In a typical assembly optimisation, Assembly Sequence Planning and Assembly Line Balancing are
performed independently. However, competition has compelled the manufacturer to innovate by
integrating the optimisation of both problems. To incorporate ASP and ALB optimisations into a single
integrated optimisation, a clear prerequisite is the availability of integrated ASP and ALB representation.
Although many assembly representation works has been proposed, none of them fully meet the
requirements of integrated optimisation because they were developed independently from various needs.
In this paper, an integrated representation scheme for ASP and ALB that incorporate essential
optimisation information is developed. The proposed representation scheme is built based on assembly
tasks and represented using precedence graph and data matrix. The outcome from presented example
showed that the information for ASP and ALB optimisation can be integrated and represented using task based
precedence graph and data matrix, without discarding important attributes

Ab Rashid, Mohd Fadzil Faisae

Hutabarat, Windo

Tiwari, Ashutosh

English

Cranfield CERES

Proceedings of the 9th International Conference on Manufacturing Research ICMR 2011, pp. 125-131,6-8 September 2011, Glasgow, UKAN INTEGRATED REPRESENTATION SCHEME FOR ASSEMBLY SEQUENCE PLANNINGAND ASSEMBLY LINE BALANCINGMohd F. RashidAshutosh TiwariWindo HutabaratSchool of Applied SciencesCranfield UniversityCranfieldBedford, MK43 0AL, UKm.abrashid@cranfield.ac.ukABSTRACTIn a typical assembly optimisation, Assembly Sequence Planning and Assembly Line Balancing areperformed independently. However, competition has compelled the manufacturer to innovate byintegrating the optimisation of both problems. To incorporate ASP and ALB optimisations into a singleintegrated optimisation, a clear prerequisite is the availability of integrated ASP and ALB representation.Although many assembly representation works has been proposed, none of them fully meet therequirements of integrated optimisation because they were developed independently from various needs.In this paper, an integrated representation scheme for ASP and ALB that incorporate essentialoptimisation information is developed. The proposed representation scheme is built based on assemblytasks and represented using precedence graph and data matrix. The outcome from presented exampleshowed that the information for ASP and ALB optimisation can be integrated and represented using task-based precedence graph and data matrix, without discarding important attributes.1 INTRODUCTIONIn manufacturing, assembly optimisation is an important process which allows a company to identifyand eliminate any inefficiency in assembly. Assembly Sequence Planning (ASP) and Assembly LineBalancing (ALB) are classified among major topics in assembly optimisation because both are directlyrelated to assembly efficiency. In conventional assembly optimisation, ASP and ALB activities areperformed independently since these activities are considered as belonging to different productdevelopment and production phases (Marian, 2003). In relation with assembly optimisation, the ASP andALB optimisation that was previously performed in serial presents a good opportunity to be integrated toreduce time-to-market for the product.Although there are many works on assembly representation that has been done, most of the paperspresent an independent representation scheme for ASP or ALB problem that were built on the differentbasis. Most of the existing representation schemes for ASP are based on assembly parts, while ALBrepresentation schemes are all based on assembly tasks which lead to difficulties in integrating bothproblems. There are several works that represent ASP problem based on assembly task, but theoptimisation objectives that are applicable to this type of representation is very limited. In order to enablethe ASP and ALB optimisation to be done concurrently, a single representation scheme that can be usedto represent both of the problems is required.Prior to this work, a survey on published papers in ASP and ALB optimisation from 2000 until 2010has been conducted. From this survey, it was found that the most frequent ASP optimisation objectivesM. Rashid, A. Tiwari and W. Hutabaratthat have been used are to minimise assembly direction change and to minimise number of tool change.Meanwhile, in ALB, the dominant optimisation objectives are to minimise cycle time, minimise number ofworkstation and minimise workload variance (Rashid et al., 2011). These findings show the importanceand relevance of these objectives in ASP and ALB optimisation.Previous researchers have successfully developed various ASP representation schemes to fit withtheir particular problem characteristics and attributes. One of the common similarities among theseschemes is they are based on assembly part. On the other hand, the most dominant and successfulrepresentation method in ALB