Advanced Engineering Informatics 26 (2012) 306–316

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Advanced Engineering Informatics

journal homepage: www.elsevier .com/ locate /ae i

Disassembly sequence structure graphs: An optimal approachfor multiple-target selective disassembly sequence planning

Shana Smith ⇑, Greg Smith, Wei-Han ChenDepartment of Mechanical Engineering, National Taiwan University, Taiwan, ROC

a r t i c l e i n f o

Article history:Received 16 February 2011Received in revised form 24 November 2011Accepted 30 November 2011Available online 29 December 2011

Keywords:DSSGOptimalMultiple targetSelective disassembly sequence planningDisassembly sequence structure graph

1474-0346/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.aei.2011.11.003

⇑ Corresponding author. Address: No. 1, Sec. 4, RoROC. Tel.: +886 2 33662692; fax: +886 2 23631755.

E-mail address: ssmith@ntu.edu.tw (S. Smith).

a b s t r a c t

Modern green products must be easy to disassemble. Specific target components must be accessed andremoved for repair, reuse, recycling, or remanufacturing. Prior studies describe various methods forremoving selective targets from a product. However, solution quality, model complexity, and searchingtime have not been considered thoroughly. The goal of this study is to improve solution quality, minimizemodel complexity, and reduce searching time. To achieve the goal, this study introduces a new ‘disassem-bly sequence structure graph’ (DSSG) model for multiple-target selective disassembly sequence planning,an approach for creating DSSGs, and methods for searching DSSGs. The DSSG model contains a minimumset of parts that must be removed to remove selected targets, with an order and direction for removingeach part. The approach uses expert rules to choose parts, part order, and part disassembly directions,based upon physical constraints. The searching methods use rules to remove all parts, in order, fromthe DSSG. The DSSG approach is an optimal approach. The approach creates a high quality minimum-sizemodel, in minimum time. The approach finds high quality, practical, realistic, physically feasible solu-tions, in minimum time. The solutions are optimized for number of removed parts, part order, part dis-assembly directions, and reorientations. The solutions remove parts in practical order. The solutionsremove parts in realistic directions. The solutions consider contact, motion, and fastener constraints.The study also presents eight new design rules. The study results can be used to improve the productdesign process, increase product life-cycle quality, and reduce product environmental impact.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Modern green products must meet economic, environmental,and social design constraints. To meet the constraints, productsmust be easy to disassemble. During their life cycle, productsmay be selectively disassembled to repair or replace parts. Atend of life, products must be fully, partially, or selectively disas-sembled to recover, reuse, or recycle parts and materials [1,2].Therefore, disassembly planning is an important part of the prod-uct design process.

During the design process, many different design options anddisassembly plans must be considered. For even simple structures,the process can be computationally complex. Therefore, designersneed effective, efficient disassembly planning methods, to solvethe problem. Prior studies describe various methods for selectivedisassembly planning. However, solution quality, model complex-ity, and searching time have not been considered thoroughly.

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In general, the goal of any disassembly planning method is tofind an optimal solution, in minimum time. Most methods use dis-assembly graph (DG) models. Due to model complexity, they can-not guarantee that they will find an optimal solution (the overallbest solution). They can only guarantee that they will find an opti-mized solution (the best solution found). Therefore, methods mustbe compared by solution quality, model complexity, and searchingtime.

The goal of this study is to improve solution quality, minimizemodel complexity, and reduce searching time. In this study, highquality solutions are optimized for number of removed parts, partorder, part disassembly directions, and reorientations. Practicalsolutions remove parts in practical order. Realistic solutions re-move parts in realistic directions. Physically feasible solutions con-sider contact, motion, and fastener constraints.

This study introduces a new DSSG model for selective disassem-bly planning, an approach for creating DSSGs, and methods forsearching DSSGs. The DSSG model contains a minimum set ofparts, with an order and direction for removing each part. The ap-proach uses expert rules to choose parts, part order, and part dis-assembly directions, based upon physical constraints. Thesearching methods use rules to remove all parts, in order, fromthe DSSG.

