International Journal Of Mechanical & Mechatronics .

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International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06114Design of Worker Assignment in a Dynamic CellularManufacturing System by Meta-heuristic AlgorithmsM. Saravanan#1, S. Karthikeyan*2, S. Ganesh Kumar#3#Principal, Sri Subramanya College of Engineering and Technology, Palani, Tamil Nadu, India.1drmsaravanan@yahoo.com*2Assistant Professor, Christian College of Engineering and Technology, Oddanchatram, Tamil Nadu, India.#3Assistant Professor, RVS College of Engineering and Technology, Dindigul, Tamil Nadu, India.2mekarthikeyan@yahoo.co.in, 3ammu gan@yahoo.co.inAbstract-The dynamic cellular manufacturingsurroundings are projected changes of demand or productionprocess for several time periods. Hence workers have aimportant role in performing the jobs on the machines,assignment of workers to cells become a major factor forcomplete utilization of cellular manufacturing systems. Theobjective is to minimize back order cost and holding costcompared through bench mark problem available in theliterature. Most real world cellular manufacturing problemsare NP-hard in nature. The vital complexity of the problemnecessitates the make use of meta-heuristics for solvingdynamic cellular manufacturing problems. In this paperaddresses design of dynamic cellular manufacturing systemusing Genetic Algorithm (GA) and Particle SwarmOptimization (PSO). Computational result shows that the PSOproduces optimal results than GA algorithm for the cellularmanufacturing in a dynamic environment.I. INTRODUCTIONManufacturing is the backbone of any industrializednation. Manufacturing and technical staff in industry mustknow the various manufacturing processes, materials beingprocessed, tools and equipment for manufacturing differentcomponents or products with optimal process plan usingproper precautions and specified safety rules to avoidaccidents. Beside above, all kinds of the future engineersmust know the basic requirements of workshop activities interm of man, machine, material, methods, money and otherinfrastructure facilities needed to be positioned properly foroptimal shop layouts or plant layout and other supportservices effectively adjusted or located in the industry orplant within a well-planned manufacturing organization.Cellular manufacturing is one of the primary applicationsof group technology which involves a number of machinecells where each cell is responsible for manufacturing orprocessing similar part families. Dynamic cellular systemsaddress this problem. Dynamic cells were consequent fromtwo explanations, one connecting to virtual cells and theother connecting to the management of cellular systems.Montreuil states that virtual cells task finest with mobileprocessors. Though, points to the case of companies that usemanufacturing cells to produce very low product familiesand then dissolve the cells when production is complete. Arelated practice was also observed in different studiesobtained through the Bombardier Chair in RecreationalProducts, in different manufacturing sectors including theproduction and assembly of seat cover, machine tooling andpressure aluminium moulding. Dynamic cells can thereforebe defined as physically reconfigurable virtual cells. Theyare based on a paradigm surrounded by which allworkstation or machine can be moved at several times,where inexpensively justifiable. The mathematicalprogramming addressed for the dynamic cellularmanufacturing system to optimize the production planningand worker assignment [1]. The virtual cellularmanufacturing system addressed the multi-objective cellformation problems to minimize the operations sequence,alternative process plans for part types, machine time–capacity, worker time–capacity, cross–training, lot splitting,maximal cell size, balanced workload for cells and worker[2]. The linear programming embedded particle swarmoptimization algorithm is efficient and effective in searchingfor near optimal solutions. The dynamic cellularmanufacturing problems are proved by NP-hard problems[3]. The computational results show that the hybridapproach obtained the best result than the simulatedannealing algorithm. The hybrid approach based on geneticalgorithm with neural network proposed for incrementalcellular manufacturing process [4]. The branch and boundand heuristic based on multi stage programming applied forincremental cellular manufacturing problems to optimize theoperation sequence, processing times and productionvolumes for cell formation [5].The branch and bound techniques gives a superiorquality solutions and heuristic based on a multi stageprogramming approach is superior in computational time.Formulation of a non-linear integer programming model forcell formation to identify part families and machine groupare discussed [6]. An art review a meta-heuristic in cellularmanufacturing, evolutionary approaches on a meta-heuristicmethod was discussed by several authors [7-10], and theyproposed multi-objective GA to solve and get the fitness cturing problem for cell formation with cost basedmulti-objective functions using genetic algorithm.Evolutionary optimization techniques presented twodifferent forms of hybridization are demonstrated, such ascomponent exchange among meta-heuristic co-operativesearch [11]. Developed a comprehensive mathematicalmodel for dynamic manufacturing cell formation with amulti-item and multi-level lot sizing a product quality theyformulated a model incorporating a number ofmanufacturing features such as dynamic systemconfiguration alternative routings [12]. Investigate theincorporated manufacturing attributes in an integratedDCMS and them taken example for comprehensivenumerical problem is solved by the lingo software toillustrate the performance of the proposed model in handlingthe PP decisions [13]. A multi objective mathematical modelfor dynamic cellular manufacturing system model is socomplicated, so it is verified with lingo software. Sinceparticle swarm optimization approach less than much othertechnique [14]. In a cellular manufacturing system, interintra cellular movements and the sum of cost consisting145506-8484-IJMME-IJENS December 2014 IJENSIJENS

