Backup Strategy for Failures in Robotic U-Shaped Assembly Line Systems

The application of robotic U-shaped line layouts is becoming more important for manufacturing companies. Compared to straight assembly line layouts, U-shaped assembly lines result in cost savings, easier material handling and higher production rates. The reason for this is that U-shaped lines improve visibility and skill sharing between operators, increase production quality, reduce work in process inventory and facilitate problem-solving of appearing production failures which is shown in several researches. Key companies such as Toyota and Boeing are using U-shaped assembly lines to benefit from the advantages of U-shaped line layouts. However, few breakdown strategies are designed especially for U-shaped lines even though machine breakdowns are common. Breakdowns reduce the throughput rate and product quality and therefore strategies are needed which can ensure the targeted throughput and product quality of companies during breakdowns. In this thesis a breakdown strategy IS designed for a robotic U-shaped line which uses versatile backup robots on backup stations to cover the failures of workstation robots. Versatile backup robots are only considered in one prior study for a straight line layout and, in that study, the backup robots demonstrated a better performance than other breakdown strategies used for straight lines. The concept of backup stations with versatile robots is adapted to the robotic U-shaped line layout to identify whether backup robots can be an efficient breakdown strategy for robotic U-shaped lines. This adaptation is the placement of the backup stations between the arms of the U-shaped line layout. An automotive body shop assembly line configuration is selected for the U-shaped line layout. Ten workstations are used in the line configuration. Four positions exist for the placement of backup stations. Each combination of workstations and placement positions have been analyzed to find the most efficient backup strategy for line configuration designed. The analysis starts with the one backup station, then considers two backup stations and finally three backup stations on the four possible placement options. The best option of the one, two and three backup stations are compared with four backup stations and the current breakdown strategies which are the usage of manual repair stations only and the workload reallocation of broken robots by working robots downstream the line. The criteria for the performance comparison are the cycle time and product quality which are generated for a 5%, 10% and 15%-line breakdown. For the generation of the criteria, a genetic algorithm is used which is modified from a straight line layout to the robotic U-shaped line backup strategy and current breakdown strategies. The analyses of the best placement options for the one, two, three and four backup stations options identify that the three and four backup stations options have the best cycle time and product quality for breakdowns, because they cover each workstation without the use of manual repair stations. It is shown that the three backup stations option is the best choice for the designed automotive body shop assembly line configuration. The three backup stations option has the same cycle time and product quality as the four backup stations option, but it uses one less backup station. Furthermore, the robotic U-shaped line backup strategy using three backup stations has a much better performance than the current breakdown strategies. Its cycle time for breakdowns is half as much as the cycle time of the current breakdown strategies and the robotic U-shaped line backup strategy does not use manual repair stations that generate a high product quality consciously. Due to these facts, the robotic U-shaped line backup strategy is an efficient breakdown strategy for the robotic U-shaped line, because it ensures production with a smooth line flow, a continuously high product quality and the avoidance of work in process inventories for breakdowns. Nevertheless, the robotic U-shaped line backup strategy has three major disadvantages. The first disadvantage is that the backup robots have to be maintained after each operating period to ensure that they do not break down. The next disadvantage is the requirements of an intelligent conveyor system so that the backup station can be accessed without disrupting the material flow when a breakdown occurs. The last disadvantage is that the backup robots have to been equipped with several possibly costly tools, to cover the workstation robots. The final decision on which backup strategy to use is therefore conditional on the cost of equipment, but this study can easily be extended to include these factors when the data is available.

for breakdowns, because they cover each workstation without the use of manual repair stations. It is shown that the three backup stations option is the best choice for the designed automotive body shop assembly line configuration. The three backup stations option has the same cycle time and product quality as the four backup stations option, but it uses one less backup station. Furthermore, the robotic U-shaped line backup strategy using three backup stations has a much better performance than the current breakdown strategies. Its cycle time for breakdowns is half as much as the cycle time of the current breakdown strategies and the robotic U-shaped line backup strategy does not use manual repair stations that generate a high product quality consciously. Due to these facts, the robotic U-shaped line backup strategy is an efficient breakdown strategy for the robotic U-shaped line, because it ensures production with a smooth line flow, a continuously high product quality and the avoidance of work in process inventories for breakdowns. Nevertheless, the robotic U-shaped line backup strategy has three major disadvantages. The first disadvantage is that the backup robots have to be maintained after each operating period to ensure that they do not break down. The next disadvantage is the requirements of an intelligent conveyor system so that the backup station can be accessed without disrupting the material flow when a breakdown occurs. The last disadvantage is that the backup robots have to been equipped with several possibly costly tools, to cover the workstation robots. The final decision on which backup strategy to use is therefore conditional on the cost of equipment, but this study can easily be extended to include these factors when the data is available. viii

Current Situation and Problem Statement
The methods of manufacturing have changed significantly over the centuries and these changes are described as Industrial Revolutions. In the 18th century, the first Industrial Revolution began with the use of powered machine tools [1]. The first Industrial Revolution resulted in a fundamental change from agricultural to industrial societies. Henry Ford pioneered the second Industrial Revolution by inventing mass production and assembly lines [1]. The third Industrial Revolution started in the nineteen-seventies with the development of automated manufacturing systems and programmable machines. In addition, manufacturing principles such as Lean Manufacturing have made the current production system more efficient by eliminating waste and continuous production process improvements [2,1]. The National Science Foundation gives an American example of the consequences of ignoring manufacturing trends in their study [3]. In the nineteen-eighties the American market was overflowing with products coming from more efficient Japanese factories using the principles of Lean Manufacturing for an improved production process with less production waste, while the focus of American factories was to produce as many products as possible in the mass production flow lines. The elimination of waste in the production process leads to a higher product quality and lower prices compared to the mass production flow lines.
Thus the consumer preferred to buy the products from the Japanese factories [3]. The examples from the National Science Foundation about the American markets should demonstrate that manufacturing companies have to keep their eyes open for changing trends and production environments [3].
A study made by MHP -A Porsche Company presents that the fourth Industrial Revolution arises, which involves the use of Smart Factories. Smart Factories are companies connected intelligently with their production environment which includes the connection of human, machines and resources with each other. The continuous growth of the internet and information technologies provides factories and their resources with more information that leads to transparency of information. Figure 1 illustrates an example from the MHP -A Porsche Company study of Smart Factories connected over Computer Processing Systems with their environment which consist of Smart Logistic, Smart Buildings, Smart Products, Smart Grids and Smart Mobility [1]. Increasing individual customer needs, volatile global markets, scarcity of resources, ecological requirements and cost pressure are the current challenges for factories. The fourth Industrial Revolution will help to handle these challenges by providing factories more information about their environment that will help factories to react more flexibly to changes. According to the study of MHP -A Porsche Company, the ability to react to demand variability which includes time and value aspects, using resources efficiently, customer oriented product design and production will be important features resulting from flexibility [1]. The study of MHP -A Porsche Company is only a survey of the slowly increasing awareness of German companies about the upcoming trend of the fourth Industrial Revolution. Nevertheless, challenges such as individual customer needs, volatile global markets and cost pressure exist already and solutions have to be developed to handle these challenges [4]. Production optimization is one important step to increasing companies' efficiency [4]. Production flow lines exist in many manufacturing companies and they require high investment and running cost.
These costs have a significant influence on economic performance of the company and therefore the line balancing problem is important for the production optimization [5].
Robotic assembly lines are highly automated systems to produce finished goods.
Although much research has been done in the broad field of the line balancing problems, only a few papers consider robot breakdowns despite the fact that breakdowns are common. Another common topic in assembly line balancing problems considers Ushaped layouts. Compared with the straight assembly line layout, U-shaped assembly lines result in reduced cost, easier material handling and higher production rates. The reason for this is that U-shaped lines improve visibility skills between operators, increase production quality, reduce work in process inventory and facilitate problemsolving of appearing production failures which is shown in several researches [6,7].
Companies such as Toyota and Boeing are starting to use U-shaped assembly lines to become more efficient [8]. Therefore, the objective of this thesis is to design a breakdown strategy for a robotic U-shaped assembly line which ensures an efficient line flow for breakdowns.