S. Smith et al. / Advanced Engineering Informatics 26 (2012) 306–316 307

The DSSG approach is an optimal approach. The approach im-proves solution quality, minimizes model complexity, and mini-mizes searching time. The approach creates a high qualityminimum-size model, in minimum time. The approach finds highquality, practical, realistic, physically feasible solutions, in mini-mum time. The solutions are optimized for number of removedparts, part order, part disassembly directions, and reorientations.

This paper describes disassembly planning, prior studies, thegoal of this study, the DSSG model, approach, and methods, timecomplexity, case studies, and eight new design rules.

Fig. 1. Example assembly.

2. Disassembly planning

Disassembly planning consists of two major steps, creating adisassembly model and generating disassembly sequences (disas-sembly sequence planning) [3]. Disassembly models are usuallygraphs. Graph nodes represent parts. Graph links represent con-straints between the parts [4–10]. Parts may be components,which have specific design functions, or fasteners [8]. Graphs aregenerally converted into matrices for computer processing [4].

Disassembly sequence planning consists of searching a graph(moving from node to node along individual links in the graph)to find optimal paths [5–8]. Optimal paths have maximum qualityand minimum length. Therefore, model quality and complexity af-fect solution quality and searching time. Graphs that contain moreinformation improve solution quality. Graphs that contain lessinformation reduce searching time.

2.1. Prior models

Prior studies describe two graph models for disassembly plan-ning, disassembly graphs and disassembly constraint graphs. Thisstudy shows that a new graph model is needed.

2.1.1. Disassembly graphsDisassembly graphs (DGs), such as non-directional blocking

graphs (NDBGs), contain nd graphs, one for each disassembly direc-tion [4–10]. Each graph contains np nodes and O(np

2) links. Nodesrepresent all parts, links represent all physical constraints, graphsrepresent all disassembly directions, and directions are determinedby all part surfaces. Therefore, DGs can be used to find high qualitysolutions.

However, DG model complexity and searching time are high.DG model complexity is O((nd � np)! � no) paths, for no optimizationcriteria. Minimum time complexity for creating a DG is O(nd � np

2)[4]. Time complexity for searching all paths is O((nd � np)! � no).Time complexity for searching all paths, from nt targets to nb

boundary parts, is Oðnt � ðnd � npÞnp � noÞ.In Fig. 1, with a DG, components 5, 1, 2, 8, and 9 can be removed,

in order. The disassembly directions for all fasteners and compo-nents are realistic and feasible. For nt = 3, nd = 6, np = 19, andno = 2, model complexity is O((6 � 19)! � 2) = 5 � 10186 paths. Timecomplexity for searching all paths, from targets to boundary parts,is over 2 � 1026 years, at 1 ls per path.

2.1.2. Disassembly constraint graphsDisassembly constraint graphs (DCGs), such as removal influ-

ence graphs (RIGs), contain one graph [5,11]. The graph containsnp nodes and O(np

2) links. Nodes represent all parts, links representall disassembly constraints, and the graph does not contain disas-sembly directions. Therefore, DCGs cannot be used to find highquality solutions.

However, DCGs reduce model complexity and searching time.DCG model complexity is O(np! � no). Time complexity for extract-ing a DCG from a DG is O(nd � np

2). Time complexity for searching

all paths, between nb boundary parts and nt targets, is O(max(nb,nt) � np

3 � no).In Fig. 1, with a DCG, components 2, 8, and 9 can be removed, in

order. The disassembly directions for f9, 8, and 9 are unrealistic andinfeasible. However, for nt = 3, nd = 6, nb = 13, np = 19, and no = 2,model complexity is O(19! � 2) = 2.4 � 1017 paths. Time complexityfor searching all paths, between boundary parts and targets, is178 ms, at 1 ls per path.

2.2. Prior methods

Prior studies describe three rule-based graph searching meth-ods for selective disassembly sequence planning. This study showsthat a new rule-based graph searching method is needed.

