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Machine Layout Design and Optimization

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Machine Layout Design and Optimization

  1. 1. MACHINE LAYOUT DESIGN & OPTIMIZATION A PROJECT REPORT Submitted by NARESH KUMAR.K (070111303029) NIVAS.S (070111303033) SENTHIL NATHAN.R (070111303050) In partial fulfillment for the award of the degree of BACHELOR OF ENGINEERING IN MECHANICAL ENGINEERING INSTITUTE OF ROAD AND TRANSPORT TECHNOLOGY ERODE-638316 ANNA UNIVERSITY OF TECHNOLOGY, COIMBATORE 641047 APRIL 2011 i
  2. 2. TABLE OF CONTENTS CHAPTER NO TITLE PAGE NO ABSTRACT vii LIST OF TABLES viii LIST OF FIGURES x LIST OF ABBREVIATIONS xi 1 MACHINE LAYOUT AND OPITIMIZATION 1.1 INTRODUCTION 2 1.2 INTRODUCTION TO MACHINE LAYOUT 3 1.3 BASIC LAYOUT TYPES 1.3.1 PROCESS LAYOUT 3 1.3.2 CELL LAYOUT 4 1.3.3 PRODUCT LAYOUT 4 1.4 CYCLE TIME 5 1.5 HIERARCHY OF MACHINE LAYOUT DATA 5 2 INTRODUCTION 2.1 COMPANY PROFILE 8 2.2 CNC MACHINE SHOP 9 2.3 STEERING KNUCKLE 10 2.4 OPERATIONS PERFORMED 11 2.5 TIME STUDY FOR ALL COMPONENTS 13 3 INTRODUCTION TO GENETIC ALGORITHM 3.1 DEFINITION OF GENETIC ALGORITHM 15 3.2 BASIC GENETIC ALGORITHM 16 3.3 OTHER SEARCH TECHNIQUES ii
  3. 3. 3.3.1 HILL CLIMBING 17 3.3.2 ENUMERATIVE 17 3.3.3 RANDOM SEARCH ALGORITHM 18 3.3.4 RANDOMIZED SEARCH TECHNIQUES 18 3.4 THE DIFFERENCE BETWEEN GENETIC ALGORITHM AND TRADITIONAL METHODS 18 3.5 BASIC GENETIC ALGORITHM OPERATIONS 3.5.1 REPRODUCTION 19 3.5.2 CROSS OVER 20 3.5.3 MUTATION 22 3.6 POWER OF GENETIC ALGORITHM 23 4 LAYOUT MODELLING USING EXCEL 4.1 PROBLEM STATEMENT 25 4.2 APPLICATION OF GENETIC ALGORITHM 25 4.3 ASSUMPTIONS 26 4.4 COMPONENT DETAILS 26 4.5 MATHEMATICAL MODEL 29 4.6 EXISTING LAYOUT WITH STEERING KNUCKLE FLOW 30 4.7 CENTROID CALCULATION 31 4.8 PART ROUTING MATRIX 32 4.8.1 COST MATRIX 32 4.8.2 DISTANCE MATRIX 33 4.8.3 FLOW MATRIX 35 4.9 MATERIAL HANDLING COST FOR EXISTING LAYOUT 35 5 LAYOUT OPTIMIZATION 5.1 GA PARAMETERS 39 5.2 OPTIMIZER OUTPUT 39 5.2.1 PROPOSED LAYOUT #1 (NEW) 40 iii
  4. 4. 5.2.2 PROPOSED LAYOUT #2 (NEW) 41 5.2.3 PROPOSED LAYOUT #3 (NEW) 42 5.2.4 PROPOSED LAYOUT #1 (MODIFIED) 43 5.2.5 PROPOSED LAYOUT #2 (MODIFIED) 44 5.3 SELECTION OF LAYOUT 46 6 CONCLUSION 49 7 REFERENCES 51 8 APPENDIX 53 iv
  5. 5. ABSTRACT The basic layout problem is the arrangement of the departments according to flow of materials between them. The design criterion routinely used in most of the layout deign procedures - a measure of long-term material handling efficiency, fails to capture the impact of layout configuration on operational performance measures such as cycle time, queue times at processing departments, throughput rates etc. As a result, layout performance tends to deteriorate significantly with fluctuations in product volumes, mix, or routings. In this project, an approach that combines meta-heuristic algorithm with simulation to optimize the layout for manufacturing effectiveness and evaluate the same based on operational performance measures is proposed. Application of meta-heuristic algorithms like Simulated Annealing, Genetic Algorithm and Hybrid algorithms are helps us in reaching near optimal or optimal solutions for the medium, large size facility layout problems without much computation difficulties. Due to the advances in computer technology, simulation become more dominant tool for analyzing manufacturing systems based on quantitative and qualitative criteria. In view of this a combined approach of Meta-heuristic algorithms and system simulation to solve facility layout problems is proposed here. v
  6. 6. LIST OF TABLES TABLE TABLE NAME PAGE NO NO SEQUENCE OF OPERATION AND NO OF MACHINES USED 2.1 11 FOR COMPONENT #1 SEQUENCE OF OPERATION AND NO OF MACHINES USED 2.2 12 FOR COMPONENT #2 SEQUENCE OF OPERATION AND NO OF MACHINES USED 2.3 12 FOR COMPONENT #3 SEQUENCE OF OPERATION AND NO OF MACHINES USED 2.4 13 FOR COMPONENT #4 MACHINES INVOLVED IN PRODUCTION OF STEERING 4.1 25 KNUCKLE 4.2 SEQUENCE OF MACHINES USED FOR 4 COMPONENTS 26 MACHINING TIME AND SEQUENCE OF OPERATION FOR 4.3 27 COMPONENT #1 MACHINING TIME AND SEQUENCE OF OPERATION FOR 4.4 27 COMPONENT #2 MACHINING TIME AND SEQUENCE OF OPERATION FOR 4.5 28 COMPONENT #3 MACHINING TIME AND SEQUENCE OF OPERATION FOR 4.6 28 COMPONENT #4 CALCULATION OF AREA REQUIRED FOR EACH 4.7 31 MACHINES 4.8 BATCH SIZE OF 4 COMPONENTS 32 4.9 COST MATRIX OF EXISTING LAYOUT 33 4.10 DISTANCE MATRIX OF EXISTING LAYOUT 34 4.11 FLOW MATRIX OF EXISTING LAYOUT 35 vi
  7. 7. MATERIAL HANDLING COST MATRIX OF EXISTING 4.12 36 LAYOUT 5.1 MATERIAL HANDLING COST OF ALL SOLUTION LAYOUTS 39 COMPARISION OF ALTERNATIVE LAYOUT 5.2 47 CONFIGURATIONS vii
  8. 8. LIST OF FIGURES FIGURE FIGURE NAME PAGE NO NO 1.1 PROCESS LAYOUT 4 1.2 HIERARCHY OF MACHINE LAYOUT DATA 5 DISTANCE TRAVELLED BY PARTS REDUCED BY CHANGING 1.3 6 MACHINE LAYOUT 2.1 STEERING KNUCKLE 10 2.2 STEERING KNUCKLE 10 3.1 BASIC GENETIC ALGORITHM - FLOW CHART 16 4.1 EXISTING LAYOUT WITH STEERING KNUCKLE FLOW 30 PROPOSED LAYOUT #1 (NEW) WITH 5.1 40 STEERING KNUCKLE FLOW PROPOSED LAYOUT #2 (NEW) WITH 5.2 41 STEERING KNUCKLE FLOW PROPOSED LAYOUT #3 (NEW) WITH 5.3 42 STEERING KNUCKLE FLOW PROPOSED LAYOUT #1 (MODIFIED) WITH 5.4 43 STEERING KNUCKLE FLOW PROPOSED LAYOUT #2 (MODIFIED) WITH 5.5 44 STEERING KNUCKLE FLOW GRAPH (NO OF TRIALS Vs VALUES) OF MODIFIED LAYOUT 5.6 45 #1 AND MODIFIED LAYOUT #2 viii
  9. 9. LIST OF ABBREVIATIONS GA ----- GENETIC ALGORITHM SACL ----- SAKTHI AUTO COMPONENTS LIMITED CNC ----- COMPUTER NUMERICAL CONTROL SLA ----- SHORT LONG ARM ix
  10. 10. CHAPTER 1 MACHINE LAYOUT AND OPTIMIZATION