is precedence graph that is built based on assembly task. An integratedrepresentation for both problems must use similar basis. After considering the available alternatives, theirflexibility, and their success in previous works, the assembly task basis is chosen.In this paper, an integrated representation scheme for ASP and ALB problem based on assembly taskwill be built. In contrast with existing work, the proposed representation will consider all of the mostfrequently used optimisation objectives as reported in previous survey (Rashid et al., 2011). An integratedrepresentation scheme for ASP and ALB enable both of the problems to be optimised together, whichshorten the time-to-market for the product. Section 2 of this paper presents the proposed representationscheme and example of application. Section 3 discusses the proposed representation, benefits andlimitations and finally followed by conclusion in section 4.2 PROPOSED METHOD AND EXAMPLEIn this paper, the proposed model is divided into two main sections; Representation and Evaluation asin Figure 1. The proposed representation scheme will be built based on the assembly task. To representboth ASP and ALB problems, precedence graph and data matrix will be used. The assembly of wall rackin Figure 2 will be used to explain the proposed representation application.2.1 Basic AssumptionsBefore presenting the proposed approach, certain assumptions need to be stated in order to define therepresentation scheme. The assumptions are listed as follows:Figure 1: Flowchart of theproposed representationschemeFigure 2: Assembly of wall rackM. Rashid, A. Tiwari and W. HutabaratAssumption 1: For an assembly task, only two parts or subassemblies are involved. It mightcontain a combination of ‘part and part’, ‘part and subassembly’ or ‘subassemblyand subassembly’.Assumption 2: Only one part or subassembly is moved during one assembly task. Therefore, onepart or subassembly will be moving part and another one will be fixed part.2.2 RepresentationIn this approach, the ASP and ALB information such as design variables, constraint and optimisationparameters can be represented using precedence graph and data matrix. Therefore, the main activities inthis stage are to establish a precedence graph and data matrix from the assembly drawing.2.2.1 Establish liaison matrixIn the proposed method, the liaison matrix will be expressed using unique numbering system. Forproduct with n parts, the relation between kth and lth parts is presented in the liaison matrix. If there existsan assembly relation between k and l, L(k, l)= ai (i=1,2,...,r), otherwise, L(k,l) is left blank. Here, r is thenumber of liaison that exists in the assembly. For assembly example in Figure 2, the liaison matrix isshown in Table 1.k 1 2 3 4 5 6 7 81 - a1 a2 a3 a4 a52 - a63 -4 - a75 - a8 a96 -7 -8 -Task De Fazio’s Q&A1 2a1 a3 a2a2 a1, a3 -a3 - a1a4 - -a5 a4 -a6 a3 -a7 a6 -a8 a3 -a9 a8 -2.2.2 Apply De Fazio’s question-and-answerQuestion-and-answer (Q&A) procedure is applied to determine precedence relations in assemblyliaisons. This procedure is adopted from (De Fazio and Whitney, 1987) which consists of two questionsfor each liaison. For liaison i;Question 1: What liaisons must be done prior to doing liaison i?Question 2: What liaisons must be left to be done after doing liaison i?For example above, assembly task a1, task a3 needs to be done prior to a1, while task a2 must be left tobe done after task a1. The summary of De Fazio’s question-and-answer (Q&A) is presented in Table 2.2.2.3 Map precedence graphAfter answering these questions, all of the assembly precedence will be determined. The precedenceconstraint for this problem is given as C[(a3, a1), (a1, a2), (a3, a2), (a4, a5), (a3, a6), (a6, a7), (a3, a8), (a8,a9)]. In this set, (a3,a1) bring information that a3 must be done prior to a1. The predecessor task isrepresented with outgoing arc and successor task is shown by incoming arc. According to the transitivityof the precedence constraints, the shortest paths between two generic nodes are removed (Fouda et al.,lTable 1: Liaison matrix for wall rackassemblyTable 2: Summary of the resulting DeFazio’s Q&AM. Rashid, A. Tiwari and W. Hutabarat2001). Once the precedence graph is established (Figure 3), the design space that contains designvariables and constraints are defined.2.2.4 Establish data matrix, DMThe assembly data is represented by matrix r×3 (r is number of assembly liaison). The first column,D represents assembly direction. In this case, six major direction (+x,-x,+y,-y,+z,-z) are considered.Meanwhile the second and third column shows assembly tool, T and assembly time, M respectively. Theassembly direction, D is obtained by determining fix and moving part in each assembly task. Forexample, the assembly direction for task a1 is the direction of bringing part 2 to be assembled with part 1,which is in +x direction. Meanwhile, T is assembly tool that involve in the assembly task. Then, theassembly