2.2.1. Smith et al.’s approachSmith et al.’s approach [8] creates a DG. The approach uses rules

to search the DG, from targets to boundary parts, along all pathsthat have higher qualities than other complete paths. The approachcalculates qualities with a multi-criteria function, to reduce no toone.

The approach finds high quality solutions for general 3D struc-tures. The approach reduces model complexity to O((nd � np)!)paths. The approach reduces time complexity for searching a disas-sembly graph to Oðnt � ðnd � npÞnp Þ. However, searching time is stillhigh.

For 3D structures, minimum time complexity for creating andsearching a DG is O(nd � np

2). Minimum time complexity for search-ing a DG is O(nt � (nd � np)np), for Smith et al.’s approach. Therefore,Smith et al.’s approach does not search a disassembly graph inminimum time.

2.2.2. The wave propagation approachThe wave propagation approach [12] extracts a DCG (RIG) from

a DG (NDBG). The approach uses rules to search the DCG, in waves,from both boundary parts and targets, to create a partial DCG, andsearches the partial DCG to find solutions.

The approach finds solutions for 3D structures. However, thesolutions may be unrealistic or infeasible. DCG model complexityis O(np! � no) paths. Time complexity for creating a partial DCG isnot given. Time complexity for searching the partial DCG isOð2nt � n2

pÞ

308 S. Smith et al. / Advanced Engineering Informatics 26 (2012) 306–316

For 3D structures, minimum time complexity for creating a par-tial DCG is O(nt � np

2). Time complexity for searching a DCG, fromboth boundary parts and targets, is O(max(nb,nt) � np

3). Therefore,the wave propagation approach does not create a partial DCG inminimum time.

2.2.3. Garcia’s methodGarcia’s method [11] extracts a DCG (RIG) from a DG. The ap-

proach uses rules to search the DCG for the shortest paths betweenboundary components and all other components, merges the pathsto create a partial DCG, and searches the partial DCG to findsolutions.

The method finds solutions for simple stacked structures. Thesolutions may be unrealistic or infeasible. Model complexity isO(np) paths. Time complexity for creating a partial DCG isO(max(nb,nt) � np � log(np)). Time complexity for searching the par-tial DCG is O(np

2).For simple stacked structures, minimum time complexity for

creating a partial DCG is O(nt � np). Time complexity for creating apartial DCG is O(max(nb,nt) � np � log(np)), for Garcia’s method.Therefore, Garcia’s method does not create a partial DCG in mini-mum time.

2.3. Prior techniques

Prior studies describe various techniques for improving solutionquality, reducing model complexity, or reducing searching time.This study shows that new techniques are needed.

2.3.1. Techniques for improving solution qualityPrior studies add directions. This study shows that adding opti-

mized directions to a DSSG improves solution quality. Adding alldirections to a DCG, converts the DCG into a DG [3,13]. Adding ac-tual directions to a DCG does not optimize the directions [14].

Prior studies consider motion constraints. This study shows thatconsidering motion constraints, with single-translation motions,improves solution quality [6–10]. Considering motion constraints,with motion planning, can produce unrealistic or infeasible solu-tions [15].

Prior studies consider fastener constraints. This study showsthat considering fastener type, with fastener motion, improvessolution quality [6–10]. Considering fastener type, without fas-tener motion, can produce unrealistic or infeasible solutions [3].

2.3.2. Techniques for reducing model complexityPrior studies group parts. This study shows that grouping can be

used, during design, to reduce model complexity and remove ob-structed parts. Grouping parts, after design, can produce infeasiblesolutions or make a structure impossible to disassemble [3,16–18].

Prior studies remove paths. This study shows that removingpaths from a DSSG, by directions, can be used to reduce modelcomplexity. Removing paths from a graph, by optimization criteria,can produce sub-optimal results [3,13,14,16,19–22].

2.3.3. Techniques for reducing searching timePrior studies use rules or heuristic searching algorithms. This

study shows that using rules to search a DSSG minimizes searchingtime. Other studies show that using rules or heuristic searchingalgorithms to search DGs or DCGs reduces searching time[5,8,12,20–27].