Objectives and Approach
The objective of this thesis is to design a breakdown strategy for robotic U-shaped flow lines which ensures a production with a smooth line flow and a continuously high product quality. The approach for the breakdown strategy starts with a general description of the flow line balancing problem. Chapter 2 explains in detail the different constraints, optimization goals, and solution approaches which are essential to model and solve a flow line balancing problem.
Subsequently, a brief description of U-shaped lines will follow in Chapter 3. The advantages of U-shaped assembly lines compared to straight assembly lines will be discussed. Furthermore, the requirements of U-shaped assembly lines will be shown and which breakdown strategies already exist for U-shaped assembly lines and for straight assembly lines. The reason for the consideration of breakdown strategies for the straight assembly lines is that the research field of breakdown strategies is limited. The consideration of a wider breakdown research field will ensure that an efficient breakdown strategy can be designed for the robotic U-shaped assembly line.
Chapter 4 evaluates the existing breakdown strategies and it designs a U-shaped line configuration which is an adaptation of an automotive assembly line body shop.
For this line configuration is a breakdown strategy design that uses the various number of one, two, three and four robotic backup station on the four possible placement options in the robotic U-shaped line layout configured. Furthermore, the functionality of the various design options of the robotic U-shaped line backup strategy are described.
Chapter 5 analyzes the various number of one, two, three and four backup station on the four possible placement options of the robotic U-shaped assembly line backup to identify the best performing option. In addition, the robotic U-shaped assembly line backup strategy is compared with current breakdown strategies based on its performance. The performance of the various design options for the robotic U-shaped line backup strategy and current breakdown strategies are investigated for 5%, 10% and 15%-line breakdown scenarios.
Afterwards, a critical view on the generated robotic U-shaped backup strategy follows in Chapter 6. This critique shows some drawbacks which have to be considered to make the robotic U-shaped backup strategy a useable implementation for factories.
The critique leads to further research requirements in the assembly flow line breakdown strategy field. At the end of this thesis is a summary of the chapters and the generated results. Figure 1.2 illustrates the chapters of this thesis. The Line Balancing Problem has been widely researched. It is important for researchers as well as practitioners, because flow lines require high investment cost and can lead to high running cost [9]. Furthermore, the line balancing problem consider various restrictions and constraints, which break the line balancing down and specify it.
Especially the constraints could specify the line balancing problem to current challenges of factories. An example for line balancing problem dealing with current challenges of factories is in a journal article published by Chicaet et al. [10]. It deals with the optimization of an assembly line balancing problem considering the constraints varying work time, space and uncertain demand, which are equivalences to the aspects individual customer needs and volatile global markets as current challenges of factories [10]. This chapter will review the literature relevant to the restrictions and constraints.
Subsequently, the general line balancing will be zoomed in to the robotic U-shaped assembly line balancing problem.

Industrial environments
The industrial environment specifies the general term line balancing problem by giving it a functionality. Common industrial environments in the academic research are machining, assembly and disassembly lines [5]. In machining lines, operations on parts such as drilling, welding, grinding and etc. are completed on several machines.
Machining and assembly lines are highly automated and have to follow given precedence relations. Assembly lines produce final products and the significance is that several operations can be done simultaneously on a station with more than one machine or robots. Assembly configurations are also being investigated by disassembly line types. The research on disassembly lines is growing because of the rising governmental regulation for product recycling and therefore parts have to recycled or reused as good as possible. Nevertheless, the most disassembly lines are manual and just reversing of the precedence relations of the assembly graph gives not a working disassembly graph [5]. Figure 2.1 illustrates from the literature, an example for precedence graphs in the typical industrial environments. The circles with numbers represent a task and the arrows are the relationships between tasks. As an example, in Figure 2.1, the assembly line task 4 can just start after tasks 2 and 3 have been completed, but task 5 has just to wait for task 3 to be proceed. Companies decide their industrial environments by considering the products they are producing which leads to other two important aspects of the line balancing problem the product design and process selection.

Product design and process layout selection
A product design translates into a set of tasks which have to be executed to produce a specific product. Therefore, tasks are the breakdown of the full production process into logical and small steps. Following these steps leads to the required product in the defined Quality. The steps generate the precedence relationship between each other. In assembly lines a final product just could be assembled after subassemblies and components of subassemblies has been done. The technology used is also an important consideration for the precedence relationships [9]. In new facilities, the set of tasks defines the production technology that has to be purchased and the product design creates the process sequences through the whole facility.  Thereby the line balancing problem generates the schedule design using the defined constraints and objectives. A more detailed explanation about constraints and objectives will be given in section 2.3 and 2.4. However, when using existing production facilities, the designed product has to be completed with the existing line technology. In basic straight lines, a workpiece runs through each workstation in the given order. Thereby the required set of tasks is done one after the other and the workpiece comes from the last station as a finished good, if the industrial environment is an assembly line [7].
A single straight assembly line works for simple products. Complex products and high production intensities require a straight line layout with multiple workplaces or a U-shaped line layout for a smooth production flow. In a straight line with multiple workplaces layout several tasks can be performed simultaneously at each station. This is essential for a smooth line flow where a specific amount of subassembly has to be done before the workpiece can enter the next station [11].
Lines with circular transfers place their workstation around a rotating table as illustrated in figure 2.3. The table is used for loading and unloading the workstations with the required material to produce the finished good. A line layout with a circular transfer can be seen as being equivalent to a line balancing problem for a basic straight line and straight line with multiple workplaces. The frequency of the turn tables decides which optimization method could be used. A single turn is equivalent to basic straight lines and multi-turn for straight line with multiple workplaces [12].
As Figure 2.3 shows, U-shaped lines have their start and end point at the same place and operator could work inside the line layout. The literature mentioned several advantages of U-shaped line layouts compared to straight line layouts [8,13], which will be detailed further in Chapter 3.

Constraints and attributes leading to line balancing constraints
Constraints construct a border for the line balancing problem in which the optimal task to workstation scheduling has to be found. Thereby constraints arise from logical, mathematical, practical conditions and from attributes of the objectives considered in the optimization [5].
A logical constraint mentioned in Section 2.1 is the precedence relationship between tasks, which have to be fulfilled to produce the required product. Another logical constraint is the number of workstations. The line balancing optimization cannot schedule task to an eleventh workstation, if just ten workstations are given [14].
The cycle time is one of the most important constraints in the line balancing problem and it belongs to the mathematical constraints. In the literature two different definitions for the cycle time are given. The first definition describes the cycle time as the time needed to produce a finished product from the start to end of a production line in a facility. The second definition describes the cycle time as the amount of time given to each workstation to fulfill their scheduled tasks [15]. The second cycle time definition is more commonly used and the following formula shows how the upper bound of the cycle time could be calculated. /

