A Genetic Algorithm for Solving Assembly Sequence Cost and Time - Report Example

GЕNЕTIС АLGОRITHM FОR SОLVING АSSЕMBLY SЕQUЕNСЕ СОST АND ТIMЕ NAME OF STUDENT PROFESSORS NAME DATE OF SUBMISSION А GЕNЕTIС АLGОRITHM FОR SОLVING АSSЕMBLY SЕQUЕNСЕ СОST АND ТIMЕ Introduction Assembly sequence is a process by which a certain product undergoes from the point of the raw material to the point where there is a final product that is developed. This process is normally very expensive when the wrong implementation is done. The processing of various parts of a product needs several considerations to save on cost and time. Assembly sequence planning is a significant factor in ensuring that production of various commodities is optimized to be able to reduce the time of production and cost. This is applied when there are many parts to be assembled in a certain production line. The assembling process involves many parts to be integrated into the final product. Various parts of the product vary regarding precedence, accessibility, type of constrains and geometry of the components. When there is a large-scale production with several constraints, numerous combinations are generated for the assembly. There is a need for an effective sequence in the assembly for the production to be cost and time effective. In this research, I will be able to discuss the use of a genetic algorithm as a method used in the optimization of the assembly process to ensure that the production is cost and time effective. A genetic algorithm is a concept which was developed from the reproduction process in the various organism. This method is applied to ensure that the assembling process is effective and cost efficient. It has been successfully tested and hence it’s the most preferred method of optimizing various assembly sequence planning processes. The genetic algorithm will be applied in this research to develop an effective assembly sequence planning for production of mobile phones. This method is effective since it can handle several search spaces in the production process. This method is also preferred due to its ability to provide a flexible way of defining constraints. According to (Whitley, 2014, pp 45-56), Using genetic algorithm ensure that there is an easy way of deriving the fitness function for any assembly sequence. The application of penalty function is also simple with the use of the genetic algorithm for computing the fitness value in any given assembly sequence. A genetic algorithm is normally computer based function which facilitates the development of approximate solutions for optimizing and searching for difficulties. The main aim of using genetic algorithm is to ensure that the assembling process takes the shortest time possible. The other aim of the use of this method in optimizing assembly sequence is the fact that with this method, the cost of production is minimized to the most efficient level (Whitley, 2014). The comparison between the results of various assembly processes applied in production indicates clearly that genetic algorithm is more superior than design for assembly. This is the method that will be applied to the assembly of a mobile phone. A genetic algorithm is applied to ensure that there is less time wasted in the assembly of mobile phones. This method will be rolled out in various stages: Assembly generation and modeling Sequence generation Evaluation Optimization This is main stages through which genetic algorithm method of obtaining the optimum result of an assembly is composed. The research will consider the generation and modeling stage of a mobile phone to help in the determination of constraints. Assembly modelling To develop the sequence planning, there is need to develop a representation model which will be used to represent the parts to be used in the assembling of mobile phones. This is implemented by the use of a Liaison graph. The graph will provide the sequence of various components in the assembly. This procedure consists of contact matrix, interference matrix and connection matrix. Below is an assembly precedence matrix for a mobile. This would use 13 components used in the assembly of the mobile phone; printed circuit board, top case, main button, keyboard, frame, right button, camera, bottom case, battery, a top button, LCD, screen cover, right button. Assembly precedence matrix = In the assembly of a mobile phone, there are 13 components which need to be used to come up with one unit of mobile phone. This depends on the available capabilities of the firm as indicated in the plant capability table. F is used to represent the number of the set of available plants and P is the set of available components. For this case for a mobile assembly, there are 13 components, and we just assume there is only four plant. This information helps in determining the component and the plant which has been assigned. For the case of mobile phone plant, we assume that the plants are located in a place in the company premises. Therefore, all operations of assembling will be done in the same location. The information will then be used in the generation and evaluation of the assembly sequence (Whitley, 2014). Solving using genetic algorithm Chromosome encoding scheme is then formulated to represent the plants that would be used to assemble the components. This is made up of components and plants in an ordered manner as shown in the table below. Assembly sequence order 1 2 3 4 5 6 7 8 9 10 11 12 13 Name of component 13 12 11 8 7 10 9 5 4 3 2 6 1 Plants 2 2 2 3 3 3 3 1 1 1 1 4 4 The chromosome will then give a solution of sequence gene. The sequence from left to right represents the components in the assembly sequence. This makes each component encounter the gene in the plant from left to right. An example is a chromosome with eight components and four plants. The genes from C1 to C10 represent a component, then the remaining to 13 will be reprinting the plants i.e. 1,2,3 will stand for plants. This gives a chromosome 2, 1, 9, 11, 8, 3, 13, 7, 6, 5, 10, 12. The resultant for this would be resolved as C2, C1, C9, C11, C8, C3, F3, C13, C7, C6, F1, C5, C10, C12, F2. This will mean that the components C2, C1, C9, C11, C8, C3 are assembled in plant F3. Also C5, C10, C12 will be assembled in plant F2 and finally C13, C7, C6 would be assembled in plant F1. Development of fitness function There are many items to be considered in derivation of the fitness function which describes the cost of various items; assembly accessibility cost (AAC); assembly instability cost (ASC); assembly tool setup cost (ATC); assembly operation cost (ACC); assembly weight effect cost (WAI); general transport cost (GTC). The cost of various operations listed above is considered to be in dollars. The function of the total cost will be denoted as (TC), this the sum of all the cost incurred in the assembly. TC = AAC + ATC + ACC + WAI+ GTC+ ASC The chromosome that is developed will be a function of the fitness function, the chromosome which has a smaller value of the fitness function is considered for use in the generation of proceeding chromosome. fit(I) = TC(I), (3) where fit(I) is the value of fitness function chromosome, TC(I) cost of the chromosome. Crossover operator will be used as applied in the roulette wheel selection; this will be used to combine elements from the two parents to develop new offspring. This is calculated as (C Number) = (C Rate) × (P Size). After crossing over the mutation process will occur as per the adaptation of the new chromosome, this is calculated as (M Number) = (M Rate) × (P Size). G Number is a number which indicated where the evolution stops, P Size is the size of determining the population of the chromosome, C Rate is the rate of crossover, M Rate is the rate of mutation (Whitley, 2014). Evaluating solution The genetic algorithm is implemented and tested on the computer, shows that the assembly has been optimized. The time is taken to assemble the components as seen in the implementation of a mobile phone assembly. The Taguchi’s orthogonal array has been used to implement numerical values of the genetic algorithm. The G Number = 80, , C Rate = 0.5, P Size = 20 and M Rate = 0.3 are used as the most appropriate values to be set for the assembly of mobile phones. The test result is a shown below. cost generation The graph above shows the point of convergence is 44 which gives a cost of $ 332; this will be the optimized cost for the assembly of a single mobile phone. This indicates that the listed sequence that was generated by the genetic algorithm is the most effective as compared to any other method of assembly. This method can hence be useful when low cost and less time is required during an implementation of various assembling processes. In conclusion, a genetic algorithm is able to assign a plant to a certain component and at the same time develop the most suitable sequence of the assembling process. The fitness function helps in the integration of various assembly cost of operations. The cost and time for operations are optimized for the application of the genetic algorithm. References Whitley, D., 2014. An executable model of a simple genetic algorithm.Foundations of genetic algorithms, 2(1519), pp.45-62. Read More

