard for the process. Adhering to this standard will ensure that the problems experienced in the past do not occur any more. It is important to understand that transformation to Lean is a continuous improvement process.

Assembly line

A critical problem that is faced in almost all production systems is the uncertainty of the delivery lead times at the assembly section. Marc et al (2004) demonstrated that this problem may be because of unreliable machines, queuing congestion such as starvation and blockage of material on the production line, yield uncertainty and other environmental factors that prevent efficient coordination of a production system. In addition to this late delivery of part, the parts to be assembled to make a product will cause a longer delay making significant loss of productivity and throughput in a production system.

Moallem (2003) researched on the lead time uncertainty, cost optimization, and inventory control for the products but could not discuss lead time variability that causes productivity and throughput significantly. The operational characteristics of a production system (e.g., Takt time, lead time, machining time, walking time, etc.) have significant statistical effects on the overall system productivity and lead-time decision (Grasso & Taylor, 1984).

Simulation method can be used for a manufacturing facility through which bottlenecks within the plants can be identified (Bruce& Saeid, 1996). Bruce & Saeid (1996) developed a tool that automatically predicts the optimum level of work in progress, depending on parameters such as product mix and batch sizes. Redin (1996) said that one must not only improve the inherent reliability, but also should minimize the downtime on the assembly line due to the lack of machined parts. Kurosu, Ohmae & Kashiwa proposed a method and an apparatus for ordering a working operation in an assembly lines having sub lines in which parts from different models are assembled.

They also claimed that for an automobile body assembly line where products for different models are manufactured in a common assembly line identification of each product on the lines with codes, sub codes, serial and sub serial numbering will be useful to better order and identify the parts. Haq, Jayaprakash and Rengarajan dealt with mixed model assembly line balancing for n models, and used a classical genetic algorithm for minimizing the number of work stations. They also incorporated the modified ranked positional method to reduce the search space within the global space there by reducing the search time.

Researchers developed different algorithms either mathematical (Randhawa et al., 1985; Ji et al., 1994) or heuristic (Mettala and Egbelu, 1989; Sadiq et al., 1993; Kim et al., 1996), to optimize different factors in an assembly. These genetic algorithms were introduced by Holland in 1975 (Holland, 1975), is one of the heuristic methods to find a near-optimal solution. Vhed and Moghaddam proposed a memetic algorithm to determine the suitable sequence where a variety of products models similar to product characteristics are assembled in a just in time production system.

Tamura, Long, and Ohno researched on the diversification of customer preferences and installed mixed model assembly lines in many manufacturing plants. They dealt with the sequencing problem with a bypass line and formulated the goals of leveling part usage rates and workloads using goal chasing method, tabu search and dynamic programming. Bock, Rosenberg and Breckel proposed a new approach for an adaptive real-time control of assembly lines by extending the sequencing problem by integration of specific line balancing and mapping of the distribution scenarios.

Lead & Delay time

Minimizing the lead time in a production line may be of a different type. Some researchers worked a variety of situations like optimizing the production line with all parts processed on all the machines with or without random lead times. Peters and Degraeve (2006) proposed an easy-to-compute performance bounds for a single-product assembly system. Jing-Sheng & David (1996) carried out a similar research where the components (subassemblies) are built to stock with which a final product is to be assembled.

They proposed that it is desirable to keep higher base-stock levels for components with longer lead times (and lower costs). But, none of them worked on the assembly lines with few parts needed some operations and other parts need all the operations to be done on an assembly line having random lead times.

A eight-level hierarchical, factor/decision taxonomy is derived and organized that could impact the design, balancing and scheduling of assembly systems that is used to assess the progress in assembly system design and operation (Gagnon& Ghosh, 2002 ). The application of genetic algorithms for the optimization of asynchronous automatic assembly stochastic systems are initiated that are subjected to blocking and starvation effects (Wellman & Gemmill, 1995).

By optimizing the production lead time, lead time for manufacturing a product including assembly can be optimized/minimized through which productivity and throughput can be increased greatly. The reduction of production cycle time (the time from when an order is placed until it is delivered) is an extremely important and challenging problem facing the manufacturing industry (Kodek and Krisper, 2004).

The algorithm that is going to be proposed in this study allows us to obtain new insights regarding the machining operations, lead time delivery reliability, production line design and optimization of lead times along any production line. This algorithm designs a production line that can be composed of both typical and flexible machines which is much faster than the general integer programming approaches that are used so far for optimizing the production lead times, production costs.

Algorithm

Boolos & Jeffery (1974, 1999) defined algorithm as a well-defined set of instructions to accomplish a task. When the initial conditions are given, it will proceed through a set of instructions and eventually terminates in the end-state. They also stated that the purpose of the algorithm is to run enumerable infinite sets with the given initial condition which is a time consuming process for a human being to calculate, run or execute such infinite sets. Algorithms are expressed in many ways such as programming language, pseudo code, flowcharts and natural languages. In this study, a flow chart is developed to represent the set of instructions to accomplish the goal. Then a programming language is written to execute the algorithm with the help of Microsoft Visual Basic. Microsoft Excel tool is used to record and analyze data.

Fable (2006) described a depth-first, branch and bound algorithm for solving the type one line balancing problem where the objective is to minimize the number of work stations if the cycle time is given. With this Fable algorithm found good solutions to instances containing 1000 or more tasks, continued to find the optimal verifiable solution for minimizing the number of work stations. Much research has been carried out by Japanese manufacturers in creating algorithms in the field of assembly lines fro minimizing the cycle time by balancing U shaped JIT lines and number of work stations.