  11. 11. 1.1 INTRODUCTION The traditional facility layout problem in a manufacturing setting is defined as the determination of relative locations for, and allocation of, the available space among a given number of workstations. Although most facility layout solutions have, in the past, focused on minimizing the amount of transportation, the effect of a given layout design on the production function of a manufacturing system is much more than just the cost of material handling. While material handling cost remains critical, shorter cycle times have become much more important in today’s manufacturing systems. Rapid developments in new products, coupled with short delivery times demanded by customers, are the bases of the time-based competitive strategies rapidly being adopted by inventory and short manufacturing cycle times are practical considerations that have strong impacts on the layout design and should be incorporated into the layout design process as genuine concerns. But, the difficulty in linking the layout configurations and operational performance measures via mathematical or analytical models has been recorded in the literature by various researchers and practitioners for the past few years. However, we require new design models and solution procedures that account for uncertainty and variability in design parameters such as product mix, production volumes, and product life cycles, for complex manufacturing system analysis and rational decision making while handling
  12. 12. 1.2 INTRODUCTION TO MACHINE LAYOUT One of the most important factors to consider in designing the manufacturing facilities is finding an effective layout. Laying out a factory involves deciding where to put all the facilities, machines, equipment and staff in the manufacturing operation. Layout determines the way in which materials and other inputs (like people and information) flow through the operation. Relatively small changes in the position of a machine in a factory can affect the flow of materials considerably. This in turn can affect the costs and effectiveness of the overall manufacturing operation. Getting it wrong can lead to inefficiency, inflexibility, large volumes of inventory and work in progress, high costs and unhappy customers. Changing a layout can be expensive and difficult, so it is best to get it right first time. 1.3 BASIC LAYOUT TYPES Once the type of operation has been selected (jobbing, batch or continuous) the basic layout needs to be selected. There are three basic types:  Process layout  Cell layout  Product layout 1.3.1 PROCESS LAYOUT In process layout, similar manufacturing processes (cutting, drilling, wiring, etc.) are located together to improve utilisation. Different products may require different processes so material flow patterns can be complex.
  13. 13. 1.3.2 CELL LAYOUT In cell layout, the materials and information entering the operation are pre-selected to move to one part of the operation (or cell) in which all the machines to process these resources are located. After being processed in the cell, the part-finished products may go on to another cell. In effect the cell layout brings some order to the complexity of flow that characterises process layout. 1.3.3 PRODUCT LAYOUT Product layout involves locating the machines and equipment so that each product follows a pre-arranged route through a series of processes. The products flow along a line of processes, which is clear, predictable and relatively easy to control. To design a process layout, the designer needs to know:  The area required by each work centre.  The constraints on the shape of the area allocated for each work centre.  The degree and direction of flow between each work centre (for example number of journeys, number of loads, cost of flow per distance travelled).  The desirability of work centres being close together.
  14. 14. 1.4 CYCLE TIME The cycle time of a product layout is the time between completed products emerging from the operation. Cycle time is a vital factor in the design of product layouts and influences most other detailed design decisions. It is calculated by considering the likely demand for the products over a period and the amount of production time available in that period. 1.5 HIERARCHY OF MACHINE LAYOUT DATA:
  15. 15. Machine Machine Machine Machine 9 11 14 10 15 15 7 3 5 Machine Machine 3 Machine 3 Machine 12 5 2 7 15 1 7 Machine 1 Machine Machine Machine 8 6 3 1 23 23 7 Machine Machine 4 13 Part 1: 4-5-7 Part 15: 6-9-8-14 Part 3: 2-10-3-11 Part 23: 4-5-13 Part 5: 8-9 Part 7: 1-12-7-13 Movements of parts at Generation 1 : Distance Travelled = 234 CELL 1 CELL 2 Machine Machine Machine 1 Machine 14 9 4 23 5 15 15 5 23 15 1 Machine Machine Machine Machine 7 6 8 7 13 7 CELL 3 Machine 3 Machine Machine Machine 10 2 12 7 1 3 Machine 3 Machine 11 3 Part 1: 4-5-7 Part 15: 6-9-8-14 Part 3: 2-10-3-11 Part 23: 4-5-13 Part 5: 8-9 Part 7: 1-12-7-13 Movement of parts at Generation 100: Distance Travelled by parts: 109
  16. 16. CHAPTER 2 INTRODUCTION
  17. 17. 2.1 COMPANY PROFILE SAKTHI AUTO COMPONENTS LIMITED (SACL) Sakthi Auto Component Limited is one among the MULTI FACETED Sakthi Group situated at Mukasi Pallagoundenpalayam, Erode District, Tamilnadu State, India, established in the year 1983. Presently the Sakthi Auto has a capacity to produce 24000 Tonnes / annum of S.G.IRON Castings, on a 100 Acre Land with all amenities for Workmen and Officers like Housing, Transport etc. Sakthi Auto is one of the major producers of S.G.Iron Castings, meeting the needs of most of the Automotive and other general Engineering Industries Sakthi Auto Component Limited is a major supplier of critical components to passenger car manufacturers. The components are Steering knuckles, Brake drums, Brake discs, Hubs , Brake calipers, Carriers, Differential cases and Manifolds etc. Presently the supplies of these components are made to Maruti Udyog Ltd., Hyundai, Ind Auto Ltd., Ford, Honda Siel Cars and Tractors and farm Equipment Ltd. etc,. Castings meant for trucks and refineries are exported to USA. The quantum of exports per month ranges between 250 MT to 500 MT. It is likely to go up to 1000 MT in near future Supplying most CRITICAL COMPONENTS like STEERING KUNCKLE, BRAKE DRUMS and MANIFOLDS for all Suzuki Vehicles Manufactured in India by M/s. Maruti Udyog Limited at New Delhi & to many leading passenger car manufacturers in fully machined condition. R&D Lab is attached to our Sakthi Auto with modern computerised equipments like Direct Reading Spectrometer, Carbon Sulphur determination, Universal Testing Machine, Scanning Electron Microscope, Industrial X-RAY Scanner etc. Sakthi Auto is equipped with DISAMATIC FOUNDRY with the state of the art manufacturing technology which is regarded as the best anywhere in the World. And equipped with many sophisticated special purpose and CNC machines to produce precision oriented component for passenger car and automobile industries.