This method will be rolled out in various stages: Assembly generation and modeling Sequence generation Evaluation Optimization This is main stages through which genetic algorithm method of obtaining the optimum result of an assembly is composed. The research will consider the generation and modeling stage of a mobile phone to help in the determination of constraints. Assembly modelling To develop the sequence planning, there is need to develop a representation model which will be used to represent the parts to be used in the assembling of mobile phones.

This is implemented by the use of a Liaison graph. The graph will provide the sequence of various components in the assembly. This procedure consists of contact matrix, interference matrix and connection matrix. Below is an assembly precedence matrix for a mobile. This would use 13 components used in the assembly of the mobile phone; printed circuit board, top case, main button, keyboard, frame, right button, camera, bottom case, battery, a top button, LCD, screen cover, right button. Assembly precedence matrix = In the assembly of a mobile phone, there are 13 components which need to be used to come up with one unit of mobile phone.

This depends on the available capabilities of the firm as indicated in the plant capability table. F is used to represent the number of the set of available plants and P is the set of available components. For this case for a mobile assembly, there are 13 components, and we just assume there is only four plant. This information helps in determining the component and the plant which has been assigned. For the case of mobile phone plant, we assume that the plants are located in a place in the company premises.

Therefore, all operations of assembling will be done in the same location. The information will then be used in the generation and evaluation of the assembly sequence (Whitley, 2014). Solving using genetic algorithm Chromosome encoding scheme is then formulated to represent the plants that would be used to assemble the components. This is made up of components and plants in an ordered manner as shown in the table below. Assembly sequence order 1 2 3 4 5 6 7 8 9 10 11 12 13 Name of component 13 12 11 8 7 10 9 5 4 3 2 6 1 Plants 2 2 2 3 3 3 3 1 1 1 1 4 4 The chromosome will then give a solution of sequence gene.

The sequence from left to right represents the components in the assembly sequence. This makes each component encounter the gene in the plant from left to right. An example is a chromosome with eight components and four plants. The genes from C1 to C10 represent a component, then the remaining to 13 will be reprinting the plants i.e. 1,2,3 will stand for plants. This gives a chromosome 2, 1, 9, 11, 8, 3, 13, 7, 6, 5, 10, 12. The resultant for this would be resolved as C2, C1, C9, C11, C8, C3, F3, C13, C7, C6, F1, C5, C10, C12, F2.

This will mean that the components C2, C1, C9, C11, C8, C3 are assembled in plant F3. Also C5, C10, C12 will be assembled in plant F2 and finally C13, C7, C6 would be assembled in plant F1. Development of fitness function There are many items to be considered in derivation of the fitness function which describes the cost of various items; assembly accessibility cost (AAC); assembly instability cost (ASC); assembly tool setup cost (ATC); assembly operation cost (ACC); assembly weight effect cost (WAI); general transport cost (GTC).

The cost of various operations listed above is considered to be in dollars. The function of the total cost will be denoted as (TC), this the sum of all the cost incurred in the assembly. TC = AAC + ATC + ACC + WAI+ GTC+ ASC The chromosome that is developed will be a function of the fitness function, the chromosome which has a smaller value of the fitness function is considered for use in the generation of proceeding chromosome. fit(I) = TC(I), (3) where fit(I) is the value of fitness function chromosome, TC(I) cost of the chromosome.

Crossover operator will be used as applied in the roulette wheel selection; this will be used to combine elements from the two parents to develop new offspring.

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