15
The line balancing problem should consider several attribute which influence optimization [5]. Each workstation has attributes which influence the distribution of tasks to a specific workstation. These attributes could be the type and number of workers and tools assigned to a specific workstation and the buffer capacity of each workstation [5]. In the literature these types of optimization problems are described as Assembly Line Design Problems (ALDP), because they try to set up workstations optimally for the assembly tasks [16].
Worker distribution can also be considered in the line balancing problem and they too can be defined by specific attributes. A current optimization model of Ramezanian et al. considers the different skill levels of workers and the amount of cost they cause with the scheduling to specific workstations [17].
Another important attribute mentioned in the context of the line balancing problem is that of the task attributes which could be constant, dynamic, uncertain or dependent on the assignment to a workstation. Dynamic and uncertain attributes or lead times make the line balancing problem very complex and increase the computing time required to find a feasible solution compared to that for constant and assignment dependent problems. On the other hand, dynamic and uncertain attributes reflect the practical manufacturing and even an attribute considered constant such as the task time, could become uncertain [18]. However, the optimization with constant attributes is needed to find optimal solution approximations and establish a foundation for further researches.
For example, the Simple Assembly Line Balancing problem which considers constant task times, an upper bound of a given cycle time for every station and respects the precedence constraint between the tasks was introduced in 1955 and was used to minimize the number of the workstations used in a basic straight line design. Since this initial problem formulation, the related body of research has grown continuously and in just the period from 2007 to 2012, 267 scientific papers were published for this line balancing problem [5].
In practice, companies produce not just one product, but several models of a basic product and/or several different products. The literature defines the optimization problems which consider the number of products a Single-model lines, Mixed-model  lines and Multi-model lines. Single-model just considers one basic product, Mixedmodel lines consider a similar products and the Multi-model line consider different products, which are usually produced in batches [5]. It is obvious that the complexity of such problems increases significantly with the number of the products and differences between them.
It is not just the number of products, that are considered in the line balancing problem. The number of flow lines is also a constraint because factories usually have more than one production line. The line balancing problem therefore includes cases with multiple lines (with identical or different configuration workstations) and workers assigned to more than one line and several parallel lines with crossover [19,20].
Multiple lines are very complex to configure, because they must also consider constraints previously listed such as task and workstation attributes. Therefore, finding the solution becomes a time intensive and complex task [5]. However, considering every constraint mentioned above makes the line balancing problem too complex. Thus the literature has started to categorize the line balancing problem. single model assembly line with deterministic task times in a U-shaped line layout is the simplest mentioned research field for U-shaped lines. Nevertheless, it simplifies the functionality of a production line and offers a foundation for the complex backup strategy research. Therefore, the single model assembly line with deterministic task times in a U-shaped line layout will be considered in this research.

Objective function
Another difference between line balancing problems is in the objective function.
The first formulations of the assembly line balancing problem sought the minimum number of workstations to manufacture a product [21]. The types of the objective functions considered have since increased. Besides the minimization of the workstation, other objective functions are:  Minimization of the cycle time.     The list of objective functions shows that constraints can became objective functions, because the cycle can be used as objective and constraint. The researcher defines his/her optimization goal and chooses the best fitting objective function for his purpose. Each objective function requires its own constraint variations and therefore the models in the literature vary considerably [5,22]. Current research tries not just to optimize the production lines, but also to make them robust. In Xu et al. definition "robust approaches try to find a solution or a set of solutions that performs well across all scenarios and hedges against the worst of all possible scenarios" [23]. Taguchi introduced a methodology for robust optimization and defined three stages to attain robust design. The first stage is the systems design where the parameters of a product are defined in general. In the second stage these parameters are optimized to create quality requirements. These two steps are the usual steps of optimization problems which were mentioned above. The creation of a tolerance for the design parameters is the last step of this methodology [24]. Thereby tolerances are uncertainties and they could be deterministic, probabilistic and possibilistic. Deterministic tolerance gives an area in which a parameter for a task and/or workstation can vary. The second tolerance type works with probabilities in which an event change the parameters to a specific value. Possibilistic tolerances are fuzzy measures in which probabilities could appear to change parameters in to a plausible range [25].  The theoretical methods for robust optimization such as the robust counterpart   approach and the aggregation approach are not considered in the flow line balancing   literature, because their complexity needs an enormous amount of computing power and time to generate a possible solution [25].
Practical methods to solve robust optimizations include evolutionary approaches such as genetic algorithms. Evolutionary approaches belong to approximate methods which do not give an optimal solution for a problem. Rather they generate a feasible solution for a problem in an acceptable computing time [5,25]. A more detailed description about solution method will be given in the following section. Robust line balancing approaches are developed to handle uncertain data. Robust means also that the flow line should continue to operate even if one or more machines break down.
Break downs are practical problems and should also be considered in robust design. against break downs as further research [5,26]. The literature of the assembly line balancing offers studies about break downs, because of their practical application. Therefore, in Section 3.3 the current state of the break down research will be given and especially which break down strategies could be adapted for robotic U-shaped assembly lines.

Solution procedures
After considering all the parameters above, the last step in the line balancing is to choose a solution procedure to solve the problem. The solution procedures have to find the best solution for the defined constraints and objective function. In addition, the solution procedure has to execute fast. In the line balancing problem, the performance of solution procedures is measured with the required time to find an optimal solution [27]. Another important factor in the performance is the solution value. Some solution procedures provide better solutions than other procedures and therefore the literature classify the solution procedures in exact and heuristic methods.

Exact methods
As their name suggests, exact methods find the best solution for an optimization by considering a specific number of tasks and constraints. Therefore, the objective function and the constraints have to be defined in a mathematical model. The most common model for the assembly line balancing problem is the mixed integer program. To illustrate how a mixed integer program works, the simple assembly line balancing problem (SALBP) 1 and 2 will be taken as example. These two optimization problem are very simple defined. As mentioned in section 2.3 the SALBP-1 optimizes the number of used machines by considering the constraints cycle time and precedence relationship between tasks. The SALBP-2 is similar to the SALBP-1. It uses also a limited amount of constraints, but it optimizes the cycle time for a given number of 20 machines. The following parameters were assumed to generate a mathematical model for the multi integer program [28,29]: SALBP -2 [29] . ∑ ∀ .
The equation (1.1) is the mathematical formulation for the objective function of this optimization problem, which searches for the minimum number of used machines.
The constraint (1.2) defines in a mathematical form, that each task could be just assigned to one machine. In the equation ( it impossible to create a linearized mathematical model and therefore a non-linear model was created to find an exact solution [30]. The linear and nonlinear integer programming model is used to create mathematical equations, which have to be solved to find the exact solution. It is practical to use special solver as Cplex, LINGO, ILOG to generate a solution. These solvers follow the branch and bound algorithm to generate the exact solution [5]. The branch and bound algorithm can be seen as a tree diagram. It creates several levels of branches. At each level the algorithm compares the value of the branches and let just the branch grow, which has the best value. Here best means a low value if it is a minimization problem and a high value if is a maximization problem. The branch and bound algorithm creates as long level of branches as the entire of set parameters are considered in the tree diagram [31]. It is difficult to illustrate a line balancing problem in a branch and bound algorithm, because it becomes very huge even with a small set of parameters. Therefore, Figure 2.5 shows the basic idea of the branch and bound algorithm. In this example 4 task has to be ordered in an optimal position and from the start point the task 1 and 4 have the same value and a better value than task 2 and 3. Thus the branch and bound algorithm follow these branches to find the optimal solution. The possibility to find an exact solution is just one aspect of evaluating the performance of solution procedures. Another criterion is the required amount of time to find the exact solution. Thus the researchers try to modify their mathematical model with task specific bounds. A current example for a modified model is the branch, bound and remember algorithm from Sewell el al. which is branch and bound approach combined with dynamin programming [32]. The branch and bound part eliminates sub problems, which cannot offer a better solution than the current found branch solution.
The dynamic program remembers all calculated solution and avoid that a solution option is calculated twice solve. Thus branch, bound and remember algorithm can solve the simple line balancing problem faster than any other exact algorithm [32].
Dynamic programming is a fast method to generate an exact solution. It divides a problem in sub-problem and generates solutions for the sub-problem. Afterwards the best solution is generated out of the sub-solutions by changing the sub-problems until the best solution is found for the initial problem [33].
The literature describes line balancing as NP-hard. Thus the required solution time increases exponentially with the parameters such as task size and the number of workstation used. With more parameters and uncertain data, exact solution may not be found. Therefore, approximate procedures have been developed to solve optimization problems with a large amount of sets, uncertain data and several objective function [10,34].