Yeo, Yong & Yeongho (1996) created a genetic algorithm for assembly line balancing with various objectives such as minimizing number of work stations, minimizing cycle time, and minimizing work load smoothness. Simaria & Vilarinho (2004) presented a mathematical programming model and iterative genetic algorithm procedure for the mixed model assembly line balancing problem for parallel work stations to maximize the production rate of the line for a pre-determined number of operators.

Microsoft Excel is a tool developed by Microsoft Corporation. It helps to compile and execute the logic mentioned in algorithm. The data is retrieved and read from the Microsoft Excel, which serves as an input data for the program to execute. There are many algorithms developed in the mixed model assembly lines to minimize the delay time, but no research has been carried out on mixed model assembly lines where the delay time at the assembly point id reduced. This study deals with the algorithm that minimizes the delay time at assembly section.

Summary

Lean manufacturing is proving to be the 21st century manufacturing strategy. All the tools properly implemented, and integrated will prove beneficial. This chapter provided the background information required for the understanding the independent study. Discussed in the next chapter is the methodology for an algorithm and the data collection used for the independent study.

Chapter III Methodology

Introduction

This study is designed to explore the knowledge needed to create a mixed-model assembly line algorithm for small and medium sized manufacturing industries. More specifically, the delay time at the assembly section is minimized with the help of mixed-model assembly line algorithm there by improving throughput and productivity. Many small and medium sized manufacturing companies are facing a challenge in designing algorithm for mixed-model assembly lines that allow the assembly of a similar model of products at a time in a random order and mix.

Because of the current competitive market and customer focus on higher product variability, times needed to accomplish the assembly of parts at the end of assembly line are different from product to product. Once the algorithm is created, small and medium sized can implement in their industries to improve productivity there by minimizing delay time which is a form of waste.

In this chapter, the researcher introduced methods utilized to conduct this independent study. This chapter will include the method used and why it was used, the procedure to analyze, how and why a random data was developed, and the observation of production rate on each assembly line for this generated random data. Throughout the rest of the chapter I will also explain the data collection process and the number of products included in this study.

Guiding research questions

The primary research question explored was: What algorithm will arrange the order of parts of a production line achieve a minimum delay time? The secondary research question was: How to prioritize the parts and what is the reference level to prioritize so as to optimize the delay time? Additional questions may be answered in this study, including:

• What are the various tools needed to optimize the production work order?

• How does one find out the delay time between the parts of each product and between preceding and succeeding products in a real-time situation?

• How does one find out the total time taken by each product to process and assemble on a production line?

Restatement of the problem

A product has many parts (say A, B, C and so on) and they are made separately on different branch production lines and are put together at the end of the production lines. Times needed to accomplish all these parts are different from product to product. The time standards of some work stations vary according to the customer demands in a range. Because of the variation of these work stations, the time that sub products arrive at the assembly point is unpredictable and thus generates delay in that station. My work is to find a way to optimize the work order so that least delay time is achieved in the line at the assembly station.

Research Design

For every research proposal, a definite framework exists to follow a certain pattern. Creswell (2003) suggested that from lots of different types and terms in the literature, mainly focused on three approaches: quantitative, qualitative, and mixed methods approach. The first two has been available for decades, and the last is new and still developing in form and substance. To understand them, we need to consider three framework elements: philosophical assumption about what constitute knowledge claims, general procedures of research called strategies of inquiry, and detailed procedure of data collection, analysis and writing, called methods.

For that Creswell (2003) proposed (which was developed by Crotty) three questions to the design of research:

• What knowledge claims are being made by the researcher?

• What strategies of inquiry will inform the procedures?

• What methods of data collection and analysis will be used?

This study utilizes the quantitative methods of research. Creswell (2003) stated that the quantitative approach is “one in which the investigator primarily uses post-positivist claims for developing knowledge (i.e., cause and effect thinking, reduction to specific variables and hypothesis and questions, use of measurement and observation, and the test of theories), employs strategies of inquiry such as experiments and surveys, and collects data on predetermined instruments that yield statistical data”.

Framework Elements of Quantitative Research

Knowledge claims

Stating a knowledge claim means that researcher start with a project with certain assumptions about how we will learn and what we will learn during their inquiry. These are called as paradigms. Philosophically, researchers make claims about what is knowledge (ontology), how we know it (epistemology), what values go into it (axiology), how we write about it (rhetoric), and the process for studying it (methodology). There are four schools for knowledge claims as what follow. Those are post positive knowledge claims, socially constructed knowledge claims, advocacy or participatory knowledge claims and finally pragmatic knowledge claims.

For quantitative research, the knowledge claims are post positivism which includes determination, reductionism, empirical observation and measurement, and theory verification. Post positivism refers the thinking after positivism; challenging the absolute truth and recognizing that we can not be “positive” about claims of knowledge when studying the behaviors and action of human.

Post positivism reflects in determining the effects or outcomes, examining the causes that reflect the outcomes by doing experiments, reducing the ideas into a small, set of ideas to test such as variables that constitute hypothesis and research questions, developing numeric measures of observations and studying the behavior of individuals. The problem studied by post positivist reflects a need to examine causes that influence outcomes. It is also reductionism; testing selected variables that constitute hypothesis and research questions, so it is based on careful observation and measurement of the objective reality in the world.

The quantitative method allow researcher to make generalizations about the population being generated random data. These generalizations will be able to be passed on to various industries. The generalizations made in this study may be able to be replicated should another research decide to replicate this study. This concept that the research could be replicated is unique to a quantitative study.

Strategies of inquiry

A stage of inquiry in quantitative research includes numerical summaries, generalizations across populations and comparisons between populations. Strategies of inquiry provide specific designs for procedures in the research design. Like knowledge claims, strategies have multiplied over the years as the computer technology has pushed forward data analysis and the ability to analyze complex models.