  18. 18. The sakthi group of companies performs, contributes and touches the lives of many with operation in the fields of sugar, alcohol, tea, soft drinks, soya foods, synthetics, gems, textiles, transport, retreading, finance and foundry. The company has strategically invested in the most modern foundry facility and looks forward to set the pace for the industry in the years to follow... Auto and engineering component slack adjusters, wing nuts and unions, steering knuckles in machined condition auto and engineering component slack adjusters, wing nuts and unions, steering knuckles in machined condition automotive parts, component. Technical know how from Georg Fischer is expected that the unit will double its output by Foundry Systems. This has helped meeting June 2004 and further look at some expansion in increasing demands from indigenous and 2005. This is due to the fact that the Indian auto overseas original equipment manufacturers, market is growing at more than 20% and the especially in automobile sector. Other facilities global players like Delphi, Visteon, Rover and include engineering workshop, testing Haldex have approached the company for laboratories, spectrometer, X- ray scanner, etc. further components. 2.2 CNC MACHINE SHOP: SACL is the sole vendor for many critical components like steering knuckles, brake CNC DIVISION drums, brake discs, exhaust manifolds and case The CNC machine division of SACL has imported differentials for leading manufacturers in India equipments for machining rough castings to like Maruti, Suzuki, Huyndai, FIAT and Delphi. exacting standards of dimensional specifications. www.sakthiauto.com SACL has also received a purchase order for 2.5 million dollars per annum from Delphi and has begun shipping the components to the US. SACL is one of the first units in the Asia Pacific zone to export castings to the Delphi north American markets. Delphi is in the process of negotiating a new purchase order for about 18 million dollars per annum. It is expected that this order will be received by the first quarter of 2004. At present the domestic and export enquiries at the plant are for about 150% of the capacity.
  19. 19. 2.3 STEERING KNUCKLE A forging that usually includes the spindle and steering arm, and allows the front wheel to pivot. The knuckle is mounted between the upper and lower ball joints on a SLA suspension, and between the strut and lower ball joint on a MacPherson strut suspension.
  20. 20. There are four different type of steering knuckle components are manufacturing in CNC machine shop, SACL. There are given below:  J200 Knuckle  MCI Knuckle  GIO Knuckle  MXI Knuckle 2.4 OPERATIONS PERFORMED: The operations performed for these components are given by, COMPONENT 1: J200 KNUCKLE: The sequence of operations and no of machines used of component 1 are given below, NO OF Operation MACHINE OPERATION NAME MACHINES NO NO USED 1 Turning 2 1&2 SBA Milling Drilling, Caliber arm Milling, 2 1 3 Drilling & Coverhole tapping 3 Kingpin arm milling Drilling 1 4 Milling, slitting, drilling, tie rod arm milling, 4 1 5 drilling 5 ABS milling, Drilling, Tapping 1 6
  21. 21. COMPONENT 2: MCI KNUCKLE: The sequence of operations and no of machines used of component 2 are given below, NO OF Operation MACHINE OPERATION NAME MACHINES NO NO USED 1 Turning 1 7 2 Caliber arm Milling, Drilling 1 8 SBA milling drilling,Tie rod arm milling 3 drilling,Kingpin arm milling Drilling, 1 9 Tapping COMPONENT 3: GIO KNUCKLE: The sequence of operations and no of machines used of component 3 are given below, NO OF Operation MACHINE OPERATION NAME MACHINES NO NO USED 1 Turning 1 10 SBA Milling Drilling, Mounting hole drilling, 2 1 11 Tapping Tie rod arm milling drilling, Taper reaming, 3 1 12 Kingpin arm milling Drilling 4 Kingpin arm drilling slitting milling 1 13
  22. 22. COMPONENT 4: MXI KNUCKLE: The sequence of operations and no of machines used of component 4 are given below, NO OF Operation MACHINE OPERATION NAME MACHINES NO NO USED 1 Turning 2 14 & 15 2 Caliber arm Milling,Drilling 1 16 3 SPI milling 1 17 4 Tie rod arm milling 1 18 Kingpin arm machining, Tie rod 5 1 19 arm milling SBA drilling, Kingpin arm drilling 6 1 20 & slitting 2.5 TIME STUDY FOR ALL COMPOENTS: The time required to produce a steering knuckle can be obtained by the following table: Component Component Component Component #1 #2 #3 #4 Machining 19 min 37 sec 11 min 49 sec 12 min 33 sec 12 min 3 sec Time Loading Time 2 min 25 sec 1 min 15 sec 2 min 33 sec 1 min 55 sec Unloading 1 min 50 sec 55 sec 2 min 18 sec 1 min 46 sec Time TOTAL 23 min 52 sec 13 min 59 sec 17 min 24 sec 15 min 44 sec TIME
  23. 23. CHAPTER 3 INTRODUCTION TO GENETIC ALGORITHM
  24. 24. 3.1 DEFINITION OF GENETIC ALGORITHM: “Genetic algorithms are search algorithms based on the mechanics of natural selection and natural genetics” Bauer gives a similar definition as follows: “Genetic algorithms are software , procedures modelled after genetics and evolution” GA exploits the idea of the survival of the fittest and an interbreeding population to create a novel and innovative search strategy.A population of strings, representing solutions to a specified problem , is maintained by the GA. The GA then iteratively creates the new populations from the previous population by ranking and interbreeding the fittest to create new strings, which are closer to the optimum solution to the problem. GA is a form of randomized search,in that way in which strings are chosen and combined is a stoichastic process. This is a radially different approach to the problem solving methods, which are tends to be more deterministic in nature. The idea of survival of the fittest is of great importance to genetic algorithms. GAs use what is termed as a fitness function in order to select the fittest string that will be used to create new and better populations of strings. The fitness function takes a string and assigns a relative value to the string. The method and the nature of the fitness value does not matter. The fitness function must do is to rank the strings by producing the fitness value. These values are then use to select the fittest strings.
  25. 25. 3.2 BASIC GENETIC ALGORITHM The following flowchart shows the iterative cycle of a basic genetic algorithm. Firstly, an initial population of strings is created. The process then iteratively selects individuals from the population that undergo some form of transformation (via the recombination step) to create new population. The new population is then tested to see if it fulfills some stopping criteria. If it does, then the process halts, otherwise iteration is again performed.
  26. 26. 3.3 OTHER SEARCH TECHNIQUES: We will look at some of the other, more traditional, optimization techniques, and show both their strengths and shortcomings when compared with GAs. 3.3.1 Hill climbing: Hill climbing optimization techniques have their roots in the classical mathematics developed in the 18th and 19th centuries. In essence, this class of search methods finds an optimum by following the local gradient of the function (they are sometimes known as gradient methods). They are deterministic in their searches. They generate successive results besed solely on the previous results. There are several drawbacks to hill climbing methods. Firstly, they assume that the problem space being searched is continuous in nature. In other words, derivative of the function representing the problem space exists. This is not true of many real world problems where the problem space is noisy and discontinuous. Another major disadvantage of using hill climbing is that hill climbing algorithm only find the local optimum in the neighbourhood of the current point. They have no way of looking at the global picture in general. However, parallel methods of hill climbing can be used to search multiple points in the problem space. This still suffers from the problem that there is no guarantee of finding the optimum value, especially in very noisy spaces with a multitude of local peaks or troughs. 3.3.2 Enumerative: The basis of Enumerative techniques is simplicity itself. To find optimum value in a problem space (which is finite), look at the function values at every point in the space. The problem here is obvious. This is horribly inefficient. For very large problem spaces, the computational task is massive, perhaps intractably so.