Heuristic procedures
Heuristic procedures may not find the optimal solution for a line balancing problem, but they find acceptably good solutions even for complex problems in an acceptable amount of time [5]. The literature categorizes approximate procedures into simple heuristic and metaheuristic methods.
Simple heuristic methods use greedy algorithms or priority rules to generate a feasible solution for a large problem size in an acceptable time amount. Most priority rules are used for tasks or workstation attributes, which increase the complexity for the solution finding as mentioned in section 2.3 [35]. In addition, the user of simple heuristics methods can decide what an acceptable solution search time is. Therefore, they have to define how many iterations their method does until it stops and delivers the feasible solution. Needless to say that a low number of iterations do not usually generate near optimal solutions. Nevertheless, simple heuristic methods are often used to generate an upper bound for exact solution methods and these are used to find an optimal solution for a large problem size [35].
Metaheuristic methods are used for optimization problems with large problem sizes and complex constraints. Mostly a mathematical model cannot be created to solve such problems and metaheuristic methods are able to generate a near optimal solution.
Metaheuristic methods are build up in a programming language as C, C+, Pascal or Python and follow specific algorithms.
Some of the heuristic approaches used in the literature for the solving of the line balancing are: • Neighborhood methods [36] • Evolutionary approaches [37] • Swarm intelligence approaches [38] The neighborhood methods are used for the optimization of multi-objective problems. The optimization starts by finding the best solution for the first objective.
Afterwards, the second objective is considered and the neighborhood methods searches near the area (neighborhood) of the best solution for the first objective to find the best trade off solution for both objectives [36].
The swarm intelligence approaches base on the natural behavior of animal swarms in the food search process. In the optimization problems, the objective represents the food and a several number of search function, which is defined by the user of the swarm intelligence approach, represent the individuals in a swarm. The search functions start the solution search process simultaneously over the whole search area. After the finding of a good solution that has to be defined by the user in the initial phase of the swarm intelligence approach, all research functions concentrate on the area of this good solution generated, to find a better solution for the optimization problem [37].
The evolutionary approaches are based on natural behavior as well. The complexity of these methods makes it difficult to illustrate them. Thus the genetic algorithm will be used to demonstrate the evolutionary approaches. The genetic algorithm is a part of the evolutionary approaches and the most widely used metaheuristic method [5]. John Holland introduced the genetic algorithm for the first time in 1975. The Genetic algorithm is an abstraction of the biological evolution process adapted in a computer system [39]. Figure 2.6 illustrates how the biological evolution process adapts in an algorithm. Thereby all stages will be explained with the biological logic in them and how this logic gets translated into an algorithm. The first step of a genetic algorithm is to initialize a population. These will be the first parents of several generations that follow. In the line balancing problem this population exist of a chosen amount of possible solution for an optimization problem. All the parameters of the considered constraints are genes and their connection build up a string called chromosome [40]. In programming languages all kind of alphabets can be used to design chromosomes. A binary alphabet will be used to show how the genetic algorithm work based on example of Goldberg [41]. Nevertheless, numerical and characters can also be used as alphabets.
The process to choose an alphabet and design the chromosomes is called coding in the computer language. The second stage in the genetic algorithm is to evaluate the fitness of the population. Fitness is the value which gets generated by chosen chromosomes. A high value is good or bad depends on the objective function. If the objective is to minimize the cycle time, a lower cycle time is better than a higher. Goldberg choose in his example the function f(x) = x 2 in an interval from 0 to 31 and he wanted to maximize the value of f(x). Therefore, he chooses randomly 4 numbers as population, programs them as chromosomes in a binary algorithm and evaluate their fitness as shown in Table   2  Constraints Satisfaction is the third stage of the genetic algorithm. In this stage it has to be proven whether all parents fulfill the defined constraints. In Goldberg's example the only constraint is that the number found should be in the interval between 0 and 31. All chosen parents in Goldberg's example are in this interval and there they all fulfill the given constraints [41]. However, the best solution for f(x) = x2 in the interval between 0 and 31 has not been found yet. Therefore, the genetic algorithm has an additional constraint. This constraint is the number of iterations, which the algorithm has to do. Iterations means how many generations of possible solution the algorithm produce until it can stop. In the given example the algorithm is in it 0 iteration, because it is first generation of solution. The following stages will show how generations of solutions are created [39].
The fourth genetic algorithm stage is select survivors. The programmers decide how many parents of the population will be used in the next stage. This shows that genetic algorithms are individual designed to solve optimization problem and a general genetic algorithm does not exist [10,39]. Nevertheless, it is logical to use the parents with the best fitness. Goldberg use 4 parents in his example. Therefore, he chose the best 3 parents to randomly vary individuals [41].
Randomly varying individuals is the next stage of the genetic algorithm. This is the reproduction stage in where the children of the survival population are made. Two methods exist to produce the next generation. These methods are crossover and mutation [40].
Crossover means that two parents generate two offerings. Each offspring has the genes of the two parents. The programmer of the genetic algorithm decides how many genes of a parent go to an offspring. Thereby, the parent chromosome can be cut down in a chosen number of genes and distributed to the two offspring. Figure 2.7 shows a crossover with one cutting point.
Mutations modify one or more genes in the created offspring. As in nature the mutation probability should be low in the genetic algorithm [40]. In the end the programmer has to decide which mutation probability is used or if the genetic algorithm should use only crossover to search for the best solution. Eiben et al. recommend to use mutation to find better solutions [42]. The crossover search consists only of solutions, which are combined of the two parents. Using mutation brings new information in the solution area and can identify much better solution, because the first parent generation is generated randomly. In Figure 2.8 is the mutation of a binary string shown. Goldberg's example use just crossover to create the first offspring generation, because the probability for mutation in the first iteration is very low. In addition, he uses the best three parents as survivors. As mentioned above two parents create two offspring. Therefore, Goldberg uses the best solution twice to create four offspring [41]. The stage randomly varies individuals ends with the creation of the offspring and leads the algorithm to evaluate fitness and afterwards to the constraint satisfaction stage again, which work the same as illustrated above. In this stages the offspring created become the new parents and the stages will repeat until the defined amount of iterations has been completed. If this happens, the algorithm will go to the last stage to output results. In the last stage the current offspring is taken and the offspring with the best fitness is presented as the best solution for the problem. As mentioned above approximate solution procedures may not deliver the best possible solution but a near optimal solution. In Goldberg's example a near optimal solution could be found even after first iteration (see Table 2.3).
The detailed explanation of the genetic algorithm should underline the key factors, which make the genetic algorithm to most used method for complex optimization methods:  Solution search start from a population and not just from a single point  Parent population can be generated randomly  Using probabilities for creating offspring (mutation and cut points)  User creates coding part individually to design the chromosome and to validate their fitness [41] These criteria make the genetic algorithm to flexible optimization method which can be used for a large amount of optimization problems, because the user created coding part can be adapted to numerous optimization problems. The random research starting points offers the chance to find good solution in several solution areas, which allows to solve complex problems. Furthermore, the more iteration the genetic algorithm does, the merrier the response will be as shown in table 2.3. Thus the user can get a good solution even for a self-defined number of iterations.

U-SHAPED LINE LAYOUT
Japanese factories started the use of U-shaped production layout to build up a justin-time (JIT) production. Miltenburg underlies in his survey of U-shaped production lines, that some writers see the U-shaped line design as the most effective technique for a just-in-time production [43], which will be shown in this chapter. JIT belongs to the Lean Management principles. Therefore, the following chapter will give a short overview of Lean Management. Afterwards the idea and the advantages of U-shaped production lines will be presented. In the end of Chapter 3 an overview of breakdown strategies for assembly line will be given and shown which breakdown strategies are especially used for U-shaped production lines.