These include true experiments and less vigorous experiments called quasi-experiments and correlational studies (Campbell & Stanley, 1963), and specific single-subject experiments (Cooper, heron, & Heward, 1987). But, these days, quantitative research strategies involved complex experiments with many variables and treatments like factorial designs and repeated measure designs. Strategies associated with quantitative approach are:

Experiment: It is about random assignment of subject to treatment conditions and includes quasi-experiment with nonrandomized design. My study used experimental strategy for generating the randomized data and analyzing the data with Microsoft office tools.

Non-experimental designs, such as Surveys: it is studying by using questionnaires or structured interviews with the intent of generalizing from sample to a population. These include cross-sectional and longitudinal studies using questionnaires or structured interviews for data collection, with the intent of generalizing from a sample to a population (Babbie, 1990). The quantitative method was selected because it can be interpreted numerically and communicated through the use of statistical figures. The problem of how to put a total of 500 or so such products in an order so the delay time is least when the parts are assembled together.

Research methods

The third major element that goes into a research approach is the specific methods of data collection and analysis. For quantitative research, the research methods the researcher used are predetermined instrument based questions such as performance data, attitude data, observational data and census statistical data using Microsoft Excel. The researcher considered full range of possibilities for data collection in the study by organizing these research methods with the use of closed-ended versus pen-ended questions and their focus on numeric versus non-numeric data analysis.

The specific methods for this study is developmental designs consisting of a pure experimental (cause and effect relationship between variables) cross-sectional study. The definition of developmental designs, according to Leedy (2005) is “the method enables the researcher what to study how a particular characteristic changes another characteristic over a period of time.”

The specific research method utilized for achieving the minimum delay time was a developmental design involving a pure experiment. A pure experiment, according to Ismail (2005), is “type enables us to manipulate an independent variable (IV) in order to see the effect on the dependent variable (DV).” In this study, independent variable is the order or arrangement of products for feeding on assembly lines and dependent variable is delay time. Pure experiment manipulates an independent variable (IV - arrangement of products) in order to see the effect on the dependent variable (DV-delay time).

Procedure of the study

The following were the key points in the procedure of the study. The procedures were to:

• Generate a random data with Microsoft Excel

• Analyze the generated data for the delay time with the normal calculation methods

• Then, analyze the generated data with the developed algorithm by arranging the work orders and

• Finally, compare the results of the analyzed data with the results of the initial data.

Data Collection

In order to observe the flow of parts on an assembly line, data can be of anything in a real-time situation. As the algorithm should fit for any time of data, a random data is generated using operators in Microsoft Excel. A random data is a data, generated with the help of Excel that produces a difference or a variable numbers between ranges of numbers. The random data generated with the help of Microsoft Excel is used to determine the variability in the lead times in the work stations for a universal application. It is believed that the random data will show that there is a significant difference between the lead-times along the sub lines and at the assembly point.

Random data generation using Microsoft Excel

Product 1:

=RAND ( ) is the general formula used to generate random data.

A data for 500 products was created containing numbers ranging from 1.0 to 10.0. This was generated on the Microsoft Excel sheet. The data is generated for an assembly of three different products each processing on three assembly lines. Each assembly line consists of three different processes. The random data was created for product number 1 by copying the cells along the row.

Products 2-500:

After the data for product 1 is created, it is copied to create data for rest 499 products. The entire row containing values of product 1 is copied using copy function – Ctrl + C or Standard tool bar – Edit – Copy. It is pasted on 499 cells below the product 1 data that is created.

Data under study

The created data values are copied to another Excel sheet for analysis. Because, each and every time the data changes on hitting the ENTER key. The large sample can be justified by several different arguments. Many industries produce variety of products in a random mix order. These products are in very a big n umber.

These industries may produce other types of products larger than the sample taken, and may not be adequately represented in a smaller sample. The next step was to analyze the data. After the first task, that is generation of a random data of a production line, it is ready for analysis.

From the data obtained, the researcher will be able to analyze the algorithm from flow of parts on the assembly line to discover the usefulness of this algorithm.

Instrumentation

The instrument used to gather the data was Microsoft Excel, a powerful tool of Microsoft Office suite. Microsoft Excel is a spread sheet application written and distributed by Microsoft Corporation. The tool “Microsoft Excel” is an electronic spread sheet that allows a researcher to manipulate data displayed in the form of a table. The table, known as a spreadsheet, is divided into rows and columns to form a grid; you simply insert the data you have collected into appropriate cells within the grid.

Excel also has a variety of features such as calculation, graphic tools, and a macro programming language called Visual basic for Applications which can be used for an algorithm. Microsoft Excel was an essential tool in my study for determining the various formulae using operators either to create a random data or extract data from the raw data file or to analyze the existing data or to format the graphical system of the analysis. The beauty of electronic spreadsheets is that once you enter the data into them, the software can quickly and easily make the instructed calculations.

Microsoft Excel tool is used to generate a random data, and customize the random data to arrange the order of products, and analyze the obtained results to make more informed decisions, because the process of organizing large amounts of data was a cumbersome, time-consuming, and tedious task. Microsoft Excel window has many of the same attributes as other windows in the Microsoft Office Suite. The table below lists the new features and provides a brief description of each one.

Table 2: MS Excel spread sheet terminology

Attribute	Description
The Menu Bar	The words listed atop the application window, immediately underneath the Title bar. You can access all application commands from the Menu Bar.
The Standard Toolbar	The row of icons immediately underneath the Menu Bar, which provide quick access to commonly used function commands.
The Formatting Toolbar	The second row of icons immediately underneath the Standard Toolbar, which provides quick access to commonly used formatting commands. The Standard and Formatting Toolbars might share the same row when you first open Excel.
The Formula Bar	Located immediately underneath the Formatting Toolbar, it displays the constant value or formula used in an active cell.
The Name Box	The box at the left end of the Formula Bar that identifies the selected cell, chart item or drawing object.
Column Heading	The lettered gray area at the top of each column.
Row Heading	The numbered gray area to the left of each row.
The Sheet Tabs	The tabs near the bottom of the workbook window that displays the name of the various worksheets.
The Task Pane	The area on the right hand side of the screen that allows you to easily access various commands, such as opening a new or existing workbook.