  27. 27. 3.3.3 Random search algorithms: Random searches simply perform random walks of the problem space, recording the best optimum values discovered so far. Efficiency is a problem here as well. For large problem spaces, they should perform no better than enumerative searches. They do not use any knowledge gained from previous results and thus are both dumb and blind. 3.3.4 Randomized search techniques: Randomized search algorithms use random choice to guide themselves through the problem search space. But these are not just simply random walks. These techniques are not directionless like the random search algorithms. They use the knowledge gained from previous results in the search and combine them with some randomizing features. The result is a powerful search technique that can handle noisy, multi model search spaces with some relative efficiency. The two most popular forms of randomized search algorithms are simulated annealing and genetic algorithms. 3.4 THE DIFFERENCE BETWEEN GENETIC ALGORITHM AND TRADITIONAL METHODS: The following list is a very quick look at the essential differences between GAs and other forms of optimization.  Genetic algorithms a coded form of the function values (parameter set), rather than with the actual values themselves, So, for example, if we want to find the minimum of the function f(x)=X3+X2+5, the GA would not deal directly with X or Y values, but with strings that encode these values. For this case, strings representing the binary X values should be used.  Genetic algorithms use a set, or population, of points to conduct a search, not just a single point on the problem space. This gives GAs the power to search noisy spaces littered with local optimum points. Instead of relying on a single point to search through the space, the GAs looks at many different areas of the problem space at once, and uses all of this information to guide it.
  28. 28.  GAs are probabilistic in nature, not deterministic. This is a direct result of the randomization techniques used by GAs.  GAs are inherently parallel. Here lies one of the most powerful features of genetic algorithms. GAs, by their nature, is very parallel, dealing with a large number of points (strings) simultaneously. Holland has estimated that a GA processing n strings at each generation, the GA in reality processes n3 useful substings.  GA use only payoff information to guide themselves through the problem space. Many search techniques need a variety of information to guide themselves. Hill climbing methods require derivatives, for example. The only information a GA needs is some measure of fitness about a point in the space (sometimes known as an objective function value). Once the GA knows the current measure of ―goodness‖ about a point, it can use this to continue searching for the optimum. 3.5 BASIC GENETIC ALGORITHM OPERATIONS: There are three basic operators found in every genetic algorithm. (Although some algorithms may not employ the crossover operator, we shall refer to them as evolutionary algorithms rather than genetic algorithms) 1. Reproduction 2. Crossover 3. Mutation 3.5.1 Reproduction: The reproduction operator allows individual strings to be copied for possible inclusion in the next generation. The chance that a string will be copied is based on the string’s fitness value, calculated from a fitness function. For each generation, the reproduction operator chooses string that are placed into a mating pool, which is used as the basis for creating the next generation.
  29. 29. There are many different types of reproduction operators. One always selects the fittest and discards the worst, statistically selecting the rest of the mating pool from the remainder of the population. There are hundreds of variants of this scheme. None are right or wrong. In fact, some will perform better than others depending on the problem domain being explored. 3.5.2 Crossover: Once the matting poll is created, the next operator in the GA’s arsenal comes into play. Remember that crossover in biological terms refers to the blending of chromosomes from the parents to produce new chromosomes for the offspring. The analogy carries over to crossover in GAs. The GA selects two strings at random from the mating pool. The strings selected may be different or identical, it does not matter. The GA then calculates whether crossover should take place using a parameter called the crossover probability. This is simply a probability value p and is calculated by flipping a weighted coin. The value of p is set by the user, and the suggested value is p=0.6, although this value can be domain dependent. If the GA decides not to perform crossover, the two selected strings are simply copied to the new population (they are not deleted from the mating pool. They may be used multiple times during crossover).If crossover does takes place, then a random splicing point is chosen in a string, the two strings are spliced and the spliced regions are mixed to create two (potentially) new strings. These child strings are then placed in the new population. As an example, say that the strings 10000 and 01110 are selected for crossover and the GA decides to mate them. The GA selects a spacing point of 3.the following then occurs 100 00 100 10 011 10 011 00 Crossover in Action The newly created strings are 10010 and 01100.
  30. 30. Crossover is performed until the new population is crested. Then the cycle starts again with selection. This iterative process continues until any user specified criteria are met (for example, fifty generations, or a string is found to have a fitness exceeding a certain threshold). Single point crossover - one crossover point is selected, binary string from beginning of chromosome to the crossover point is copied from one parent, the rest is copied from the second parent 11001011+11011111 = 11001111 Two point crossover - two crossover point are selected, binary string from beginning of chromosome to the first crossover point is copied from one parent, the part from the first to the second crossover point is copied from the second parent and the rest is copied from the first parent 11001011 + 11011111 = 11011111 Uniform crossover - bits are randomly copied from the first or from the second parent 11001011 + 11011101 = 11011111
  31. 31. Arithmetic crossover - some arithmetic operation is performed to make a new offspring 11001011 + 11011111 = 11001001 (AND) 3.5.3 Mutation: Selection and crossover alone can obviously generate a staggering amount of differing strings. However, depending on the initial position chosen, there may not be enough variety of strings to ensure the GA sees the entire problems space. Or the GA may find itself converging on strings that are not quite close to the optimum it seeks due to a bad initial population. Some of these problems are overcome by introducing a mutation operator into the GA. The GA has a mutation probability, m, which dictates the frequency at which mutation occurs. Mutation can be performed either during selection or cross over. For each string element in each string in the mating pool, the GA checks to see if it should perform a mutation. If it should , it randomly changes the element value to a new one. In our binary strings, 1s are changed to 0s and 0s to 1s.For example, the GA decides to mutate bit position 4 in string 10000: Mutate 10000 10010 The resulting string is 10010 as the fourth bit in the string is flipped. The mutation probability should be kept very low ( usually about 0.001% ) as a high mutation rate will destroy fit strings and degenerate the GA algorithm into a random walk, with all the associated problems.
  32. 32. But the mutation will help prevent the population from stagnating, adding ― fresh blood‖, as it were, to a population. Remember that much of the power of a GA comes from the fact that it contains a rich set of strings of great diversity. Mutation helps to maintain that diversity througthout the GA s iterations. Bit inversion - selected bits are inverted 11001001 => 10001001 3.6 POWER OF GENETIC ALGORITHM: Selection + crossover = innovation - Selection gives us a population of the strongest individuals - Crossover attempts to combine parts of good individuals to make even better new ones Selection + Mutation = Stochastic Hill Climbing - Mutation makes slight alternations to these - We essentially have the equivalent of stochastic hill climbing All put together we get, Selection + Crossover + Mutation = The Power of GA Add crossover to that, and we have stochastic hill climbing with a means of jumping to potentially ―interesting‖ parts of the search space.