Lean Manufacturing
Lean Manufacturing based on the Toyota Production System, which development started in 1959 by Dr. Shigeo [44]. It is a continuous improvement in the production process to satisfy the customer requirements in terms of cost, quality and delivery times by reducing lead time, cost, improving the process flow and on the elimination of waste generated in the production environment and all activities that do not add value to the enterprise [45,46]. Toyota proofed, that the principles of Lean Manufacturing are successful and today Toyota is a benchmark for other manufacturing companies. The identification and elimination of seven types of wastes is one of the basic principles of Lean Manufacturing.
The first type of waste is the waste from producing defects. The later a defective product is detected, the more this defect will cost. A defect product identified by a customer has to be repaired or replaced and can lead to the loss of customer. But even if defects are detected as soon as possible, they lead to cost in detecting and repairing them. In the worst case the unfinished good has to be thrown away and this leads to additional cost, which the customers are not willing to pay. Therefore, the production process should be done right and every step of the productions should be defined in the product design phase correctly [47].
Another type of waste is the waste in transportation. Material has to move through different stations until it becomes a finished good. Thus the layout of the facilities and the routing sequence of operations should be optimized to deliver the minimum transportation cost as possible [47].
The third waste is the waste from inventory. "Toyota calls inventory the roof of all evil" [47]. Every item, which sits in the inventory, causes cost and binds money that could be invested in other opportunities. Moreover, inventory hides the company problems as inadequate market intelligence, instability and worse quality of the production process. To perform a better productions process, inventory should be eliminated [47].
Waste from overproduction belongs also to the seven wastes of lean manufacturing.
The production output of companies is much higher than the customers demand for a product, which leads to inventories. Companies do this to keep their workers and machines busy and get low unit prices. But unsold units produce also cost, which has to be carried by the sold units. In the end each over production unit just leads to more cost.
Furthermore, if everyone has to be busy, no one gets the chance see the emerging problems of the company [47].
The next waste in Lean Manufacturing is the waste of waiting time. This waste includes waiting for orders, parts, materials, items from preceding processes, or for equipment repairs [47]. It is a sign for a flawed process flow, if waiting appears.
Moreover, waiting time increases the unit cost, for which the customer has to pay, and in addition the customer has to wait longer [48].
Another waste is the waste in processing. Every task, which doesn't add value to a product, should be eliminated. Additionally, each process should be improved, if the improvement makes the process more efficient [47].
The last waste of lean manufacturing is the waste of motion. This waste takes a deeper look on every step of a process and tries to eliminate each unnecessary movement to make the process much more efficient [48].
Eliminating the seven wastes of Lean Manufacturing results in an efficient production process with a high quality. For achieving this a Total Quality Management System is needed, which is also an important part of Lean Manufacturing.
The term Quality is defined it from the interaction of the customers and producer's perspective. Customers buy products to fulfill their needs, which have to be translated by the producers to the basic quality of their products. This translation occurs in form of the product design and manufacturing. By including the other departments as engineering, manufacturing, marketing, sales and the suppliers the Total Quality Management gets defined. Thus everybody shares an idea of how their performance should be. The workers start to proof the work in process and give a feedback to their predecessor, because a failure performance of the predecessor cannot be recovered by the current station. In addition, everybody has to be watchful and flexible, because the needs of the customers are changing continuously and therefore the companies have to change and improve their understanding of quality continuously.
The elimination of the seven wastes and Total Quality Management stipulates, that only goods should be produced, which fulfill the quality and the demand of the customers. Hence it is logical, that Lean Manufacturing includes a process of controlling production and this starts with the customer [47]. Pull Production is the term for this method and it was developed in the 1950s by Toyota. American supermarkets first implemented these methods and they were adopted to the manufacturing industry. Each time a customer buys a product, the predecessor station is allowed to send an order to their predecessor station [48].
This procedure should ascertain, that only needed goods are produced and it deviates from the old form of Push Production. Push Production is the opposite production method, which try to produce as much goods as possible. The idea behind Push Production is to get low unit cost. Discounts should secure, that customers are buying this huge amount of products [48].
It is difficult to state in general terms whether pull or push production is better, because it depends on the products. If a product is standardized such as toothpicks, push production is better to get low unit cost and a huge volume of products. But if a products get more specific, then the pull production is better suited to fulfill the needs of the customers [47].
To realize the concept of pull production, the two aspect of Lean Manufacturing needed are Just in Time and SMED.
Just in Time is a concept with the main idea being that a station gets its required material in the needed moment and in the right amount. This concept supports the idea of the elimination of inventory. To fulfill the requirements of Just in Time, the delivery of the material has to be optimized and the delivered material has to fulfill the standards of Total Quality Management [48].
SMED means Single Minute Exchange of Die. This concept is more a methodology developed by Shingo [47], which has the goal to reduce the time, where a machine or an operation has to been stopped to change a tool, to a single minute. In the practice a minute to exchange a tool could not be realized for a long time [47]. Today, automotive assembly line robots use more than one welding gun for their tasks execution and could change the welding guns used in a few seconds [9].
Lean manufacturing follows the concept of a continuous improvement, also called Kaizen, which makes it to a dynamic production strategy. Continues improvement means that mistakes are analyzed in-depth to find and solve the reason for the mistake, learn from it and never repeat the mistake again. The concept of Kaizen also extends to the workers. They should get the chance to improve and raise their knowledge and skills through different projects and task to become an important part of the company.

Functionality of a U-Shaped line
In a U-Shaped production line are the producing machines arranged in a U form.
Thereby the start and the end of the production line are at the same vicinity. Operators work inside the U-Shaped line design as illustrated in the following Figure [6]. It is possible to place the operators outside the line, if the machines allow an operation from both sides. Nevertheless, the literature places the operators in the middle of lines and this concept will be used in the following.
The movement of the Operator and the production flow can be clockwise or counterclockwise [6]. The flow direction can be decided by the line balancing decision and which balancing direction delivers the best line efficiency. In Miltenberg's description of the U-shaped line, no further material is allowed to enter the line while a product is still in work [43]. Thus the idea of Just-in-Time should be fulfilled to produce just a product then it is needed. Additionally, it become easier to stop the machines if a problem with a product or machine appears. This production flexibility should be able to generate the required quality with zero product defects. Miltenberg defined, in his survey of U-shaped production lines, the chase mode. Originally the chase mode means that one operator works at a U-shaped line and convoys the products through all the workstations. More common is that two or three operators run a U-shaped line. In this scenario the operators are assigned to a specific section of the line and fulfill their scheduled tasks for each product.  One operator is able to run a whole production line, because there is a separation of work by the operator and the machine work. The operators work usually consists of: 1. bring the work in process part to the required machine 2. load the machine with the part and other requirements 3. start the machining process 4. wait a short to check if everything is alright 5. unload the work in process part 6. check the quality of the part [43] The machine work is the automated part work with the machining functions as drilling, welding, assembly or other machining process which are needed to produce a product in the required quality [43]. One big advantage of U-shaped lines over straight lines is the better rebalancing possibilities. Rebalancing includes the following three functions:  varying the production rate  moving machines  changing standard operations [43] Varying the production rate means including operates to increase the production rate or removing operators to decrease it. Flexible and multi-skilled workers are needed to adapt the current production rate to the required demand. This leads to better educated workers and make the production job more interesting [43].
Moving machines and changing standard operation are necessary for new products and technological production innovation. As mentioned in section 2.2 the product design and production technology are the decisive part for the production tasks. With innovations, new tasks appear which requires additional precedence relationship and other machines. Therefore, moving machines and changing standard operations is essential for a smooth production and flexible production rates [43].
The current description of U-shaped production lines refers on the simple U-shaped line design. In Section 2.3 it was mentioned how complex the line balancing problem can become with multi-lines. In practice it is common to have more than one simple line. The following figures illustrate how other configurations of more complex Ushaped lines are discussed in the literature. All the U-shaped lines above are designed for a practical use with multi-product production. It is not common and too laborious to reorganize the whole production line for product changes. In addition, each layout can vary their production rate by adding workers to the lines. Figure 3.7 is the most complex layout design, because it structures the whole facility in a U-shaped layout [43]. These complex U-shaped line designs illustrate the advantages of U-shaped lines.
The first advantage of the U-shaped layout is the increased visibility and communication in the production process. Thus the production quality increases and problems are solved much faster, because workers recognize problems faster and can help each other to solve it [6].
Another advantage is that workers become much more skilled. Workers are scheduled between workstations and different lines to vary the production rate. This work rotation makes the work more interesting and the workers learn many more tasks, which also helps them to react more efficiently to emerging problems [6].
The next advantage is the possibility of the line rebalancing. The flexible reaction to demand helps companies to fulfill the requirements of lean manufacturing to avoid inventory, overproduction and to increase the production quality [6].
The last advantage is that U-shaped lines requires fewer workstations than straight lines, because they offer more possibilities to schedule tasks. This leads to less investments for U-shaped lines and a higher production quality can be reached with less invested money [6].