time, M is acquired by performing time study of the product. The detail of assembly data forexample in Figure 2 is shown in Table 3.Task D T M (timeunit)a1 +x - 4a2 +x T1 12a3 +x - 7a4 -x - 4a5 -x T1 12a6 +x - 5a7 +x T2 12a8 -x - 5a9 -x T2 122.3 EvaluationThe main purpose of assembly representation scheme is to enable assembly sequence to be evaluatedfor optimisation process. In this work, five optimisation objectives are considered according to frequentlyused objectives in previous survey: (i) Minimise number of assembly direction change, (ii) Minimisenumber of assembly tool change, (iii) Minimise cycle time, (iv) Minimise number of workstation, and (v)Minimise workload variation2.3.1 Assembly sequence evaluationFor a feasible assembly sequence, number of assembly direction change is counted when the nextassembly task requires a different assembly direction compared with the present assembly task. In thiscase, similar approach also goes to second objective in determining number of assembly tool change.Meanwhile, to evaluate third and fourth objectives, the maximum allowable cycle time, ctmax isrequired. Normally, ctmax is determined from number of demand or required output in assignment period.Once ctmax is determined, the assembly tasks can be assigned into workstations. The cycle time (ct) forparticular assembly sequence is the highest processing time among all workstations. Processing time (pt)refers to total assembly time in a particular workstation. Once the total processing time for the currentworkstation is larger than ctmax, the present assembly task will be assigned into the next workstation.Then, the workload variation (v) for the fifth objective is calculated using the following formula.Here, ws refer to number of workstations in assembly line.a7a2a4a3a5a9a8a6a1StartEndTable 3: Data matrix, DMfor wall rack assemblyFigure 3: Precedence graph forwall rack assemblyM. Rashid, A. Tiwari and W. HutabaratEquation 1To evaluate an assembly sequence, a feasible assembly sequence based on precedence graph needs tobe established. As an example, a feasible assembly sequences F1[a4 ,a5 , a3 , a1 , a6, a8, a9, a7 , a2] isconsidered. In this case, number of assembly direction change (D) and tool change (T): Sequence F1 has D = 3and T = 4.Table 4: Assembly direction and tool change evaluationAssembly time (M): Let ctmax= 20 time unit, which is the maximum allowable cycle time for aworkstation. As an example, for workstation 1 (ws1), the total assembly time for a4 and a5 is 16 time unit.If the assembly task a3 is also included in ws1, the total assembly time will become 23 time unit which isexceeding the ctmax. Therefore, the assembly task a3 is assigned into ws2. Similar procedure is also appliedto the subsequent workstations.Table 5: Assembly tasks allocation for F1ws ws1 ws2 ws3 ws4 ws5F1 a4 a5 a3 a1 a6 a8 a9 a7 a2M 4 12 7 4 5 5 12 12 12pt 16 16 17 12 12From the assembly assignment for sequence F1, the highest processing time, pt in all workstations is 17time unit. Therefore, the cycle time, ct = 17 time unit. Meanwhile to assign all of assembly task with ctmaxconstraint, five workstations are required. From there, the workload variance, v for sequence F1 can becalculated using Equation 1, which is equal to 2.4 time unit/workstation.3 DISCUSSIONIn this paper, an integrated representation and evaluation scheme for ASP and ALB had beenproposed. The proposed representation scheme is built on the basis of assembly task as widely used inrepresenting ALB problem. In this case, ASP representation that usually built based on assembly part istransformed into assembly task. In transforming ASP problem into task-based representation, the mainproblem is to determine the assembly direction because no previous work had represented assemblydirection based on assembly task. This problem has been solved by redefining assembly directionaccording to Assumptions 1 and 2 (Section 2.1).Previously, there are researchers that integrate ASP and ALB representation using a singlerepresentation scheme. In contrast with (Chen et al., 2002) works that only consider assembly tool forASP problem, the proposed representation also considered the assembly direction that brings newdefinition of this parameter to associate with assembly task representation. Therefore, the proposedrepresentation scheme provided more assembly parameters that can cover all important optimisationobjectives as stated in Section 2.3.Another integrated representation scheme proposed in (Tseng et al., 2008) was based on assemblyconnectors. In this approach, the assembly parameters refer to the connectors. For example, the assemblydirection and assembly time are referred to connector direction and time to assemble the connectorrespectively. In contrast, the proposed representation considered the assembly parameters in terms ofassembly task, which is closely linked to assembly process rather than connector, because not allF1 a4 a5 a3 a1 a6 a8 a9 a7 a2 TotalD -x -x +x +x +x -x -x +x +x3Change 0 0 1 0 0 1 0 1 0T - T1 - - - - T2 T2 T14Change 0 1 1 0 0 0 1 0 1M. Rashid, A. Tiwari and W. Hutabaratassembly components needs for a connector as shown in assembling part 1 and 5 in Figure 2. In thisexample, this operation does not utilise any connector.In section 2, an example of wall rack assembly has been presented in demonstrating how to transformthe assembly product to the proposed representation. This example shows that the ASP and ALB problemcan be represented in a single representation scheme. In the proposed representation scheme, allinformation needed for ASP and ALB problems are represented using precedence graph and data matrix.The design variable that is assembly sequence can be generated from the precedence graph. Meanwhile,the optimisation constraint which is precedence constraint is presented by directed arc in the precedencegraph. Then, the optimisation parameter is presented in the data matrix.There are some limitations of the proposed approach. The first limitation is that the proposedapproach cannot deal with an assembly task for more than two parts. To apply the proposed approach, theassembly task needs to be redefined by assembling only two parts at one time. The second limitation isthe difficulty of generating the precedence graph. The proposed approach to generate a precedence graphmight be messy for manual processing of a large assembly task. In the future, to simplify the process, it ishighly recommended that the precedence graph can be generated automatically using the input ofassembly task and precedence constraint.4 CONCLUSIONThe best approach to ensure simultaneous optimisation of ASP and ALB problem is by employing anintegrated representation of solutions. A successful integrated approach will be able to combine andretains the important characteristics of the problem such as optimisation objectives that usually used inindependent works. This work shows that the proposed representation scheme is able to integrate ASPand ALB representation and at the same time consider all important optimisation objectives as been usedin individual ASP and ALB.Although there is only small difference between the proposed representation and previous work, animportant contribution is a new description of assembly direction by distinguishing between fixed andmoving parts in the assembly task. By using this approach, the assembly direction parameter can beassociated with task-based representation. Therefore, the assembly task-based representation for ASP andALB that takes into account all important optimisation parameters has successfully been proposed.REFERENCESChen, R., Lu, K. and Yu, S. (2002), "A hybrid genetic algorithm approach on multi-objective of assemblyplanning problem", Engineering Applications of Artificial Intelligence, vol. 15, no. 5, pp. 447-457.De Fazio, T. L. and Whitney, D. E. (1987), "Simplified generation of all mechanical assemblysequences.", IEEE Journal of Robotics and Automation, vol. RA-3, no. 6, pp. 640-658.Fouda, P., De Lit, P., Rekiek, B. and Delchambre, A. (2001), "Generation of precedence graphs for aproduct family using a disassembly approach", Proceedings of the IEEE International Symposium onAssembly and Task Planning, 2001, pp. 226-231.Tseng, H., Chen, M., Chang, C. and Wang, W. (2008), "Hybrid evolutionary multi-objective algorithmsfor integrating assembly sequence planning and assembly line balancing", International Journal ofProduction Research, vol. 46, no. 21, pp. 5951-5977.Marian, R. M. (2003), "Optimisation of Assembly Sequences using Genetic Algorithm", PhD thesis,University of South Australia, ProQuest.Rashid, M., Tiwari, A. and Hutabarat, W. (2011), “A Review on Assembly Sequence Planning andAssembly Line Balancing Optimisation using Soft Computing Approaches”, accepted inInternational Journal of Advanced Manufacturing Technology.Whitney, D. E. (2004), "Mechanical Assemblies: Their Design, Manufacture and Role in ProductDevelopment", Oxford University Press, New York.

A hybrid genetic algorithm approach on multi-objective of assembly planning problem&quot;,

A Review on Assembly Sequence Planning and Assembly Line Balancing Optimisation using Soft Computing Approaches”, accepted in

Generation of precedence graphs for a product family using a disassembly approach&quot;,

Hybrid evolutionary multi-objective algorithms for integrating assembly sequence planning and assembly line balancing&quot;,

Mechanical Assemblies: Their Design, Manufacture and Role in Product Development&quot;,

Optimisation of Assembly Sequences using Genetic Algorithm&quot;,

Simplified generation of all mechanical assembly sequences.&quot;,

An integrated representation scheme for assembly sequence planning and assembly line balancing

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An integrated representation scheme for assembly sequence planning and assembly line balancing

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