  33. 33. CHAPTER 4 LAYOUT MODELLING USING EXCEL
  34. 34. 4.1 PROBLEM STATEMENT To minimize the material handling cost by the optimal arrangement of machines in the shop floor. 4.2 APPLICATION OF GENETIC ALGORITHM Genetic algorithm search technique is applied to the above problem in order to find the minimum material handling cost in the production of Knuckle Joint in the CNC Machine shop. The following table gives the list of various machines involved in the production of Knuckle Joint. 1 Turning machine 2 SBA milling drilling 3 Caliber arm milling drilling 4 Drilling and cover hole tapping 5 King pin arm milling drilling 6 Tie rod arm milling drilling 7 Slitting machine 8 Tapping machine 9 Drilling machine 10 Taper reaming machine 11 Mounting hole drilling tapping 12 King pin arm drilling and slitting 13 Tie rod arm milling machine 14 SPI milling machine
  35. 35. 4.3 ASSUMPTIONS  The work areas of the work stations are rectangular in shape and their orientations are known.  Lot size does not change with the distance of travel between the machines that it connects.  Every workstation works only one part at a time.  Every transporter carries only one type of part at a time.  The operating sequences of tasks are the same for the same part types.  Transportation cost between facilities is assumed to be unit/m/part. 4.4 COMPONENT DETAILS There are 20 machines involved in the machining of 4 steering knuckle components. In these machines, 12 machines are Vertical Machining Centre, 6 machines are Turning machines, 2 machines are Milling machines. Machines which are used for 4 components and sequence of machines are given below: COMPONENT SEQUENCE LH—1-3-4-5-6 COMPONENT 1 RH—2-3-4-5-6 COMPONENT 2 7-8-9 COMPONENT 3 10-11-12-13 COMPONENT 4 14/15-16-17-18-19-20
  36. 36. COMPONENT 1 J200 KNUCKLE: The machining time and the sequence of operation for component 1 are as follows: Operation MACHINE TIME OPERATION NAME NO NO (Min) 1 4 min 17 sec 1 Turning 2 4 min 48 sec SBA Milling Drilling,Caliber arm 2 3 3 min Milling,Drilling & Coverhole tapping 3 Kingpin arm milling Drilling 4 1 min 38 sec Milling,slitting,drilling,tie rod arm 4 5 3 min 41 sec milling,drilling 5 ABS milling,Drilling,Tapping 6 2 min 13 sec COMPONENT 2 MCI KNUCKLE: The machining time and the sequence of operation for component 2 are as follows: Operation MACHINE TIME OPERATION NAME NO NO (MIN) 1 Turning 7 3 min 5 sec 2 Caliber arm Milling, Drilling 8 4 min 16 sec SBA milling drilling,Tie rod arm milling 3 drilling,Kingpin arm milling Drilling, 9 4 min 28 sec Tapping
  37. 37. COMPONENT 3 GIO KNUCKLE: The machining time and the sequence of operation for component 3 are as follows: Operation MACHINE TIME OPERATION NAME NO NO (MIN) 1 Turning 10 2 min 57 sec SBA Milling Drilling, Mounting hole 2 11 3 min 53 sec drilling, Tapping Tie rod arm milling drilling, Taper 3 12 3 min 39 sec reaming, Kingpin arm milling Drilling 4 Kingpin arm drilling slitting milling 13 2 min 4 sec COMPONENT 4 MXI KNUCKLE: The machining time and the sequence of operation for component 4 are as follows: Operation MACHINE CYCLE TIME OPERATION NAME NO NO (MIN) 14 3 min 13 sec 1 Turning 15 4 min 5 sec 2 Caliber arm Milling,Drilling 16 2 min 3 SPI milling 17 1 min 5 sec 4 Tie rod arm milling 18 1 min 35 sec Kingpin arm machining, Tie rod arm 5 19 2 min 13 sec milling SBA drilling, Kingpin arm drilling & 6 20 1 min 57 sec slitting
  38. 38. 4.5 MATHEMATICAL MODEL The single row layout problems for facilities with unequal lengths (Heragu, 1997) can be formulated as follows, n-1 n Minimize ---------------------------------- (1)   cij fij xi-xj Subject to xi - xj  ½ (li+lj) + dij i = 1, 2,3,….,n-1; j = i+1,….,n --------(2) Where n = no. of facilities cij = cost of moving a standard unit by a unit distance between facilities i and j fij = number of trips between facilities i and j li = length of the horizontal side of facility i dij = minimum distance by which facilities i and j are to be separated horizontally xi = distance between the center of facility i and the vertical reference line The material handling cost is calculated using the above mathematical model. Two loops are formed which calculates the material handling cost. The cost factor is the product of the following three terms.  Transportation cost between machines  Quantity of material flow  Distance between facilities
  39. 39. 4.6 EXISTING LAYOUT WITH STEERING KNUCKLE FLOW:
  40. 40. 4.7 CENTROID CALCULATION: Centroid of all the facilities are calculated by adding the clearances between them with length and width in order to find the material flow distance between the facilities. AREA Machine Width Length CLE_X CLE_Y Machine Name (X+Xc).(Y+Yc) No X(m) Y(m) Xc(m) Yc(m) (m2) 1 Turning Machine 2 4 0.5 1 12.5 2 Turning Machine 2.4 4 0.5 1 14.5 3 VMC 2.8 4.4 0.5 1 17.82 4 VMC 2.4 3.6 0.5 1 13.34 5 VMC 2.4 4 1 1 17 6 VMC 2.8 4 0.5 1 16.5 7 Turning Machine 2 4 1 1 15 8 VMC 2.8 3.6 0.5 1 15.18 9 VMC 2.4 4 1 1 17 10 Turning Machine 2.4 2.4 0.5 1 9.86 11 VMC 2.8 4 1 1 19 12 VMC 2.8 4 0.5 1 16.5 13 VMC 2.4 4 0.5 1 14.5 14 Turning Machine 2.4 2.4 0.5 1 9.86 15 Turning Machine 2 3.6 0.5 1 11.5 16 VMC 2.4 4 0.5 1 14.5 17 Milling Machine 1.2 2 0.5 1.5 5.95 18 Milling Machine 1.2 2 0.5 1.5 5.95 19 VMC 2.8 4 0.5 1 16.5 20 VMC 2.8 4 0.5 1 16.5
  41. 41. 4.8 PART ROUTING MATRIX The part routing matrix shows the Steering Knuckle flow between the facilities. Though the batch size is different for all 4 components. There are given below COMPONENT BATCH MACHINES USED NO SIZE #1 1 2 3 4 5 6 402 #2 7 8 9 207 #3 10 11 12 13 234 #4 14 15 16 17 18 19 20 294 With the help of the values from the part routing matrix, the centroid values and the cost factor the following matrices are formed. The product of the following matrices gives the material handling cost.  Cost matrix  Flow matrix  Distance matrix 4.8.1 COST MATRIX The cost matrix is formed in order to know the transportation cost between various facilities. In our problem, we had assumed an amount of one unit per meter per component or part. Since we are having the distance matrix values in meter the cost matrix values will be in 0.1 units.
  42. 42. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 2 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 3 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 4 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 5 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 6 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 7 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 8 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 9 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 10 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 11 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 12 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 13 0 0.1 0.1 0.1 0.1 0.1 0.1 0.1 14 0 0.1 0.1 0.1 0.1 0.1 0.1 15 0 0.1 0.1 0.1 0.1 0.1 16 0 0.1 0.1 0.1 0.1 17 0 0.1 0.1 0.1 18 0 0.1 0.1 19 0 0.1 20 0 4.8.2 DISTANCE MATRIX The distance matrix is formed with reference to the centroid values calculated for the facilities. Similar to the flow matrix, the diagonal values in the distance matrix will also be zero.
  43. 43. 4.8.3 FLOW MATRIX The flow matrix is formed by taking in to account the flow of components between the facilities where one to many relationship is followed. From the matrix it is clear that the diagonal values are zero, since there will be no material flow within the same machine. The remaining half of the matrix will have the mirror image values of the first half. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 0 0 201 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 201 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 402 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 402 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 402 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 207 0 0 0 0 0 0 0 0 0 0 0 0 8 0 207 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 10 0 234 0 0 0 0 0 0 0 0 0 11 0 234 0 0 0 0 0 0 0 0 12 0 234 0 0 0 0 0 0 0 13 0 0 0 0 0 0 0 0 14 0 0 147 0 0 0 0 15 0 147 0 0 0 0 16 0 294 0 0 0 17 0 294 0 0 18 0 294 0 19 0 294 20 0 4.9 MATERIAL HANDLING COST FOR EXISTING LAYOUT: For the existing layout of the facilities in the CNC Machine shop involved in the production of Steering Knuckle , the distance matrix, flow matrix and the cost matrix are formed as above. Now, the material handling cost spent for the existing layout is calculated by multiplying the three matrices as said before and is shown in the following table.