Breakdown strategies
Battaia et al. and Hazir et al. refer in their surveys about the line balancing problems to considered machine breakdowns in further research [5,22]. The research on breakdown strategies is limited and can be categorized in the following options:  Inventories  Balancing of uncompleted tasks  Rebalancing of the whole line  Backup robots All of the breakdown strategies mentioned are mainly used for straight assembly lines. Only the inventory breakdown strategy was used for the U-Shaped line layout.
Miltenburg compared the effectiveness of U-shaped lines with straight lines for machine breakdowns, which will be explained in the following [49].  Despite all their advantages are U-shaped lines are more efficient than straight lines, if inventories of work in process parts are placed after every workstation. If the placement of inventories after a workstation is not possible, a straight line layout should be used for proper high volume production even during breakdowns [49].
Another breakdown strategy is the balancing of uncompleted tasks. If a machine breakdown appears, the scheduled tasks of the broken machine cannot be performed.   Sanci's branch and bound algorithm is the Rebalancing of a whole flow line, but just with fewer workstations. The goal is to make balancing algorithm faster and to increase their reaction time on breakdowns. In addition, the Rebalancing of all tasks requires a tool redundancy at all stations, which is similar to the breakdown strategy balancing of uncompleted tasks.
The last breakdown strategy is the use of backup robots, which was introduced by Shirazi et al. and realized in a multi-objective genetic algorithm [53]. This algorithm starts with a regular line optimization by scheduling tasks to the given number of workstation under the objective of a cycle time minimization. The special feature in this algorithm is the availability of additional backup stations for workstation with a high capability [53]. Stations with a high capability have a higher probability to break down than stations with an average and low capability. Therefore, just high capability stations need a backup station to avoid breakdowns. Shirazi et al. [53] tested his algorithm in the scenario of an automotive body shop assembly line, which is illustrated in the following  The backup stations support the high capability stations in a normal situation without a breakdown by taking some tasks away from the high capability stations. In  Graph 3.1 uses the criteria cycle time and group of tasks performed on manual repair station. The lower the cycle time is the better is the performance, because a low cycle time ensure a high production throughput. Furthermore, robots offer a higher product quality than manual repair stations and therefore the fewer tasks are executed on manual repair stations, the higher is the product quality [53]. Graph 3.1 shows that the breakdown strategy with backup stations have nearly the same performance as a tool redundancy breakdown strategy with a six level redundancy. A Redundancy level is the average number of robots, which can perform one task [9].  research [50]  a lower product quality.

Breakdown strategies evaluation
These disadvantages affect the line performance dramatically, because the cycle time gets much higher and the product quality decreases. Due to these facts, the Ushaped line requires a breakdown strategy which can avoid manual repair stations, has an efficient number of backup stations and can handle breakdowns with an adequate cycle time increase. A robotic U-shaped line has the ability to provide these factors for an efficient breakdown strategy. In Section 3.2, it was noted that the place between the top and the bottom part of the U-shaped line is used by operators. A robotic U-shaped line works automatically and does not need operator to perform on the workstations [8].
Thus, robotic U-shaped lines have unused space between their arms. The following Section will demonstrate how the unused space could be used to generate an efficient breakdown strategy.

Backup strategy design and functionality
An average U-shaped line consist of ten workstations [43]. This thesis will use the average number of ten workstations to design a practical breakdown strategy. The first step for the breakdown strategy design is to illustrate the placement and the design of the chosen number of ten workstations in a robotic U-shaped line.     The backup station option A will be used as example to demonstrate how one backup station is able to cover four workstations.      to generated and a solution approach has to be chosen. This will be done in the next Section.

Genetic algorithm for the backup strategy
The robotic U-shaped line backup strategy designed has 40 workstation robots and therefore at least the number of 40 tasks is needed, because it makes no sense to let workstation robots unutilized. For the performance research of the backup strategy options designed, this thesis will use 72 tasks. Such there is the opportunity to utilize some workstation robots with two or three tasks which can be seen as above average workload compared to robots with only one task. Each task needs a time to be executed.
This execution time will vary in the range from 20 to 41 seconds based on the task elimination time of Kahan et al. which was taken for the performance research of their breakdown strategy [50]. The allocation of the execution time to each task is noted in a task time matrix.  In the illustrated section of the task time execution matrix, task 1 requires an execution of 33 seconds, task 2 requires an execution of 24 seconds and so on.
Afterwards, it has to be defined which task can be executed by which robots. This is implemented in a capability matrix. A capability matrix is a simple matrix with zeros and ones. A one indicates that a robot can perform a specific task and a zero means the robots cannot perform this specific task. Table 4.2 illustrates a capability matrix.
In this example tasks 8 and 9 can be only performed by robot 7 and tasks 15, 16 and 17 can be only performed by robot 12. The next step is the design of the precedence relationship between task matrix. An example of such a matrix is illustrated in the following table.   The task precedence matrix defines which task as to be executed before another task can be started. In Table 4.3 the first four tasks do not have a predecessor, because there are just zeros in the matrix and a zero means that no precedence relationships exist between the tasks. On the other hand, task 6 has two predecessors. The task 6 can be performed only, after the tasks 1 and 5 have been executed. If Table 4.3 is referred to the robotic U-shaped line designed, the first four tasks will be executed on the first workstation and each of these tasks will be executed on a different workstation. Which task is executed by which robot is considered in the capability matrix as mentioned above. The tasks 5 to 10 will be executed on the second workstation, where the tasks 5 and 6 will be executed on one robot and the tasks 9 and 10 will be executed on one robot. Thereby, the task 5 has to be executed before task 6 can be performed and task 9

Tasks
has to be executed before task 10 can be performed.
All the matrices described above define constraints which have to be considered for a feasible solution. An objective function is needed for the performance comparison between the different options of the robotic U-shaped line backup strategy designed. Before the algorithm starts, the user has to decide which of the backup options mentioned above the algorithm has to investigate for the U-shaped line backup strategy. 1 Shirazi's genetic algorithm research is still in progress. He presents in April the current standing of his algorithm research and proofed the efficiency of his algorithm. The literature will be published end of the summer 2016. The first step of the modified algorithm starts with a verification whether the algorithm has done enough solution replication. In the literature is the number of breakdowns for the line balancing problem not specified [9]. Due to this fact this thesis will consider a 5%, 10% and 15%-line breakdown. For each breakdown scenario 40 solutions will be generated to find an average and significant cycle time. Hence, the algorithm will end after 121 solution replications which is the step 15 in        allows the use of numerical numbers. Nevertheless, the randomly generated parent does not fulfill the constraints of the precedence relationship between task and capability matrices. Thus the randomly generated population size has to be modified. This will be done the following two steps.
The step 5 puts the population size in a feasible order which fulfill the requirements of the precedence constraints. This is implemented by a function called Order which was designed by Shirazi. The function takes each of the generated parents separately and validates their structure. If the function identifies a task that is in front of its predecessor, the Order function will take this task and place it after its predecessor. This operation will be repeated until each task is placed after their predecessor and such the whole population size will consist of parents which fulfill the requirements of the precedence constraint. The fulfillment of the capability matrix constraint is realized in the cycle time of the search process. This process is the step 6 in the modified algorithm. Nevertheless, the genetic algorithm designed by Shirazi has to be modified to consider the several backup options for the U-shaped line. The modified algorithm generates for a line flow without breakdowns ten pieces which represents the ten workstations. Figure 4.9 illustrates an example of a parent which is randomly cut in ten pieces for the allocation to a specific workstation. The first piece is allocated to workstation 1, the second piece is allocated to workstation 2 and so on. Furthermore, each piece consists of a fixed number of a fixed number tasks which have to be done by the allocated workstation. In Figure 4.9 the first piece contains the tasks 1,2,3,4,5 and is allocated to the first workstation. The following function will verify whether the workstations are able to execute all the allocated tasks.    The next function used in the step 6 is the self-generated fescheck function. This function fulfills the requirements of the capability matrix. Each piece randomly generated by the makeStation is allocated to a specific workstation and consist of several tasks. The self-generated fescheck function takes each piece separately and validates whether the number of tasks can be executed by this specific workstation. If some of the allocated task cannot be executed by their allocated workstation, the function will allocate these task to a nearby workstation, which can perform these task: Thus the precedence relationship between tasks constraint is still fulfilled and additionally the constraint is fulfilled that each task is allocated to a robot, which can execute the allocated tasks. At the end of the fescheck function, each generated station has a feasible number of tasks.     The step 9 is the offspring generation. The offspring generation bases on the initial genetic algorithm of Shirazi and use a fast method to perform crossover and mutation.
This fast methods of the offspring generation will not be explained here, but a detailed explanation can be found in Shirazi's research [53] and they will be explained in his Ph.D. Thesis, which will be published in the end of August 2016. Nevertheless, the basic idea how crossover and mutation are performed is illustrated in Section 2.5.2. After the offspring generation, each offspring has to be structured in a feasible order.
The structure of the offspring in a feasible order is step 10 in the modified algorithm. This step uses the same Order function as the step 5 to structure the offspring.
Afterwards, the step 11 follows which generate a cycle time for each offspring.  The modified algorithm is able to investigate each option of the robotic U-shaped line backup strategy. Afterwards, the cycle times of each option can be compared with each other to find the best option for the robotic U-shaped line backup strategy which will be done in Chapter 5. Nevertheless, the question arises whether the U-shaped line backup strategy generated is better than existing backup strategies. Hence, the robotic U-shaped line backup strategy will be compared with other breakdown strategies.
The inventory breakdown strategy has a discrepancy with the basic idea of a Ushaped line layout as a part of lean manufacturing and will not be used in this methodology.
Kahan et al. uses several breakdown strategies in their research which offers the potential for a cycle time comparison [50]. One of these breakdown strategies is the coverage of each broken workstation with manual repair station only [50]. Another 1. The first analysis identifies the best placement for one backup station.
2. The second analysis identifies the best placement for two backup station.
3. The third analysis identifies the best placement for three backup stations.
4. The fourth analysis compares the backup station options with current breakdown strategies.