Figure 2: Diagrammatic representation of an MS Excel spread sheet

Spreadsheets would also be useful to researchers even if they were only capable of listing data and adding up different columns ad rows. But, in fact they allow the researcher to do many other things as well. In addition to this, excel can also be used in various languages such as English, Spanish, non-Latin based languages, such as Arabic or Chinese with the help of two methods. The two methods are Set Language method and Language Bar method.

The method that you choose is based on the different languages that you use and your personal preference. Other Equipment used is Hewlett Packard 2007 model computer build with Windows Vista Home Version operating system and installed Microsoft Office Suite which includes Microsoft Office 2007. Microsoft Office 2007 is used to collect, design, and organize the data.

Some generalizations may be made from this study. A few concepts of what generalizations will be made may be between the order of parts fed into assembly lines and the delay time taken to make and assemble a complete product, the amount of total time taken at the assembly point and delay time. These generalizations are important to this study and contribute towards the research of what algorithms can de help industries to improve their productivity. Finally, the researcher finds a step-by-step process for minimizing the delay time occurring at the assembly section.

Analysis of Data

Analysis of the data was the most required part of the study. Data analysis is the act of transforming data with the aim of extracting useful information and facilitating conclusions (Wikipedia). Based on the data collected with the procedure followed above, the real time analysis is performed to find the total delay time for making 500 products on three assembly lines with each assembly constituting of three work stations. For consistency of results and the algorithm, four sets consisting of 500 products were tested. During the analysis on the generated data with Microsoft Excel, the key points to be followed for the implementation of the developed algorithm were:

Algorithm

1. Randomly create a product data using Microsoft Excel.
2. Calculate the times taken to make each part of the product on the machines.
3. Calculate the total delay time taken by each type of product.
4. Find the total time taken for making all products – Delay time without using algorithm.
5. Categorize the type of products into different patterns.
6. Group each type of the pattern products at one place. Find the delay time for each product of each pattern at the assembly station
7. Rank the products of each pattern based on the delay time and other criteria which effectively minimizes the delay time
8. Sort the patterns in a pattern to fit with other type of patterns
9. Calculate the time standard differences of each product for their respective pattern.
10. Merge the products of paired patterns by delay time so as to fit the processing times of both products
11. Merge all the merged paired products and fit the rest of the products by delay time to product minimum delay time.
12. Repeat the process for all other paired patterns. Repeat the process for all the types of patterns and rank them based on the delay time.
13. Find the delay time after implementing the algorithm – Optimized delay time using developed algorithm.

Summary

In this chapter, the researcher discussed the guiding research questions, and brought focus on the framework elements of research. The researched also explained the purpose of choosing quantitative study. Then, the researcher explained the methodology using, why the researcher chose that methodology and why not to use other methods. The method that was used to collect data is explained in detail including the instruments used for collecting the data. The next chapter will be the chapter devoted to research and analysis. It will include the created algorithm and arranged data of how the delay time is minimized.

Chapter IV Results

Introduction

The developed algorithm for the optimization of time standards at the assembly section was investigated on four different data set test cases to confirm their validity and to optimize their parameters. To assess their efficiency, an assembly line with three sub-lines and three operations in each sub-line (3´3) is solved. The problem of delay time at the assembly section can be minimized by applying the following algorithm.

Application Application of the algorithm to a three by three machine assembly line for a 500 products resulted in the following: Step 1: Randomly create a product data using excel. Each product consists of three parts. Each part is separately processed in a three-operation sub-line. Table 3 is a set of such generated data. In the table, rows refer to product numbers and column refers to operation numbers in different sub-assembly lines for the three parts. In columns, each part consists of three machines. What filled in the Table are time standards, which are ranging from 1 to 10 with one decimal.

Table 3: Representation of data of products on an Excel Spreadsheet

		Assembly line 1			Assembly line 2			Assembly line 3
		Part1			Part2			Part3
Product	M/c1	M/c2	M/c3	M/c4	M/c5	M/c6	M/c7	M/c8	M/c9
1	4.8	3.4	5.6	6.0	4.6	3.9	1.5	4.2	5.3
2	1.5	7.9	3.1	2.9	8.7	6.1	0.1	6.7	0.5
3	9.7	5.7	5.2	3.3	1.3	4.4	0.2	6.5	5.6
4	1.3	3.1	6.1	0.8	1.2	6.9	7.2	8.5	4.7
5	2.2	5.9	3.4	3.4	6.7	7.9	2.2	6.9	0.5
6	0.6	9.9	6.6	2.8	6.1	8.9	0.1	7.0	5.3
7	6.2	1.6	5.9	6.3	5.1	4.9	6.5	9.9	5.4
8	1.0	9.8	6.4	5.9	1.7	1.3	7.2	8.9	3.3
9	3.6	8.2	8.0	4.9	4.2	0.3	6.0	9.7	4.1
10	8.6	1.7	7.2	1.3	5.6	7.4	4.5	1.2	5.8

Step 2: Calculate the time taken for making each part on three machines. Then calculate the total time taken for making and assembling the product based on the order of the products and time standards listed considering the real-time situation (See Table 4). The total time is calculated as the maximum time taken by the part among the three parts that arrive at the assembly station as shown in Table 4.

