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CV, Dr. Y. Malini Reddy, 8 Feb, 2015
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Modeling of assembly line balancing for optimized number of stations and time
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1. INTERNATIONALMechanical Engineering and Technology (IJMET), ISSN 0976 – International Journal of JOURNAL OF MECHANICAL ENGINEERING 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME AND TECHNOLOGY (IJMET)ISSN 0976 – 6340 (Print)ISSN 0976 – 6359 (Online) IJMETVolume 4, Issue 2, March - April (2013), pp. 152-161© IAEME: www.iaeme.com/ijmet.aspJournal Impact Factor (2013): 5.7731 (Calculated by GISI) ©IAEMEwww.jifactor.com MODELING OF ASSEMBLY LINE BALANCING FOR OPTIMIZED NUMBER OF STATIONS AND TIME Anoop Kumar Elia1, Dr. D.Choudhary2 1,2 Guru Nanak Dev Engg.College, Bidar.585401 ABSTRACT In this work, the Buxey 29 tasks problem is solved for minimum number of stations and cycle time. The precedence matrix is presented for the 29 tasks. The classification of ALB problem and their solution procedure are presented. Single model ALB and equivalent multi model ALB are treated as similar model and common solution procedure is presented. The number of stations required for the feasible solutions are varied and cycle time are computed. The algorithm used in the derivation of the feasible solutions is presented. The advantages of using a certain number of stations are discussed. Finally important conclusions are drawn and future work is defined. Keywords: Number of stations, Number of feasible solutions, Cycle Time, Optimum Stations and Time. INTRODUCTION An assembly line is formed of a finite set of work elements which are also referred to as tasks. Each task is identified by a processing time for the operation it represents and a set of relationships for precedence, which specifies the allowable ordering of the tasks. Assembly line balancing (ALB) is defined as a process in which a group of tasks to be performed are allocated on an ordered sequence of assembly line. Systematic design of assembly lines is not a simple and easy task for the designers. Manufacturers and Designers have to deal with their existing factory layout in the initial phase. The Cost associated and reliability of the system, complexities involved in tasks, selection of equipment, operating criteria of assembly line, multiple constraints, scheduling methodologies, allocation of stations, control of inventory, buffer allocation are the most important area of concern. 152
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME The parameters that include in ALB is: (l) precedence relationships; (2) numberof workstations; (3) cycle time. The number of stations cannot be less than the numberof tasks. The cycle time must be greater than or equal to the maximum of time of anyworkstation and the time of any task. In other words, the workstation time should nothave the time higher than the cycle time. Tendencies in the design and orientation of assembly lines in themanufacturing are linked to line evolution. Information need to be collected bydesigners in this step about the tendencies of the line which need to be implemented.Balancing as well as sequencing problems depends on the types of assembly lines. Forexample, single model line delivers a single product on the line. Layout of the facility,changes required in tools, workstation indexes remains almost constant. Batch modellines deliver small number of different products over the line but in batches. In mixed-model case, different variations of a generic product are delivered at the same time butin a mixed scenario. Consideration of the problems associated with work transport system is also adesign requirement. In addition to manual work transport over the line, continuoustransfer also exists with three types of mechanized work transport systems, namely,synchronous transfer, intermittent transfer, and asynchronous transfer [1]. Differentorientations of the line need to be studied by the designer since it varies widelyaccording to the floor layout of the production unit. Generally, straight, parallel, U-shaped [2] are applied. Several design factors are important to assess and considerwith the assembly line design and balancing. The solution variations which are to bedecided depend on the factors like production approaches, objective functions andconstraints. A few of the design constraints related to assembly line balancing areprecedence constraints, zoning constraints