  44. 44. Thus the objective function value, which is the material handling cost for the existing layout is found to be 14256.42 Rupees. In order to have the objective function a maximum value the fitness value is calculated. The relation between the objective function value and the fitness value is as follows. Fitness value = (1 / Objective Function Value)
  45. 45. CHAPTER 5 LAYOUT OPTIMIZATION
  46. 46. 5.1 GA PARAMETERS: The following are the parameters that were used in the genetic algorithm optimizer in order to get the optimum solution. Population Size : 100 Cross Over : 0.6 Mutation : 0.2 No of trials : 3000 Random seed : 01 String representation : Single String 5.2 OPTIMIZER OUTPUT: With the above parameter the GA optimizer was made to run by selecting strings at random and the following results were obtained within a computational time of 28 seconds. Material handling cost for the existing layout = Rs. 14256.42 MATERIAL S.NO LAYOUT SEQUENCE HANDLING COST First Row: 12-11-3-4-5-6-7-8-9 1 Rs.1944.87 Second Row: 10-2-1-13-14-15-16-17-18-19-20 First Row: 12-11-3-4-5-6-7-8-9 2 Rs.1750.17 Second Row: 10-2-1-13-14-15-16-17-18-19-20 First Row: 12-11-3-4-5-6-7-8-9 3 Rs.1685.13 Second Row: 10-2-1-13-14-15-16-17-18-19-20
  47. 47. 1 20 19 1 1 1 1 2 9 8 1 20 19 1 1 1 1 2 9 1 3 8 7 6 3 8 7 6 4 12 11 1 1 3 4 5 6 7 11 12 1 6 5 4 3 8 7 4 5 5 1 1 0 0 MODIFIED LAYOUT #1 MODIFIED LAYOUT #2 MODIFIED LAYOUT #1 MODIFIED LAYOUT #2 GRAPH (NO OF TRIALS Vs VALUES) OF MODIFIED LAYOUT #1 AND MODIFIED LAYOUT #2 OBTAINED FROM EXCEL SHEET
  48. 48. 5.3 SELECTION OF LAYOUT: By using the genetic algorithm optimizer three feasible layouts were obtained. The relocation cost of machines is to be taken in to account when the layout is to be changed. With respect to the following comparison, the most feasible layout can be selected. NEW LAYOUT #1 12 11 3 4 5 6 7 8 9 10 2 1 13 14 15 16 17 18 19 20 NEW LAYOUT #2 12 11 3 4 5 6 7 8 9 10 13 1 2 14 15 16 17 18 19 20 NEW LAYOUT #3 11 12 2 4 5 6 7 8 9 10 13 1 3 14 15 16 17 18 19 20 MODIFIED LAYOUT #1 13 20 19 18 17 16 1 2 9 14 11 12 15 6 5 4 3 8 7 10 MODIFIED LAYOUT #2 13 20 19 18 17 16 1 2 9 8 12 11 14 15 3 4 5 6 7 10
  49. 49. When the optimizer solutions are compared with the existing layout, the solution with machine sequence as per solution layout #3 is likely to be the most feasible one. The reason for selecting solution layout #3 is as follows: When compared with the other 2 solution layouts, the distance travel by the component is less, so the material handling cost is low than the other 2 solution layouts. But So compared this two layouts modified layout #1 is likely to be most feasible one. . The reason for selecting modified layout #1 is as follows: When modified layouts #1 and #2 are compared with existing layout, 11 of the machines in the modified layout #1 and #2 need not to be altered, where as in the new solutions #1,#2 and #3 there is no machines retains the same place. But comparing modified layout #1 and #2 , modified layout #1 has minimum distance travelled, material handling cost and less backflow. Thus, from the GA optimizer output it is clear that any of the layout solution obtained can be used with respect to the relocation cost involved.
  50. 50. CONCLUSION
  51. 51. CONCLUSION: This project presented an approach for solving facility layout design problems with the consideration of material handling cost. The proposed approach integrates Genetic Algorithm to assist the end user in solving combinatorial optimization problems, and modeling and evaluating the performance of complex manufacturing systems. This shows that the approach can be used to solve single row unequal area layout problems effectively. The results of the project work carried out in the CNC Machine Shop at Sakthi Auto Components Limited, Erode for steering knuckle are given below. 1. Machining relayout of Steering Knuckle manufacturing section. Expected reduction in travel distance = (Total distance travelled in existing layout) - (Total distance travelled in proposed layout) = 647m – 64.9m = 582.1m Expected reduction in material Handling cost = (Total cost in existing layout) - (Total cost in proposed layout) = Rs. 14,256.42 – Rs. 1685.13 = Rs. 12,571.29 (Keeping the material flow and transportation cost / unit as constant) From the results, it is clear that the above practices will help the management in improving the productivity. Hence, we recommend the above practices for implementation in CNC Machine Shop with consideration of additional work in this area like, 1. Economic analysis of proposed layout like relocation cost, payback period etc., 2. Performance analysis of the proposed layout based on operational parameters like work-in-progress, queue length etc.,
  52. 52. REFERENCES
  53. 53. REFERENCES: 1. Goldberg, David E. (1989). Genetic Algorithms in Search Optimization and Machine Learning. Addison Wesley. pp. 41. 2. Fraser, Alex; Donald Burnell (1970). Computer Models in Genetics. New York: McGraw-Hill. 3. Crosby, Jack L. (1973). Computer Simulation in Genetics. London: John Wiley & Sons. 4. Syswerda, G. (1989). "Uniform crossover in genetic algorithms". In J. D. Schaffer. Proceedings of the Third International Conference on Genetic Algorithms. Morgan Kaufmann. 5. Srinivas. M and Patnaik. L, "Adaptive probabilities of crossover and mutation in genetic algorithms," IEEE Transactions on System, Man and Cybernetics, vol.24, no.4, pp.656–667, 1994. WEB SITES: 1. www.globalsecurity.com 2. www.solver.com 3. www.cs.orchester.edu