Table 4: Actual time to process products

Part 1 actual time(T1)	Part2 actual time(T2)	Part 3 actual time(T3)	Max T among 3 Parts	Min T among 3 Parts	Delay Time for 3 Parts	Time for each Products
14	15	11	14	11	3	14
12	18	7	18	7	11	18
21	9	12	21	9	12	21
11	9	20	20	9	11	20
12	18	10	18	10	8	18
17	18	12	18	12	6	18
14	16	22	22	14	8	22
17	9	19	19	9	10	19
20	9	20	20	9	11	20
17	14	11	17	11	6	17

Step 3: calculate the delay time for each product. This is calculated as the difference of the maximum time and the minimum times taken by the parts for making the product. Then, adding up all the delay times to calculate the total delay time, which is referred as a waste in the system.

Step 4: Find the total time taken for making each part individually in three separate rows. And find the difference of the maximum time and the minimum time as shown in Table 5, Table 6, Table 7 and Table 8.

Table 5: Processing time of part 1 in real-time situation

Part 1

Machine 1

Machine 2

Machine 3

Start	End	Start	End	Start	End
0.0	4.8	4.8	8.1	8.1	13.7
4.8	6.2	8.1	16.1	16.1	19.2
6.2	15.9	16.1	21.8	21.8	26.9
15.9	17.2	21.8	24.9	26.9	33.1

17.2	19.4	24.9	30.8	33.1	36.4
19.4	20.0	30.8	40.8	40.8	47.4
20.0	26.2	40.8	42.4	47.4	53.2
26.2	27.2	42.4	52.2	53.2	59.6
27.2	30.8	52.2	60.4	60.4	68.4
30.8	39.4	60.4	62.1	68.4	75.6

Table 6: Processing time of part 2 in real-time situation

Part 2

Machine 1

Machine 2

Machine 3

Start	End	Start	End	Start	End
0.0	6.0	6.0	10.6	10.6	14.5
6.0	8.9	10.6	19.3	19.3	25.4
8.9	12.2	19.3	20.6	25.4	29.7
12.2	13.0	20.6	21.8	29.7	36.6
13.0	16.3	21.8	28.5	36.6	44.5
16.3	19.2	28.5	34.7	44.5	53.4
19.2	25.4	34.7	39.7	53.4	58.3
25.4	31.3	39.7	41.4	58.3	59.6
31.3	36.3	41.4	45.7	59.6	59.9
36.3	37.6	45.7	51.2	59.9	67.3

Table 7: Processing time of part 3 in real-time situation

Part 3

Machine 1

Machine 2

Machine 3

Start	End	Start	End	Start	End
0.0	1.5	1.5	5.7	5.7	11.0
1.5	1.5	5.7	12.3	12.3	12.8
1.5	1.8	12.3	18.8	18.8	24.4
1.8	9.0	18.8	27.4	27.4	32.0
9.0	11.1	27.4	34.2	34.2	34.8
11.1	11.2	34.2	41.2	41.2	46.5
11.2	17.7	41.2	51.1	51.1	56.5
17.7	24.9	51.1	60.0	60.0	63.3
24.9	31.0	60.0	69.7	69.7	73.8
31.0	35.4	69.7	70.8	73.8	79.6

Table 8: Delay-time for products occurred in a real-time situation

MaxT among 3 Parts	Min T among 3 Parts	DelayTime for 3 Parts
14.5	11.0	3.5
25.4	12.8	12.5
29.7	24.4	5.3
36.6	32.0	4.5
44.5	34.8	9.7
53.4	46.5	6.8
58.3	53.2	5.0
63.3	59.6	3.7
73.8	59.9	13.9
79.6	67.3	12.3

Step 5: Categorize the products into six different patterns as six different types of products can be made on a three by three assembly line as shown in Table 9. These patterns are categorized based on the time standard for making each part on the respective assembly lines.

Table 9: Categorization of data into patterns

Pattern	Part 1	Part 2	Part 3
A	Low	Medium	High
B	High	Medium	Low
C	High	Low	Medium
D	Low	High	Medium
E	Medium	High	Low
F	Medium	Low	High

In Excel, this categorization is done with the help of “if – else” condition in excel.

Table 10: Sorting of the data into patterns

Assembly line 1

Assembly line 2

Assembly line 3

		Part1			Part2			Part3		PATTERNS
Product	M/c1	M/c2	M/c3	M/c4	M/c5	M/c6	M/c7	M/c8	M/c9
1	4.8	3.4	5.6	6.0	4.6	3.9	1.5	4.2	5.3	E
2	1.5	7.9	3.1	2.9	8.7	6.1	0.1	6.7	0.5	E
3	9.7	5.7	5.2	3.3	1.3	4.4	0.2	6.5	5.6	C
4	1.3	3.1	6.1	0.8	1.2	6.9	7.2	8.5	4.7	F
5	2.2	5.9	3.4	3.4	6.7	7.9	2.2	6.9	0.5	E
6	0.6	9.9	6.6	2.8	6.1	8.9	0.1	7.0	5.3	E
7	6.2	1.6	5.9	6.3	5.1	4.9	6.5	9.9	5.4	A
8	1.0	9.8	6.4	5.9	1.7	1.3	7.2	8.9	3.3	F
9	3.6	8.2	8.0	4.9	4.2	0.3	6.0	9.7	4.1	C
10	8.6	1.7	7.2	1.3	5.6	7.4	4.5	1.2	5.8	B

Table 11: Total number of products with the each pattern type

Pattern	Part 1	Part 2	Part 3	Part 1	Part 2	Part 3	Total no. of Products
A	Low	Medium	High	5	10	15	137
B	High	Medium	Low	15	10	5	28
C	High	Low	Medium	15	5	10	27
D	Low	High	Medium	5	15	10	171
E	Medium	High	Low	10	15	5	72
F	Medium	Low	High	10	5	15	65

Step 6: Group products by their patterns. For example, all pattern A products are grouped in one place, all pattern B products are grouped in another place and so on so forth.