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06machine cost, production planning, cost, reconfigurationcost, and minimization are discussed [15]. Most of thecurrent cellular manufacturing system design methods hadbeen developed for a single–period planning horizon.Product mix refers to a set of part types to be produced andproduct demand is the quantity of each part type to bemanufactured. In a dynamic environment the product mixand/or demand in each period is different but isdeterministic (i.e. known in advance) which was discussedin [16]. Chen developed mathematical programming modelfor a system reconfiguration in a dynamic cellularmanufacturing environment [17].Genetic algorithm (GAs) is used to study thetransformation of organisms in natural evolution to followtheir adaptability to the environment [18]. Genetic algorithm(GAs) is used to study the transformation of organisms innatural evolution to follow their adaptability to theenvironment.GA was later adapted to find solutions forindustrial and manufacturing problems [19].The optimization technique in which heuristic approachis the economic determination of machine group and theircorresponding component families for GT [20]. Theprocedure considers costs of work-in-process and cycleinventory, intra-group material handling, set up, variableprocessing and fixed machine costs [21]. The feature of theheuristic approach is a consideration of several practicalcriteria such as work type, series of machines, maximumnumber of machines in each cell that are assigned to a shopand the percentage of operations of parts completed within asingle cell [22]. These formulations take into account thelimitations on the number of machines in a group and thenumber of machines available of particular type [23].The mathematical programming functions which dealwith costs of inventory, machine depreciation, machinesetup and material handling are first incorporated into amathematical programming formulation. GT is an approachto manufacturing and engineering management that helpsmanage diversity by capitalizing on underlying similaritiesin products and activities [24].CM is necessary first toidentify parts and machine types to be considered in thecellular configuration. Cells using existing equipment aretypically manned and operators have major responsibilitiesfor setup, processing, material handling and inspection [25].A current approach in developing manufacturingsystems which is able to quick adaption to demandvariations without necessity to lots of reinvestment is GT[26]. CMS is one of the efficient systems in manufacturingenvironment for products with high volume and varietywhich prepare growth and development context in globalmarkets with incorporating job shop and flow shop benefits[27]. The Production planning and dynamic cell formationintegrated model with aims such as minimizing inter andintra-cell material handling cost, inventory and productioncosts, reconfiguration cost and machine operation [28].Mixed integer mathematical programming model fordesigning dynamic cellular manufacturing systems withconsidering production planning and worker assignment, inthis paper the worker assignment are discussed and othertechniques are presented in this paper is proposed forcalculating a respective workers to the machine cells for ajob shop scheduling [29]. The machine in order to minimizethe cost of allocating the machines and the cost of inter cell115movement [30]. In this paper proposed GA and PSO attemptmade to solve the dynamic cellular manufacturing problem.II. PROBLEM FORMULATIONThe dynamic cellular manufacturing problems for cellformation using objective of minimizing the back order costand holding cost. The mathematical model of the problemcan be mentioned below taken in [1].Min HQHQ ih Bih ih Iihh 1 i 1h 1 i 1NotationsThe problem has the following notations:WMkCHimhQNumber of worker typesNumber of machine typesIndex for cell (k 1, 2, , C)Number of cellsNumber of periodsIndex for part type (i 1,2, ,Q)Index for machine type (m 1,2, ,M)Index for period (h 1,2, ,H)Number of part typesInput ParametersThe problem has the following input parameters:Unit holding cost of part type i in period h.Unit backorder cost of part type i in periodh.Maintenance and overhead costs ofmachine type m.Salary cost of the worker type w in periodh.Number of machines of type m allotted tocell k in period hNumber of workers of type w allotted tocell k in period hInventory of part type I at the end ofperiod h; Ii0 0Backorder of part type i in period h; Bi0 0AssumptionsThe problem has the following assumptions: The processing time of each operation of each parttype on each machine type is known.The demand of each part type in each period isknown.The capacity of each machine type is known.The available time of each worker type is known.The number of cells is given and constant throughall periods.Only one worker is allotted for each part on eachcorresponding machine type.145506-8484-IJMME-IJENS December 2014 IJENSIJENS