The fifth analysis uses a higher task execution time on manual repair stations to
shows the performance of the breakdown strategies for more complex products.
6. The sixth analysis uses a lower task execution time on manual repair stations to shows the performance of the breakdown strategies for standardized products. These last analyses should illustrate the potential of the robotic U-shaped backup strategy in comparison with current line balancing breakdown strategies. The performance of each breakdown strategy will be evaluated by using essential criteria.
As mentioned in the previous chapter, the first criterion is the cycle time which is used in the literature as benchmark for breakdown strategies. The second criterion is the generated product quality from the considered breakdown strategies. It is difficult to describe the generated product quality with the modified genetic algorithm, because the optimization goal is the cycle time minimization only. Therefore, the product quality will be described by the number of tasks which are executed by the manual repair stations. The comparison between the best option AD and the other options shows that the option AC has comparable cycle times as the options BD and CD without the usage of a backup station on the position D. This is due the fact that the option AC is able to cover eight of the 10 workstations and therefore it can reach still a cycle time on the same level as the options BD and CD. On the contrary, options AC, AB and BC performs badly, because they can cover six workstations only. Nevertheless, the following product quality analysis will show whether option AD is the best of the two backup station options. It can be seen that option AD has the best performance in the product analysis as well. The option AD executes 81.7% fewer tasks than option AB, 40.5% fewer tasks than option AC, 73.5% fewer tasks than option BC, 38.9% fewer tasks than option BD and 59.3% fewer tasks than option CD on the manual repair stations for the 5%-line breakdown scenario. Afterwards, the option AD executes 17.9% more tasks than the options AC and BD on the manual repair station, but it executes still 63.2% fewer tasks than option AB, 62.9% fewer tasks than option BD and 43.4% fewer tasks than option CD on the manual repair station for the 10%-line breakdown scenario. The better of performance of the options AC and BD validates the importance of using the backup stations to cover as many workstations as possible. Nevertheless, the option AD has the best performance for the 15%-line breakdown again. It executes 66.2% fewer tasks than option AB, 34.0% fewer tasks than option AC, 66.5% fewer tasks than option BC, 30.5% fewer tasks than option BD and 61.6% fewer tasks than option CD on the manual repair stations.

One backup station analysis
This lead to the conclusion that the option AD performs as best of the two backup stations options. Hence, the two backup stations option AD will be used in the last analyses to find the best option for the robotic U-shaped line backup strategy designed. The error bars show that the options ABD, ACD are similar to each other and they have a significant lower mean cycle time than the options ABC, BCD for the 5%, 10%

Three backup stations analysis
and 15%-line breakdown. Thus the options ABD and ACD perform much better than the options ABD and ACD. The option ABD has a 43.3% lower cycle time than option ABC, a 2.1% lower cycle than option ACD and a 34.9% lower cycle time than option BCD for the 5%-line breakdown scenario. Afterwards, the option ACD performs better.
It has a 52.3% lower cycle time than option ABC, a 2.2% lower cycle time than option ABD and a 37.2% lower cycle time than option BCD for the 10%-line breakdown scenario. For the 15%-line breakdown scenario, the option ACD has a 46.1% lower cycle time than option ABC, a 12.0% lower cycle time than option ABD and a 45.4% lower cycle time than option BCD.
The reason for the good performance of the options ABD and ACD is that these options are able to cover breakdowns without the use manual repair stations. The error bars show that the options ABD, ACD are similar to each other and they have significant fewer tasks on manual repair stations than the options ABC, BCD for the 5%, 10% and 15%-line breakdown. Thus the options ABD and ACD offer a higher product quality than the options ABD and ACD, because they do not have to use the manual repair stations. The options ABC and BCD may be able to offer a good product quality as well, because the mean number of tasks on the manual repair station is 1 for the 5%, 2 for the 10% and 3 for the 15%-line breakdown scenario.
The number of 3 tasks executed by manual repair stations should be still be able to offer an acceptable product quality for the most products. Nevertheless, the number of 3 tasks executed by manual repair stations may be too much to offer an acceptable for products which require a premium quality. Furthermore, the execution of one task on the manual repair station increases the cycle time dramatically which is shown in Graph 5.5 for the options ABC and BCD. Hence, the option ACD will be used in the following analysis, because it has the best performance of the three backup stations options for the robotic U-shaped line backup strategy.

Breakdown strategies comparison
This section will identify the best backup station option for the robotic U-shaped  The following analyses will use various work times for the manual repair stations to verify the efficiency of the robotic U-shaped line backup strategy option ACD.

Breakdown strategies comparison using a five-time greater rework time
This breakdown strategies comparison will use a five-time greater manual rework time for manual repair stations. A five times higher work time for manual repair stations should demonstrate a scenario where the tasks are more complicated. Thus operator require much more time to execute the tasks manually. In the previous section a product quality analysis has been done for the breakdown strategies considered. It was shown that the backup strategy option offers the best product quality, because manual repair stations are not used. Nevertheless, a product quality analysis will be presented in the following to demonstrate the number of tasks, which increase cycle time dramatically. Here the question arises whether the use of the robotic U-shaped line backup strategy generates a benefit for standardized products. This question will be investigated in the following section.