Step 7: Rank the products of each pattern based on their delay times and other criteria which effectively minimizes the delay time

Step 8: Sort the products in a same pattern to fit the time standards appropriately.

Sort pattern ‘A’ type products in an ascending order and pattern ‘B’ type products in descending order

Sort pattern ‘C’ type products in an ascending order and pattern ‘D’ type products in descending order

Sort pattern ‘E’ type products in an ascending order and pattern ‘F’ type products in descending order (See First four columns of Table 12 –Table 18).

Step 9: Calculate the time standard differences of each products for their respective pattern types.

Table 12: First 10 products of sorted pattern A

A

Product	Part 1 actual time(T1)	Part2 actual time(T2)	Part 3 actual time(T3)	Difference
256	8	8	8	0
18	12	12	13	1
328	14	14	15	2
313	12	13	13	2
136	13	14	15	2
238	10	12	12	2
124	15	17	18	3
386	7	9	11	3
406	13	15	16	4
248	16	19	20	4

Table 13: First 10 products of sorted pattern B

B

Product	Part 1 actual time(T1)	Part2 actual time(T2)	Part 3 actual time(T3)
207	18	18	17	2

312	14	14	12	2
86	12	11	10	2
332	12	10	9	2
439	15	13	11	4
179	16	13	12	4
500	16	15	12	4
324	12	11	9	4
121	11	8	6	4
339	13	13	9	4

Table 14: First 10 products of sorted pattern C

C

Product	Part 1 actual time(T1)	Part2 actual time(T2)	Part 3 actual time(T3)
134	16	14	15	2
189	11	9	10	2
450	17	15	16	2
499	9	7	8	2
61	12	10	11	2
367	19	17	18	2
58	18	16	18	2
363	17	14	17	3
493	15	12	13	3
217	13	10	13	3

Table 15: First 10 products of sorted pattern D

D

Product	Part 1 actual time(T1)	Part2 actual time(T2)	Part 3 actual time(T3)
326	17	18	18	1
202	13	14	13	1
48	13	15	14	1
413	15	17	16	2
165	7	9	7	2
249	13	15	15	2
221	12	14	14	2
355	8	10	8	2
13	9	12	11	2
348	15	17	16	2

Table 16: First 10 products of sorted pattern E

E

Product	Part 1 actual time(T1)	Part2 actual time(T2)	Part 3 actual time(T3)
398	16	17	15	1
133	11	12	10	1
234	11	12	10	2
288	16	17	16	2
360	14	16	14	2
168	12	14	12	3
113	13	15	12	3
297	18	20	16	3
1	14	15	11	4
365	9	12	9	4

Table 17: First 10 products of sorted pattern F

F

Product	Part 1 actual time(T1)	Part2 actual time(T2)	Part 3 actual time(T3)
455	14	14	15	2
250	11	10	12	2
89	16	15	17	2
440	7	6	8	2
84	12	11	13	2
393	10	10	12	3
286	10	9	12	3
372	19	17	19	3
461	11	9	12	3
417	7	7	10	3

Step 10: Arrange the product patterns in such a way that they fit together leaving a minimum delay time. For instance, fit product pattern type ‘A’ having a delay time of 1 with the product patter type ‘B’ having same or approximately delay time.

Table 18: Fitting pattern A products with pattern B products

Part 1 actual time(T1)

Part2 actual time(T2)

Part 3 actual time(T3)

Ranking PATTERNS T1-T2 T2-T3 T1-T3

8	8	8	A	-0.5	0.0	-0.5	1
18	18	17	B	0.2	1.4	1.6	2
12	12	13	A	-0.1	-1.1	-1.2	3
14	14	12	B	0.7	1.2	1.8	4
14	14	15	A	-0.1	-1.5	-1.5	5
12	11	10	B	1.2	1.2	2.4	6
12	13	13	A	-1.0	-0.7	-1.7	7
12	10	9	B	2.2	0.2	2.4	8
13	14	15	A	-0.9	-1.1	-2.0	9
15	13	11	B	1.6	2.1	3.7	10

Table 19: Fitting pattern C products with pattern D products

20	9	20	C	10.4	-10.4	0.0	57
7	9	7	D	-1.7	1.6	-0.1	58

17	14	17	C	2.8	-2.6	0.2	59
13	19	14	D	-5.6	5.5	-0.2	60
19	17	18	C	2.1	-1.7	0.4	61
12	22	12	D	-10.2	10.1	-0.2	62
14	10	14	C	3.6	-3.2	0.4	63
13	14	13	D	-1.1	0.9	-0.2	64
9	7	8	C	1.9	-1.5	0.4	65
8	10	8	D	-2.3	2.0	-0.3	66

Table 20: Fitting pattern E products with pattern F products

17	10	17	F	7.5	-7.7	-0.2	114
12	19	12	E	-7.0	7.1	0.1	115
19	17	19	F	2.4	-2.7	-0.3	116
12	14	12	E	-2.8	2.9	0.1	117
11	9	12	F	2.6	-3.0	-0.4	118
16	21	16	E	-5.3	5.5	0.1	119
14	14	15	F	0.9	-1.5	-0.6	120
11	15	11	E	-4.0	4.2	0.2	121
10	7	11	F	3.3	-3.9	-0.7	122
10	17	10	E	-6.9	7.1	0.2	123
12	11	13	F	1.4	-2.4	-1.0	124

Step 11: If a particular type of the pattern has many products, then those left out products are processed at last as there are no other pattern products available to fit them. The following hierarchy should be followed to fit with other types of patterns.