and capacity constraints [3]. Efficient formulation of line design problem depends on the databaseenrichment. To collect assembly line data, knowledge related to several performanceindices and workstation indices are essential for a line designer. Assembly line designmodel and methodology for solution combine the model stage. Design tools areformulated and modeled once the input data is collected and verified. Modeling ofdesign tools includes the output data, interaction between different modules andmethods required for solution. Wide range of heuristic as Branch and Bound search, Positional weightmethod, Kilbridge and Wester Heuristic, Moodie-Young Method, Immediate UpdateFirst-Fit (IUFF), Hoffman Precedence Matrix [4] and meta-heuristic based solutionstrategies as Genetic Algorithm GA [5], Tabu Search TS, Ant Colony OptimizationACO [3], Simulated Annealing SA [6] for assembly line problems are taken for studyin industrial and research level. Verification of the developed models is a result ofperformance towards the objectives defined for that particular line. Line performancesof assembly line design are a measure of multi-objective characteristics. 153
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Figure 1: Classification of ALB Solution Procedures.Several solution procedures that are available in the literature are presented in Fig. 1.Variable objective functions are taken into account for assembly line [7]. Goal of the designeris to design a line for higher efficiency, lesser delay in balance, smoother production, andoptimized time for processing, cost effectiveness, overall labor efficiency and just in timeproduction. The aim is to develop a line by considering the best of the design methods whichmay deal in actual fact with user preferences. Design evaluation refers to a user friendlydeveloped interface where all necessary assembly data is accessible extracted from differentdatabase. Most of the solutions for assembly line balancing problems explore one finaloptimized solution. However, it is important to look for the alternative solutions [8].Validation and verification of several algorithms and methods is combined and incorporatedinto different design packages [9]. In this work, the Buxey 29 tasks problem is solved for minimum number of stationsand cycle time. The precedence matrix and solutions are presented for the 29 tasks. Theclassification of ALB problem and their solution procedure are also presented.2.0 CLASSIFICATION OF ALB PROBLEMSAssembly Line Balancing problem can be classified into two categories, namely, • Problem based on objective functions. • Problem based on problem structure. 154
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Figure 2: Classification of ALB problems.Problem based on objective functions: • Type 1: Cycle time is known, and objective is to minimize number of stations. • Type 2: Number of stations are known, and objective is to minimize cycle time. • Type 3: Objective is maximization of workload smoothness. • Type 4: Objective is maximization of work relatedness. • Type 5: Objective is maximization of multiple objectives with type 3 and 4. • Type E: Objective is maximization of line efficiency by minimizing both cycle time and number of stations. • Type F: Objective is feasibility of line balance for a given combination of number of stations and cycle.Problem based on problem structure: • SMALB: Single model ALB problems, where only single product is produced. • MuMALBP: Multi model ALB problems, where multiple products are produced in batches. • MMALBP: Mixed model ALB problems, where generic products are produced on the line in a mixed situation. • SALBP: Simple ALB balancing problems, where the objective is to minimize the cycle time for a fixed number of workstation and vice versa. • GALBP: A general ALB problem includes those problems which are not included in SALBP. 155