  54. 54. APPENDIX
  55. 55. TABLE 1 CENTROID CALCULATION FOR PROPOSED LAYOUT #1 (NEW) Coordinates Centroid Machine xy X y X y No 1 12.5 5.8 5.4 7.05 7.9 2 14.5 2.9 5.4 4.35 7.9 3 17.82 7.1 0 8.75 2.7 4 13.34 10.4 0 11.85 2.3 5 17 13.3 0 15 2.5 6 16.5 16.7 0 18.35 2.5 7 15 20 0 21.5 2.5 8 15.18 23 0 24.65 2.3 9 17 26.3 0 28 2.5 10 9.86 0 5.4 1.45 7.1 11 19 3.3 0 5.2 2.5 12 16.5 0 0 1.65 2.5 13 14.5 8.3 5.4 9.75 7.9 14 9.86 11.2 5.4 12.65 7.1 15 11.5 14.1 5.4 15.35 7.7 16 14.5 16.6 5.4 18.05 7.9 17 5.95 19.5 5.4 20.35 7.15 18 5.95 21.2 5.4 22.05 7.15 19 16.5 22.9 5.4 24.55 7.9 20 16.5 26.2 5.4 27.85 7.9
  56. 56. TABLE 2 CENTROID CALCULATION FOR PROPOSED LAYOUT #2 (NEW) Coordinates Centroid Machine xy x y x Y No 1 12.5 5.8 5.4 7.05 7.9 2 14.5 8.3 5.4 9.75 7.9 3 17.82 7.1 0 8.75 2.7 4 13.34 10.4 0 11.85 2.3 5 17 13.3 0 15 2.5 6 16.5 16.7 0 18.35 2.5 7 15 20 0 21.5 2.5 8 15.18 23 0 24.65 2.3 9 17 26.3 0 28 2.5 10 9.86 0 5.4 1.45 7.1 11 19 3.3 0 5.2 2.5 12 16.5 0 0 1.65 2.5 13 14.5 2.9 5.4 4.35 7.9 14 9.86 11.2 5.4 12.65 7.1 15 11.5 14.1 5.4 15.35 7.7 16 14.5 16.6 5.4 18.05 7.9 17 5.95 19.5 5.4 20.35 7.15 18 5.95 21.2 5.4 22.05 7.15 19 16.5 22.9 5.4 24.55 7.9 20 16.5 26.2 5.4 27.85 7.9
  57. 57. TABLE 3 CENTROID CALCULATION FOR PROPOSED LAYOUT #3 (NEW) Coordinates Centroid Machine No xy X y x Y 1 12.5 5.8 5 7.05 7.5 2 14.5 7.1 0 8.55 2.5 3 17.82 8.3 5 9.95 7.7 4 13.34 10 0 11.45 2.3 5 17 12.9 0 14.6 2.5 6 16.5 16.3 0 17.95 2.5 7 15 19.6 0 21.1 2.5 8 15.18 22.6 0 24.25 2.3 9 17 25.9 0 27.6 2.5 10 9.86 0 5 1.45 6.7 11 19 0 0 1.9 2.5 12 16.5 3.8 0 5.45 2.5 13 14.5 2.9 5 4.35 7.5 14 9.86 11.6 5 13.05 6.7 15 11.5 14.5 5 15.75 7.3 16 14.5 17 5 18.45 7.5 17 5.95 19.9 5 20.75 6.75 18 5.95 21.6 5 22.45 6.75 19 16.5 23.3 5 24.95 7.5 20 16.5 26.6 5 28.25 7.5
  58. 58. TABLE 4 CENTROID CALCULATION FOR PROPOSED LAYOUT #1 (MODIFIED) Coordinates Centroid Machine No xy x y x y 1 12.5 15.8 0 17.05 2.5 2 14.5 18.3 0 19.75 2.5 3 17.82 12.5 5 14.15 7.7 4 13.34 15.8 5 17.25 7.3 5 17 18.7 5 20.4 7.5 6 16.5 22.1 5 23.75 7.5 7 15 25.4 5 26.9 7.5 8 15.18 24.6 0 26.25 2.3 9 17 21.2 0 22.9 2.5 10 9.86 0 10 1.45 11.7 11 19 3.3 5 5.2 7.5 12 16.5 0 5 1.65 7.5 13 14.5 0 0 1.45 2.5 14 9.86 7.1 5 8.55 6.7 15 11.5 10 5 11.25 7.3 16 14.5 12.9 0 14.35 2.5 17 5.95 11.2 0 12.05 1.75 18 5.95 9.5 0 10.35 1.75 19 16.5 6.2 0 7.85 2.5 20 16.5 2.9 0 4.55 2.5
  59. 59. TABLE 5 CENTROID CALCULATION FOR PROPOSED LAYOUT #2 (MODIFIED) Coordinates Centroid Machine No xy x y x y 1 12.5 15.8 0 17.05 2.5 2 14.5 18.3 0 19.75 2.5 3 17.82 19.2 5 20.85 7.7 4 13.34 16.3 5 17.75 7.3 5 17 12.9 5 14.6 7.5 6 16.5 9.6 5 11.25 7.5 7 15 25.8 5 27.3 7.5 8 15.18 22.5 5 24.15 7.3 9 17 21.2 0 22.9 2.5 10 9.86 0 10 1.45 11.7 11 19 0 5 1.9 7.5 12 16.5 3.8 5 5.45 7.5 13 14.5 0 0 1.45 2.5 14 9.86 24.6 0 26.05 1.7 15 11.5 7.1 5 8.35 7.3 16 14.5 12.9 0 14.35 2.5 17 5.95 11.2 0 12.05 1.75 18 5.95 9.5 0 10.35 1.75 19 16.5 6.2 0 7.85 2.5 20 16.5 2.9 0 4.55 2.5
  60. 60. MATERIAL HANDLING COST MATRIX OF PROPOSED LAYOUT #1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 TOTAL 1 0 0 138.69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 138.69 2 0 192.96 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 192.96 3 0 140.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 140.7 4 0 134.67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 134.67 5 0 134.67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 134.67 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 69.345 0 0 0 0 0 0 0 0 0 0 0 0 69.345 8 0 73.485 0 0 0 0 0 0 0 0 0 0 0 73.485 9 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 195.39 0 0 0 0 0 0 0 0 0 195.39 11 0 83.07 0 0 0 0 0 0 0 0 83.07 12 0 315.9 0 0 0 0 0 0 0 315.9 13 0 0 0 0 0 0 0 0 0 14 0 0 91.14 0 0 0 0 91.14 15 0 42.63 0 0 0 0 42.63 16 0 89.67 0 0 0 89.67 17 0 49.98 0 0 49.98 18 0 95.55 0 95.55 19 0 97.02 97.02 20 0 0 1944.87
  61. 61. DISTANCE MATRIX OF PROPOSED LAYOUT #1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total 1 0 2.7 6.9 10.4 13.35 16.7 19.85 23.2 26.35 6.4 7.25 10.8 2.7 6.4 8.5 11 14.05 15.75 17.5 20.8 240.6 2 0 9.6 13.1 16.05 19.4 22.55 25.9 29.05 3.7 6.25 8.1 5.4 9.1 11.2 13.7 16.75 18.45 20.2 23.5 272 3 0 3.5 6.45 9.8 12.95 16.3 19.45 11.7 3.75 7.3 6.2 8.3 11.6 14.5 16.05 17.75 21 24.3 210.9 4 0 3.35 6.7 9.85 12.8 16.35 15.2 6.85 10.4 7.7 5.6 8.9 11.8 13.35 15.05 18.3 21.6 183.8 5 0 3.35 6.5 9.85 13 18.15 9.8 13.35 10.65 6.95 5.55 8.45 10 11.7 14.95 18.25 160.5 6 0 3.15 6.5 9.65 21.5 13.15 16.7 14 10.3 8.2 5.7 6.65 8.35 11.6 14.9 150.35 7 0 3.35 6.5 24.65 16.3 19.85 17.15 13.45 11.35 8.85 5.8 5.2 8.45 11.75 152.65 8 0 3.55 28 19.65 23.2 20.5 16.8 14.7 12.2 9.15 7.45 5.7 8.8 169.7 9 0 31.15 22.8 26.35 23.65 19.95 17.85 15.35 12.3 10.6 8.85 5.55 194.4 10 0 8.35 4.8 9.1 11.2 14.5 17.4 18.95 20.65 23.9 27.2 156.05 11 0 3.55 9.95 12.05 15.35 18.25 19.8 21.5 24.75 28.05 153.25 12 0 13.5 15.6 18.9 21.8 23.35 25.05 28.3 31.6 178.1 13 0 3.7 5.8 8.3 11.35 13.05 14.8 18.1 75.1 14 0 3.3 6.2 7.75 9.45 12.7 16 55.4 15 0 2.9 5.55 7.25 9.4 12.7 37.8 16 0 3.05 4.75 6.5 9.8 24.1 17 0 1.7 4.95 8.25 14.9 18 0 3.25 6.55 9.8 19 0 3.3 3.3 20 0 2442.7