Table 21: Fitting pattern A products with pattern D products

10	12	16	A	-2.0	-4.2	-6.2	243
11	17	12	D	-6.0	4.4	-1.6	244
12	13	18	A	-0.9	-5.4	-6.3	245
13	18	15	D	-4.9	3.3	-1.6	246
9	12	16	A	-3.2	-3.2	-6.5	247
11	22	13	D	-10.8	9.2	-1.7	248
14	15	20	A	-1.4	-5.1	-6.6	249
10	20	12	D	-9.9	8.2	-1.7	250
8	14	14	A	-5.9	-0.6	-6.6	251

Table 22: Fitting pattern E products with pattern D products

9	20	17	D	-10.7	2.8	-7.9	460
12	25	4	E	-12.8	20.2	7.4	461
14	25	22	D	-10.2	2.2	-8.0	462
14	20	6	E	-6.0	13.6	7.7	463
7	23	16	D	-15.7	7.5	-8.2	464
13	22	5	E	-8.6	16.7	8.1	465
8	18	16	D	-10.7	2.5	-8.2	466
20	23	11	E	-3.7	12.5	8.8	467
10	19	18	D	-9.2	0.8	-8.4	468
15	28	5	E	-13.8	22.9	9.1	469

Table 23: Left out products of pattern D – To be processed at the end

5	15	13	D	-10.5	2.0	-8.5	470
5	20	14	D	-14.7	6.2	-8.5	471
13	25	22	D	-11.7	3.1	-8.6	472
9	21	17	D	-12.5	3.8	-8.7	473
8	17	17	D	-8.9	0.2	-8.7	474
7	22	15	D	-15.0	6.3	-8.7	475
10	22	19	D	-11.9	3.2	-8.8	476
6	19	15	D	-13.1	4.3	-8.8	477
9	20	18	D	-10.7	1.9	-8.9	478
6	22	15	D	-16.3	7.0	-9.3	479

Table 24: Example for order priority matrix

Ordering depends on both the observation values and total number of observations

A	B	C	D	E	F
B	A	D	C	F	E
C	D	A	B	A	D

E	F	E	F	C	B
D	E	F	A	B	C
F	C	B	E	D	A

Step 12: Repeat the process for all other paired patterns. Repeat the process for all the types of patterns and rank them based on the delay time.

Table 25: A comparison of initial delay time and final delay time with four data sets

Serial No.		Initial Delay time	Final delay time
1	Data Set 1	540709.2	292540.3
2	Data Set 2	40038.8	39232.3
3	Data Set 3	77190.1	44443.9
4	Data Set 4	60546.6	20348.4

Initial delay time is the delay time occurred with the original random data without implementing the developed algorithm. Final delay time is the delay time occurred after the optimizing the production work order by implementing the developed algorithm. Change in the delay time column represents the decrease in the delay times with the initial delay time and the optimized work order delay time.

Results

Figure 3: Data 1 Delay time produced from product 1 - product 500

Figure 4: A comparison of Data 1 before adopting an algorithm with after adopting an algorithm for a delay time.

Figure 3 depicts the data 1 delay time produced from product 1 – product 500. Figure 4 depicts the comparison of data 1 before adopting the algorithm with after adopting the algorithm for the delay time.

The results that can be drawn from the above graphs are: The decrease in the delay time for data 1 before adopting an algorithm with after adopting an algorithm is 248168.9 minutes which is about 45.9% (See Figure 4). The delay time gradually decreases for the first 250 products after the product order is optimized with the algorithm, and then it starts increasing as there are more number of unfit products available from the patterns ‘A’, and ‘D’.

As the number of products of type ‘A’ and ‘D’ are more and their standard time cannot be fit, the delay time is unavoidable (See Figure 3). From Figure 4, it can be observed that the total delay time at the end of an assembly line is reduced. Finally, with the increase in the variation of the processing times among the product patterns, the delay time first decreases and then increases.

Figure 5: Data 2 Delay time produced from product 1 - product 500

Figure 6: A comparison of Data 2 before adopting an algorithm with after adopting an algorithm for a delay time.

Figure 5 depicts the data 2 delay time produced from product 1 – product 500. Figure 6 depicts the comparison of data 2 before adopting the algorithm with after adopting the algorithm for the delay time.

The results that can be drawn from the above graphs are: The decrease in the delay for data 1 before adopting an algorithm with after adopting an algorithm is 806.5 minutes which is about 2.01% (See Figure 6). The delay time gradually decreases for the first 200 products after the product order is optimized with the algorithm and then it starts increasing as there is more number of unfit products available from the patterns ‘C. As the number of products of type ‘C’ is more and their standard time cannot be fit, the delay time is unavoidable (See Figure 5). From Figure 6, it can be observed that the total delay time at the end of an assembly line is reduced. Finally, with the increase in the variation of the processing times among the product patterns, the delay time first decreases and then increases.

Figure 7: Data 3 Delay time produced from product 1 - product 500

Figure 3

Figure 8: A comparison of Data 3 before adopting an algorithm with after adopting an algorithm for a delay time.

Figure 7 depicts the data 3 delay time produced from product 1 – product 500. Figure 8 depicts the comparison of data 3 before adopting the algorithm with after adopting the algorithm for the delay time.

The results that can be drawn from the above graphs are: The decrease in the delay for data 1 before adopting an algorithm with after adopting an algorithm is 32746.1 minutes which is about 42.42% (See Figure 8). The delay time gradually decreases for the first 400 products after the product order is optimized with the algorithm and then it starts increasing as there are few unfit products available from the patterns ‘C’, and ‘F’. As the number of products of type ‘C’ and ‘F’ are more and their standard time cannot be fit, the delay time is unavoidable (See Figure 7). Finally, from Figure 8, it can be observed that the total delay time at the end of an assembly line is reduced. Finally, with the increase in the variation of the processing times among the product patterns, the delay time first decreases and then at the final stage it increases.