Breakdown strategies comparison using a two-time greater rework time
This breakdown strategies comparison will use a two-time greater manual rework time for manual repair stations. A two-time greater manual rework for manual repair stations should demonstrate a scenario where the tasks are standardized. Thus operator require less time to execute the tasks manually. The breakdown strategy workload reallocation downstream the line has a much better performance in this analysis than in the previous ones. Its cycle time is still much higher than the cycle time of the rU-sbs option ACD, but it is not twice higher as in the previous analyses. Nevertheless, the breakdown strategy workload reallocation downstream the line has only the same performance as the one backup station option D.
Standardized products require a high volume production and therefore this breakdown strategy performs poorly for breakdowns, because it has a twice higher cycle time for breakdowns than the initial cycle time of 91seconds for a line flow without failures.
Furthermore, it increases the workload of working robots for breakdowns. An increasing workload leads to a higher probability of breakdowns which is a major disadvantage of the breakdown strategy workload reallocation downstream the line. These facts verify the good performance of the robotic U-shaped line backup strategy option ACD even for standardized products.
Standardized products do not require a high quality. Nevertheless, a product quality analysis will be presented in the following to demonstrate the generated product quality.  [50]. Automotive body shops target a high volume production and therefore a continuous low cycle time is essential for a smooth line flow and the performance of assembly lines.
Another advantage of the robotic U-shaped assembly line backup strategy using three backup stations on the places A, C, and D is that it offers a high product quality continuously. The current breakdown strategies of Kahan et el. requires manual repair stations to ensure that the line flow does not stop for breakdown [50]. On manual repair stations operators execute the tasks of the broken robots manually and the quality of tasks executed manually is worse than the quality of those executed by industrial robots, because industrial robots are programmed to execute tasks precisely [53]. Automotive companies have to ensure a high product quality continuously, because failure in their products leads to repair cost, can harm their reputation, and can even lead to lives being lost [55]. Due to these facts it is important for automotive body shops to offer a high product quality continuously.
The last advantage of the robotic U-shaped line backup strategy is that it can eliminate waste in the form of inventories. The only breakdown strategy in the U-shaped line balancing problem research is the use of inventories between each workstation [49].
In Section 3.1, it is shown that work in process inventories belong to the waste in production, because they require a lot of space and bind money in each production line which can be used better in other departments. The elimination of work in process inventories makes the robotic U-shaped assembly line backup strategy the most efficient in the U-shaped line breakdown strategy research field. Nevertheless, the robotic Ushaped line backup strategy has several disadvantages.
The first disadvantage is the assumption that the backup robots cannot break down, because they are used only to cover broken robots and therefore they have a too short operating period to break down. This assumption is not realistic. The backup robots can break down even if they have short operating periods. This disadvantage may be repealed, if the backup robots are maintained after each operating period. The maintenance after each operation period ensure that the backup robots are not breaking down and thus they are able to be breakdown strategy which can be used in factories.
However, the maintenance of the backup robots after each operating period could be a costly solution to ensure the efficiency of the robotic U-shaped line backup strategy.
The second disadvantage is that the rU-sbs requires an intelligent conveyor system. is a better breakdown strategy than the current breakdown strategies which is validated in the Chapter 5. Nevertheless, an intelligent conveyor system for the rU-sbs could be much more expensive than the regular ones for the current breakdown strategies and this has to be considered to find the best breakdown strategies for factories.
The last disadvantage is the requirement of several welding guns on the backup robots for the coverage of four workstations. Müller presented in his research that newer industrial robots are able to hold several welding guns and it needs only a few seconds to change a welding gun [9]. The breakdown strategy of the workload reallocation of broken robots by working robots downstream the line has the same disadvantage. The downstream robots need the same welding gun as their previous robot for the workload coverage. Even the breakdown strategy usage of the manual repair stations only needs additional welding gun to cover robot failures. Furthermore, if several robots break down, the manual repair stations will need several operators to cover the robots in an adequate cycle time increase. Each current breakdown strategy has the disadvantage of the requirement of additional welding guns. However, the rU-sbs uses backup robots only for the coverage of broken robots and the breakdown strategies with manual repair station need several operators for breakdowns. Thus it has to be analyzed which breakdown strategy is the most cost efficient. Furthermore, the current production trend goes to individual consumer products. Individual products require a consumer demand based production volume. Thus, the optimization goal lies in the generation of a flexible production which has a consumer satisfying production time and quality.
The main goal of each manufacturing company is the maximization of profit. Cost and the right product demand belong to most important indicators. Therefore, a profit maximization research is needed to find out which breakdown strategy has the best performance for automotive companies. This research should consider a number of workstations and welding guns which are necessary to execute the tasks in an automotive body shop. Furthermore, other important cost factors have to be considered in the profit maximization which are human resources, equipment for the manual repair stations, the required conveyor system and a realistic customers demand to avoid over production. The generation of a profit optimization, which considers the cost factors of automotive body shop, could be done in cooperation with automotive body factory or an intensive cost research of the cost of automotive body shops has to be done. An optimization for a minimum cycle time was a good basis to start the backup strategy research for the line balancing problem, but the economical goal of companies is to reach an optimal profit. Hence, the line optimization with profit as objective function offers also a good research field as recommend by Hazir et al. for a further research field [22].
The disadvantages and the cost part are not the only limitations of this thesis. In Section 2.3, the constraints of the line balancing problem are presented. It is shown that factories have multiple assembly lines which interact with each other to manufacture products. Furthermore, it is common that more than one product is manufactured on one assembly line, because the product portfolio of factories increases to fulfill the individual customer needs [19,20]. The constrains of multiple lines and several products on one assembly are not considered in this thesis as they increase the complexity of the line balancing problem and the consideration would be out of the scope of a master thesis. Nevertheless, the consideration of the multiple lines and several products constraints is essential for the implementation of the robotic U-shaped assembly line backup strategy in factories.
The last important limitation of this thesis is that the constraints considered as tasks time, production layout and capability matrix are adapted from the study of Kahan et al. which concentrates on automotive assembly lines only [50]. For a general evaluation of the performance of backup robots as breakdown strategy for U-shaped lines, further researche is required which uses the task times, precedence and capability of products from various factories. Machining flow lines are widely disseminated throughout factories and they are automated to ensure a high volume production. Thus, it is essential to investigate how backup robots perform in an automated machining flow line and for this investigation is an intensive research in the machining production field required.
The research in the machining production field should offer constraints which represent realistic data of machining flow lines. A U-shaped machining line breakdown optimization using realistic data will ensure backup robots are the most efficient breakdown strategy for U-shaped lines.
Nevertheless, the used data in the robotic U-shaped assembly line backup strategy has an impact on further researches in the breakdown strategy research field. As working robots downstream the line [50]. Due to this fact backup robot has to be considered as a new breakdown strategy which has the potential to ensure smooth line flow and a continuously high product quality for breakdowns. Furthermore, this thesis has shown that a genetic algorithm can be used in practice for the analysis of breakdown strategies. In Section 4.3, the genetic algorithm, which is used for the analyses of the rU-sbs, is described and it is shown that 16 hours are required for the investigation of one robotic U-shaped line backup strategy option.
Sixteen hours is a long investigation period and therefore the modified is not an online solution which can offer the best breakdown strategy instantly. Nevertheless, the research for the best breakdown strategy for each flow line layout has to be done during the line designing period. The line designing period usually takes several month or even years when a new facility is build up and therefore 16 hours is not a long time period to investigate the performance of a breakdown strategy. In addition, the genetic algorithm can be used as a solution approach for many different optimization problems which is shown in Section 2.5.2. Due to these facts, the genetic algorithm has the potential to be used in the practice as a solution approach for the investigation of the performance of breakdown strategies in the line layout designed. shown that the three backup stations option on the placements A, C and D has the most efficient performance and it performs much better than the current breakdown strategies.
The three backup stations option on the placements A, C and D has the cycle time increase from 94 seconds for the 5%-line breakdown to 122 seconds for the 15%-line breakdown scenario which is a good performance, because the initial cycle time for a line flow without breakdowns is 91 seconds. Due to this fact this backup strategy ensures a smooth and high volume production in each breakdown scenario.
Furthermore, the robotic U-shaped line backup strategy option ACD does not use manual repair stations and therefore is offers a good product quality continuously. On the contrary, the current breakdown strategies perform much worse than the robotic Ushaped line backup strategy option ACD. They have at least a twice higher cycle time than the rU-sbs option ACD for breakdowns and they have to execute several tasks on manual repair stations which decrease the product quality.
Chapter 6 reviews critically the robotic U-shaped line backup strategy designed and the disadvantages of the rU-sbs are shown. These disadvantages are the maintains of the backup robots after each operation period, the requirement of an intelligent conveyor system and additional welding guns for the backup robots. Thus the robotic U-shaped line backup strategy could be a more cost-intensive option than the current breakdown strategies. However, the recommendation is given that a profit optimization is necessary to decide whether the robotic U-shaped line backup strategy offers the best practical performance of the current breakdown strategies.