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06Holding and backorder inventories are allotted between theperiods with known costs. Thus, the demand for a part in a116given period can be satisfied in the succeeding periods.Table IThe machine informationMachine informationMachine 03040Table IIThe input data of machine-part incidence matrixWorker12111Machine200310Work 7538020202020Table IIIThe input data of machine-worker incidence matrix1PartType11Machine 114011150020011111111Table IVThe processing time (h)TEST PROBLEMThis example includes two cells, three machines,four parts and four workers. Each part type is assumed tohave some operations where each operation can beperformed by two alternative workers. Table 1 shows themachine information such as machine availability, andinstalling.Table 4 shows the processing time matrix in whicheach part type is unspecified to have some operations thatmust be processed on machines with the corresponding145506-8484-IJMME-IJENS December 2014 IJENSIJENS

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06processing time. For example, part type 1 must be processedon machine type 1 with processing time 0.03 by worker 1 orwith processing time 0.01 by worker 2. Moreover, thenumber of cells to be formed is two and the minimum andmaximum cells sizes for each cell are 1 and3, respectively.The minimum size of each cell in terms of the number ofworkers is unspecified to be 1.III.Generate initial solutionYesStopTest: is initial solutiongood enoughMETHODOLOGYGA AlgorithmThe genetic algorithm (GA) mimics the process of naturalevolution [18]. This meta-heuristic is routinely used togenerate useful solutions to optimization and search problems.Genetic algorithms belong to the larger class of evolutionaryalgorithms (EA), which generate solutions to optimizationproblems using techniques inspired by natural evolution, suchas inheritance, mutation, selection, and crossover. In a geneticalgorithm, a population of strings (called chromosomes or thegenotype of the genome), which encode candidate solutions(called individuals, creatures, or phenotypes) to anoptimization problem, evolves toward better solutions.Traditionally, solutions are represented in binary as strings of0s and 1s, but other encodings are also possible. Theevolution usually starts from a population of randomlygenerated individuals and happens in generations. In eachgeneration, the fitness of every individual in the population isevaluated, multiple individuals are stochastically selectedfrom the current population (based on their fitness), andmodified (recombined and possibly randomly mutated) toform a new population. The new population is then used inthe next iteration of the algorithm. Commonly, the algorithmTerminates when either a maximum number of generationshas been produced, or a satisfactory fitness level has beenreached for the population. If the algorithm has terminateddue to a maximum number of generations, a satisfactorysolution may or may not have been reached. The GAalgorithm procedure is explained in figure 1.117NoA.Loop loop 1Select parents to reproduceApply crossover process andcreate set of offspringApply crossover processFig. 1. The flow chart of GA algorithm InitializationCreate an initial random population of chromosomesand evaluate fitness for each chromosome. Set thecurrent population to this initial population.ReproductionSelect two parent chromosomes from the currentpopulation. The selection process is stochastic and achromosome with high fitness is more likely to beselected.RecombinationGenerate two offspring from two parentchromosomes by exchanging bit strings (crossover).MutationApply a random mutation to each offspring (with asmall probability).ReplicationRepeat steps reproduction, recombination andmutation, until the number of offspring in the newpopulation is same as the number of chromosomes inthe old population.TerminationEvaluate each offspring. Set the current populationto the new population of chromosomes and go toback to reproduction Repeat the routine untiltermination criteria is reached.Numerical Illustration of GAThe numerical illustration of GA is mentioned below. InitializationNumber of chromosomes is referred to aspopulation. Initially, the population is generated145506-8484-IJMME-IJENS December 2014 IJENSIJENS