Figure 9: Data 4 Delay time produced from product 1 - product 500

Figure 10: A comparison of Data 4 before adopting an algorithm with after adopting an algorithm for a delay time.

Figure 9 depicts the data 4 delay time produced from product 1 – product 500. Figure 10 depicts the comparison of data 4 before adopting the algorithm with after adopting the algorithm for the delay time.

The results that can be drawn from the above graphs are: The decrease in the delay for data 1 before adopting an algorithm with after adopting an algorithm is 40198.2 minutes which is about 66.39% (See Figure 10). The delay time gradually decreases for the first 460 products after the product order is optimized with the algorithm and then it starts increasing as there are few numbers of unfit products available from the patterns ‘A’, and ‘C’. As the number of products of type ‘A’ and ‘C’ are more and their standard time cannot be fit, the delay time is unavoidable (See Figure 9).

From Figure 10, it can be observed that the total delay time at the end of an assembly line is reduced. Finally, with the increase in the variation of the processing times among the product patterns, the delay time first decreases and then it increases for the final 40 unfit products. With the increasing in the number of variety of products, dividing all the products into patterns becomes cumbersome there by the algorithm becomes complex. With the increase in the number of unequal sized patterns, the problem of fitting the patterns becomes difficult.

Figure 11: Data1, Data 2, Data 3 and Data 4 Delay time produced from product 1 - product 500

Figure 12: A comparison of data 3, data 4 and data 5 before adopting an algorithm with after adopting an algorithm for a delay time.

Figure 13: A comparison of all data before adopting an algorithm with after adopting an algorithm for a delay time.

All the data (See Table 25) and graphs show a trend representing four data sets. The graphs are ease in understanding and following the optimized data using developed algorithm makes it more effective than the original data. The label ‘1’ on X-axis represents the delay time with the original random data and the label ‘2’ represents the delay time of the optimized work order with the help of developed algorithm. All the graphs show a trend representing a decrease in the delay time comparing the initial data delay time with the optimized final data delay times.

Table 26: Delay time analysis data with Percentages

Serial No.	Test Data	Initial Delay time	Final delay time	Change in the delay time	Percentage Change (%)
1	Data Set 1	540709.2	292540.3	248168.9	45.90%
2	Data Set 2	40038.8	39232.3	806.5	2.01%
3	Data Set 3	77190.1	44443.9	32746.1	42.42%
4	Data Set 4	60546.6	20348.4	40198.2	66.39%

In the figure shown above, the column 5 shows the percentage of the delay time minimized.

For data set 1, the decrease in the delay time is 248168.9 minutes which is about 45.9% change after adopting the product order is optimized with the developed algorithm.

For data set 2, the decrease in the delay time is 806.5 minutes which is about 2.01% change after adopting the product order is optimized with the developed algorithm.

For data set 3, the decrease in the delay time is 32746.1 minutes which is about 42.42% change after adopting the product order is optimized with the developed algorithm.

For data set 4, the decrease in the delay time is 40198.2 minutes which is about 66.39% change after adopting the product order is optimized with the developed algorithm.

The algorithm can be incorporated into the knowledge base of an expert system in the form of IF-Then rules. This algorithm can also be coded into the visual basic and run on the Intel Pentium 4, processor at 2.8 GHz and Windows XP using 256 MB of RAM.

Summary

The computation results from all the graphs show that the proposed optimized algorithm has the ability to minimize the delay time especially, for all manufacturing industries consisting of producing large number of various products. The developed algorithm was used on four different data test cases each with three by three assembly lines to further demonstrate their performance. From all the above results, with the optimization of the production work order, there is a significant decrease in the delay time. The delay time is minimized to 45.9%, 2.01%, 42.42% and 66.39%.

• Minimize Total Delay time
• Stop
• Calculate Total waiting time
• Calculate Total waiting time
• Processing time for the newly ordered pattern in real-time situation
• Fitting the pattern products
• Prioritization of patterns
• Ranking products in each pattern
• Sorting each pattern products
• Grouping each pattern products
• Categorize into patterns
• Time taken for individual parts
• Processing time in real-time situation
• Random data generation

Figure 3: Standard operating procedure flow

Chapter

Conclusions and Recommendations

Conclusions

The conclusions drawn from the data generated in this study were based on the comparison of the delay times of the original random data and the optimized work order data for 500 products. Four sets of data were chosen to depict the effectiveness of one data set over the other data set. The researcher concluded that the optimized work order data has minimized delay time over the original random data. The developed algorithm in order to optimize the production work order shows a significant difference in the delay times when compared to the delay time produced without incorporating the algorithm. With the optimization of the production work order, there is a significant difference in the delay time. The delay time is minimized to 45.9%, 2.01%, 42.42% and 66.39% respectively.

The researcher also concludes that the developed algorithm is applicable universally to any number of products, assembly lines and products. The optimization algorithm based on the Excel is applicable for great number of products in many varieties of all types of manufacturing industries. The optimization algorithm obtains solutions sufficiently precise for practical use in the moderate computation time. The time taken by the computer to produce the order of the parts fed on the assembly line is very quick when compared to manual techniques.

Number of products taken is limited; though the delay time is minimized, with the increase in the number of unbalanced of some patterns of products, there is a delay time associated for the unbalanced products, there is some more delay time associated in the assembly line. This algorithm is applicable universally at all manufacturing industries.

Recommendations

In a way to improve the developed algorithm, the following recommendations were suggested:

• Testing different number of products to check for difference in the application of the algorithm when the algorithm is applied to differently sized industries

• Testing products with different parts for difference in the application of algorithm.

• Changing the sorting and ranking criteria for each of the patterns.

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