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME3.0 EQUIVALENT SINGLE MODEL Tasks of several models are combined into an equivalent single model. Combinedprecedence diagram need to be derived from all the single model diagram along with theaverage task times. The objective of balancing is to optimize the number of workstations witha pre-decided fixed cycle time. The fixed cycle time is treated as the solution lower bound,for determining desired station numbers, is increased by 1 sec per iteration. Solution lowerbound is found with minimum cycle time [10] as: For equivalent single models, the algorithm is defined below. The algorithm deliversnumber of feasible solutions. • Assign a new station STATION[1] with a cycle time T = MINCYCLETIME • Determine all the tasks that do not have the predecessor TASKSWOPRED = { i, j,…., n} • Assign one task in TASKSWOPRED to STATION[1] • Remove the taks that is assigned to STATION[1] from the graph and update it as TASKSWOPRED = { j,k,….,n }. • Update the station cycle time as T = MINCYCLETIME - ti • Repeat steps 3 to 5, until T is positive and update the T and TASKSWOPRED each time. • When T turns negative, look for any other tasks in TASKSWOPRED to fit in STATION[1], but the T should remain positive. • When T turns zero or negative for all the tasks in TASKSWOPRED, create a new station as STATION[2]. • Repeat steps 3 to 8. • Repeat step 3 to 9 for all feasible solutions. • Try the solutions for a pre-decided number of stations. If the solutions derived are not feasible, repeat 3 to 9 after update the T as MINCYCLETIME+1. • When all the feasible solutions are obtained, store the updated T.4.0 SIMULATION RESULTS For experimental; purpose, Buxey 29 tasks Problem [11] is chosen. The precedencediagram for the Buxey is presented in Fig. 3. In case of multiple models, the equivalent taskdiagram can be derived in the form shown in Fig. 3. For the sake of simplicity, a single modelprecedence diagram is shown and solved in this work. The Buxey problem has a total of 29tasks and the associated tasks are shown above each task in Fig. 3. 156
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Figure 3: Buxey 29 tasks precedence diagram.Table 1 shows the precedence matrix for the Buxey 29 tasks problem. In the matrix, thecolumns and rows represent the task number. It shows the precedence relation between thetasks. For example, in row 2 and column 6, it is indicated as 1 in the matrix, which means thetask 6 is preceded by task 2. If the value is zero, it means there is no precedence relationshipin the diagram. The last row of the Table 1 shows the time associated with each task. Table 1: Precedence matrix for the Buxey 29 Tasks problem 157
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME There are different parameters in this problem which can vary to derive a bestpossible solutions using design of experiments. However, in this case on one parameter isvaried to find out the feasible solutions. The parameter that is varies in the work is number ofstations. The number of solutions is varied from 8 to 9 and 10. For each case, the numberfeasible solutions are computed and the cycle time is determined. Also, the total timeconsumed by each station is also computed. Table 2: Feasible solutions for 8 stations for the Buxey 29 Tasks problem By running the algorithm mention Sec.3, nine feasible solutions are obtained. TheTable 2 shows the assigned stations for each task under each solution. For example, insolution 2, task 1 is assigned to station 2, task 2 is assigned to station 1 etc. Table 2 can bemodified into different for all the tasks that is assigned to each station under each feasiblesolution, which is not presented here. Table 3: Total time taken by each station for the Buxey 29 Tasks problem Table 3 shows the total time taken by each station under each solution. Of all thesolutions, Solution 1 and 2 provides the best cycle time of 324 sec. depending upon thecomplexity of tasks and ease of operation, either Solution 1 or Solution 2 can be chosen. Thecycle time for both these solutions is 41 sec. 158
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Table 4: Feasible solutions for 9 stations for the Buxey 29 Tasks problem. Again, the number of stations are varied from 8 to 9 and the algorithm as mentionedin Sec. 3 is run. In this case, there are 16 feasible solutions are obtained as shown in Table 4.By increasing the number stations, there is a significant increase in the number of solutions.However, the best solution for practical implementation to be chosen based on the minimumcycle time and the complexity involved in transportation and assignment of tasks to thesestations. The cost of other resources also should be considered when choosing the bestfeasible solution. Table 5: Total time taken by each station for the Buxey 29 Tasks problem. Here again, the solution 1 yields the best possible solution since the cycle time isminimum of all. Solution 1 takes a total time of 324 sec which is same as in the case of 8station model. The cycle time in this case is 38 sec. If the cost of installation of the stations isgiven priority, it is the 8 station model, which suits best for this problem over 9 station model. 159