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06randomly. Here, initial population size is consideredto be 20. ReproductionReproduction is a biased selection process to choose“mates” for the off spring generation. The selectionpolicy is ultimately responsible for assuring survivalof the best-fitted individuals. Proportionate selectionschemes, like the roulette wheel selection schemehave been developed to improve the performance ofGAs. RecombinationThe crossover operation takes two chromosomes andinterchanges the part of their genetic information toproduce new chromosomes. The interchange isaccomplished by sharing the genetic informationbetween two selected chromosomes. Thechromosomes are selected for crossover with acrossover probability of 0.55 in order to ensure thatvital parent chromosomes are selected to producebetter child. Single point, multipoint and uniformcrossover are commonly used techniques. The paperaddresses the single point crossover technique. Thecrossover process is as given below Parent 14 2 3 5 6 1Parent 23 5 4 2 1 6Child 13 5 4Child 24 2 3 5 1 6back to step 2. Repeat the routine until 300 numbersof iteration reached.B.PSO AlgorithmPSO is an evolutionary computation technique inspired bysocial behaviour of bird flocking or fish schooling [19].Similar to other non-traditional techniques, PSO is apopulation based optimization technique. The systeminitialized with a population of random solutions (particles),searches for optima by updating generations. However, unlikeGA, PSO has no evolution operators such as crossover andmutation. In PSO, the potential solutions called particles areflown through the problem space by following the currentoptimum particles. PSO discusses a type of biological socialsystem, where the collective behaviour of simple individualsinteracting with their environment and each other is focused.PSO has been used as an approach that can be used across awide range of applications, which include functionoptimization, artificial neural network, fuzzy system control,as well as for specific applications focused on a specificrequirement. The PSO algorithm procedure is illustrated infigure 2. Initialize a population of n particles generatedrandomly. Compute the fitness value for each particle. If thefitness value is better than the best fitness value (Pijt1). Set current value as the new pbest.Select theparticle with the best fitness value of all the particlesas gbest (gjt-1). For each particle, evaluateaccording to the relation.2 6 1MutationIn order to introduce genetic diversity from onegeneration to next generation, the mutation processis used with a probability of 0.03.The mutation is theprocess of randomly selecting some genes in achromosome, and interchanging them within therespective acceptable range, since it randomlychanges some of its genetic structures the localentrapment of the search process is avoided.Assigning a new value to the selected gene within itsinterval does the modification. The mutation processis as given belowBefore Mutation2 3 4 5 6 1After Mutation2 5 4 3 6 1ReplicationRepeat steps 2, 3 and 4, until the number of offspringin the new population is same as the number ofchromosomes in the old population.TerminationEvaluate each offspring. Set the current populationto the new population of chromosomes and go to118particlevelocity[Vij]t [ (vij)t-1 c1r1 {(pij)t-1 - (xij)t-1} c2r2 {(gj)t-1 - (xij)t-1} ][Xij]t (xij)t-1 (vij)tWhere,(vij)t-1 Velocity of particle i at t-1th iteration(Vij)t Velocity of particle i at tth iteration(xij)t-1 Position of particle i at t-1th iteration(Xij)t Position of particle i at tth iterationc1 Acceleration factor related to pbest (Choicebetween 1 and 4)c2 Acceleration factor related to gbest (Choicebetween 1 and 4)r1 Random number between 0 and 1r2 Random number between 0 and 1(gj)t-1 global best position of swarm(pij)t-1 local best position of particle Update particle velocity and position. Terminate if maximum number of iterations is reached.Otherwise, go to Step 2.145506-8484-IJMME-IJENS December 2014 IJENS

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:14 No:06 115 145506-8484-IJMME-IJENS December 2014 IJENS I J E N S machine cost .

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