  62. 62. MATERIAL HANDLING COST MATRIX OF PROPOSED LAYOUT #2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 TOTAL 1 0 0 138.69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 138.69 2 0 124.62 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 124.62 3 0 140.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 140.7 4 0 134.67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 134.67 5 0 134.67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 134.67 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 69.345 0 0 0 0 0 0 0 0 0 0 0 0 69.345 8 0 73.485 0 0 0 0 0 0 0 0 0 0 0 73.485 9 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 195.39 0 0 0 0 0 0 0 0 0 195.39 11 0 83.07 0 0 0 0 0 0 0 0 83.07 12 0 189.54 0 0 0 0 0 0 0 189.54 13 0 0 0 0 0 0 0 0 0 14 0 0 91.14 0 0 0 0 91.14 15 0 42.63 0 0 0 0 42.63 16 0 89.67 0 0 0 89.67 17 0 49.98 0 0 49.98 18 0 95.55 0 95.55 19 0 97.02 97.02 20 0 0 1750.17
  63. 63. DISTANCE MATRIX OF PROPOSED LAYOUT #2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total 1 0 2.7 6.9 10.4 13.35 16.7 19.85 23.2 26.35 6.4 7.25 10.8 2.7 6.4 8.5 11 14.05 15.75 17.5 20.8 240.6 2 0 6.2 7.7 10.65 14 17.15 20.5 23.65 9.1 9.95 13.5 5.4 3.7 5.8 8.3 11.35 13.05 14.8 18.1 212.9 3 0 3.5 6.45 9.8 12.95 16.3 19.45 11.7 3.75 7.3 9.6 8.3 11.6 14.5 16.05 17.75 21 24.3 214.3 4 0 3.35 6.7 9.85 12.8 16.35 15.2 6.85 10.4 13.1 5.6 8.9 11.8 13.35 15.05 18.3 21.6 189.2 5 0 3.35 6.5 9.85 13 18.15 9.8 13.35 16.05 6.95 5.55 8.45 10 11.7 14.95 18.25 165.9 6 0 3.15 6.5 9.65 21.5 13.15 16.7 19.4 10.3 8.2 5.7 6.65 8.35 11.6 14.9 155.75 7 0 3.35 6.5 24.65 16.3 19.85 22.55 13.45 11.35 8.85 5.8 5.2 8.45 11.75 158.05 8 0 3.55 28 19.65 23.2 25.9 16.8 14.7 12.2 9.15 7.45 5.7 8.8 175.1 9 0 31.15 22.8 26.35 29.05 19.95 17.85 15.35 12.3 10.6 8.85 5.55 199.8 10 0 8.35 4.8 3.7 11.2 14.5 17.4 18.95 20.65 23.9 27.2 150.65 11 0 3.55 6.25 12.05 15.35 18.25 19.8 21.5 24.75 28.05 149.55 12 0 8.1 15.6 18.9 21.8 23.35 25.05 28.3 31.6 172.7 13 0 9.1 11.2 13.7 16.75 18.45 20.2 23.5 112.9 14 0 3.3 6.2 7.75 9.45 12.7 16 55.4 15 0 2.9 5.55 7.25 9.4 12.7 37.8 16 0 3.05 4.75 6.5 9.8 24.1 17 0 1.7 4.95 8.25 14.9 18 0 3.25 6.55 9.8 19 0 3.3 3.3 20 0 2442.7
  64. 64. MATERIAL HANDLING COST MATRIX OF PROPOSED LAYOUT #3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 TOTAL 1 0 0 62.31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 62.31 2 0 132.66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 132.66 3 0 277.38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 277.38 4 0 134.67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 134.67 5 0 134.67 0 0 0 0 0 0 0 0 0 0 0 0 0 0 134.67 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 69.345 0 0 0 0 0 0 0 0 0 0 0 0 69.345 8 0 73.485 0 0 0 0 0 0 0 0 0 0 0 73.485 9 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 108.81 0 0 0 0 0 0 0 0 0 108.81 11 0 83.07 0 0 0 0 0 0 0 0 83.07 12 0 142.74 0 0 0 0 0 0 0 142.74 13 0 0 0 0 0 0 0 0 0 14 0 0 91.14 0 0 0 0 91.14 15 0 42.63 0 0 0 0 42.63 16 0 89.67 0 0 0 89.67 17 0 49.98 0 0 49.98 18 0 95.55 0 95.55 19 0 97.02 97.02 20 0 0 1685.13
  65. 65. DISTANCE MATRIX OF PROPOSED LAYOUT #3 ` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total 1 0 6.5 3.1 9.6 12.55 15.9 19.05 22.4 25.55 6.4 10.15 6.6 2.7 6.8 8.9 11.4 14.45 16.15 17.9 21.2 237.3 2 0 6.6 3.1 6.05 9.4 12.55 15.9 19.05 11.3 6.65 3.1 9.2 8.7 12 14.9 16.45 18.15 21.4 24.7 219.2 3 0 6.9 9.85 13.2 16.35 19.7 22.85 9.5 13.25 9.7 5.8 4.1 6.2 8.7 11.75 13.45 15.2 18.5 205 4 0 3.35 6.7 9.85 12.8 16.35 14.4 9.75 6.2 12.3 6 9.3 12.2 13.75 15.45 18.7 22 189.1 5 0 3.35 6.5 9.85 13 17.35 12.7 9.15 15.25 5.75 5.95 8.85 10.4 12.1 15.35 18.65 164.2 6 0 3.15 6.5 9.65 20.7 16.05 12.5 18.6 9.1 7 5.5 7.05 8.75 12 15.3 151.85 7 0 3.35 6.5 23.85 19.2 15.65 21.75 12.25 10.15 7.65 4.6 5.6 8.85 12.15 151.55 8 0 3.55 27.2 22.55 19 25.1 15.6 13.5 11 7.95 6.25 5.9 9.2 166.8 9 0 30.35 25.7 22.15 28.25 18.75 16.65 14.15 11.1 9.4 7.65 5.65 189.8 10 0 4.65 8.2 3.7 11.6 14.9 17.8 19.35 21.05 24.3 27.6 153.15 11 0 3.55 7.45 15.35 18.65 21.55 23.1 24.8 28.05 31.35 173.85 12 0 6.1 11.8 15.1 18 19.55 21.25 24.5 27.8 144.1 13 0 9.5 11.6 14.1 17.15 18.85 20.6 23.9 115.7 14 0 3.3 6.2 7.75 9.45 12.7 16 55.4 15 0 2.9 5.55 7.25 9.4 12.7 37.8 16 0 3.05 4.75 6.5 9.8 24.1 17 0 1.7 4.95 8.25 14.9 18 0 3.25 6.55 9.8 19 0 3.3 3.3 20 0 2406.9
  66. 66. MATERIAL HANDLING COST MATRIX OF EXISTING LAYOUT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 TOTAL 1 0 0 1925.58 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1925.58 2 0 1865.28 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1865.28 3 0 506.52 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 506.52 4 0 1149.72 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1149.72 5 0 715.56 0 0 0 0 0 0 0 0 0 0 0 0 0 0 715.56 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 1949.94 0 0 0 0 0 0 0 0 0 0 0 0 1949.94 8 0 2732.4 0 0 0 0 0 0 0 0 0 0 0 2732.4 9 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 1165.32 0 0 0 0 0 0 0 0 0 1165.32 11 0 402.48 0 0 0 0 0 0 0 0 402.48 12 0 182.52 0 0 0 0 0 0 0 182.52 13 0 0 0 0 0 0 0 0 0 14 0 0 652.68 0 0 0 0 652.68 15 0 579.18 0 0 0 0 579.18 16 0 94.08 0 0 0 94.08 17 0 47.04 0 0 47.04 18 0 205.8 0 205.8 19 0 82.32 82.32 20 0 0 14256.4

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