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Table 6: Feasible solutions for 10 stations for the Buxey 29 Tasks Problem. Again, by increasing the number of stations from 9 to 10, 16 feasible solutions areobtained. From Table7 the best solution yields 324 sec of total time and a cycle time of 34sec. By increasing the number of stations, there in change in the number of feasible solutionsand the same kind behavior is noticed when the number of stations further increased to 11, 12and so on. Although the cost of installation of stations increases when the number of stationsis increased, it provides the best flexibility in maintenance of the stations. Table 7: Total time taken by each station for the Buxey 29 Tasks problemCONCLUSIONS In this work, the single model assembly line problem or equivalent model of multimodel assembly line problem are solved for minimum number of stations and minimum cycletime. The number of stations are varied from 8 to 10 and the feasible solutions for each caseare derived. By increasing the number of stations from 8 to 10, the total time remain as 324sec for solution 1 and the cycle time has decreased from 41 sec to 34 sec. The number offeasible solutions increased from 9 to 16 when the number stations are changed from 8 to 9,but there is no improvement after that. Depending up the resources available, one can choose 160
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEMEthe number of stations as 8 or 9. Eight stations model yield less installation and maintenancecost, whereas the 9 station model provides best ease maintenance and operation. As futurework, the models can be tried with multi models as an extension and optimization of cycletime and smoothening of the task assignment can be tried.REFERNCES[1] Papadopoulos, H.T; Heavey, C. & Browne, J. (1993). Queuing Theory in ManufacturingSystems Analysis and Design; Chapman & Hall, ISBN 0412387204, London, UK[2] Becker, C. & Scholl, A. (2006). A survey on problems and methods in generalizedassemblyline balancing, European journal of operational research, Vol. 168, Issue. 3(February, 2006), pp. (694–715), ISSN 0377-2217.[3] Vilarinho, P.M. & Simaria, A.S. (2006). ANTBAL: An ant colony optimization algorithmfor balancing mixed-model assembly lines with parallel workstations, International journal ofproduction research, Vol 44, Issue 2, pp. 291–303, ISSN ISSN: 1366-588 0020-7543[4] Ponnambalam, S.G., Aravindan, P. & Naidu, G.M. (1999). A comparative evaluation ofassembly line balancing heuristics. International journal of advanced manufacturingtechnology, Vol. 15, No. 8 (July 1999), pp. (577-586), ISSN: 0268-3768[5] Sabuncuoglu, I., Erel, E. & Tanyer, M. (1998). Assembly line balancing using geneticalgorithms. Journal of intelligent manufacturing, Vol. 11, No. 3 (June, 2000), pp. (295-310),ISSN: 0956-5515[6] Suresh, G. & Sahu, S. (1994). Stochastic assembly line balancing using simulatedannealing, International journal of production research, Vol. 32, No. 8, pp. (1801-1810),ISSN: 1366-588X (electronic) 0020-7543 (paper)[7] Tasan, S.O. & Tunali, S. (2006). A review of current application of genetic algorithms inassembly line balancing, Journal of intelligent manufacturing, Vol. 19, No. 1 (February,2008), pp. (49-69), ISSN: 0956-5515[8]Boysen, N., Fliedner, M. & Scholl, A. (2006). A classification of assembly line balancingproblems. European journal of operational research, Elsevier, Vol 183, No. 2 (December,2007), pp. (674–693)[9] Rekiek, B. & Delchambre, A. (2006). Assembly line design, the balancing of mixed-model hybrid assembly lines using genetic algorithm; Springer series in advancemanufacturing, ISBN-10: 1846281121, Cardiff, UK.[10] Gu, L., Hennequin, S., Sava, A., & Xie, X. (2007). Assembly line balancing problemsolved by estimation of distribution, Proceedings of the 3rd Annual IEEE conference onautomation science and engineering scottsdale, AZ, USA.[11] Scholl, A. (1993). Data of assembly line balancing problems. Retrieved fromhttp://www.wiwi.uni-jena.de/Entscheidung/alb/, last accessed: 07 February 2008.[12] S.K. Gupta, Dr. V.K. Mahna, Dr. R.V. Singh and Rajender Kumar, “Mixed ModelAssembly Line Balancing: Strategic Tool to Improve Line Efficiency in Real World”International Journal of Industrial Engineering Research and Development (IJIERD),Volume 3, Issue 1, 2012, pp. 58 - 66, ISSN Online: 0976 - 6979, ISSN Print: 0976 – 6987. 161
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