3. The goal of this study

The goal of this study is to improve solution quality, minimizemodel complexity, and reduce searching time. To achieve the goal,

this study introduces a new ‘disassembly sequence structuregraph’ (DSSG) model for multiple-target selective disassembly se-quence planning, an approach for creating DSSGs, and methodsfor searching DSSGs.

The DSSG model contains one graph. The graph only containsthe nodes and links needed to remove target components. Nodesare arranged in practical order. Nodes contain optimized directionsfor removing each part. Links represent contact, motion, and fas-tener constraints. Therefore, the model improves solution quality.

The DSSG model contains a minimum number of nodes andlinks. The approach removes paths from the model, by directions,before searching the model. Therefore, the approach minimizesmodel complexity. The searching methods uses expert rules to re-move nodes, in order, from the DSSG. Therefore, the approach min-imizes searching time.

One of Boothroyd et al.’s design for disassembly (DFD) princi-ples states that designs should avoid obstructed access to parts[28]. In most cases, it is physically impossible for a person or a ro-bot to reach around obstacles to remove obstructed parts. There-fore, the DSSG approach removes parts with practical, realisticsingle-translation motions.

The principle does not limit part disassembly directions. Partscan be disassembled in any physically feasible disassembly direc-tion. The principle only limits part motion during disassembly.During disassembly, parts cannot change directions to avoid obsta-cles. The approach can still remove obstructed parts, by removingthe obstructed parts in sub-assemblies.

Following the principle makes products easier to build, easier touse, and easier to disassemble. Following the principle also makesthe DSSG approach more practical, realistic, and efficient. The DSSGapproach finds high quality, practical, realistic, physically feasiblesolutions, in minimum time, without complex, time consumingmotion planning calculations.

To find solutions, the DSSG approach creates a DG model, cre-ates a DSSG model from the DG model, and searches the DSSGmodel.

4. The DG model

The disassembly graph (DG) model in this study contains fivematrices: a contact constraint matrix for components (CC), a mo-tion constraint matrix for components (MC), a contact constraintmatrix for fasteners (CF), a motion constraint matrix for fasteners(MF), and a projection matrix for components (PC). The matricescontain constraints for all parts.

The matrices contain nd graphs. Matrix rows represent all parts.Matrix columns contain all contact, motion, and fastener con-straints. Components create constraints by occupying volumes.Fasteners create constraints by connecting components to othercomponents. Matrix columns represent all disassembly directions,and directions are determined by all part surfaces.

4.1. Disassembly directions

Without loss of generality, an infinite set of feasible disassem-bly directions can be reduced to a finite set of discrete disassemblydirections [4]. In this study, the examples and case studies only useparts that have horizontal, vertical, or round contact surfaces.Without loss of generality, all of the parts can be disassembled infour or six principle disassembly directions.

4.2. Contact constraint matrix for components

A contact constraint matrix for components (CC) records contactconstraints for each component. Rows represent components.

S. Smith et al. / Advanced Engineering Informatics 26 (2012) 306–316 309

Columns represent disassembly directions. For a 3D product withnc components and six part disassembly directions, the CC matrixhas nc rows and six columns. Columns represent the +x, �x, +y,�y, +z, and �z directions.

Each row element contains links to components that contact acomponent and fasteners that connect the component to othercomponents, in the given direction. A number represents a compo-nent. An ‘f’’ followed by a number represents a fastener. A ‘0’ indi-cates that the component does not have any constraints, in a givendirection. The CC matrix for Fig. 1 is.

CC ¼

CC1

CC2

CC3

CC4

CC5

CC6

CC7

CC8

CC9

266666666666666664

377777777777777775

¼

0 0 f1; f8;5 26 f2 f1;1 f3;30 0 2;4;7 f3; f4; f5

f6; f7 5;8 0 f5;3f7;4 0 f8 1

8 f2; f10;2 0 f4;70 0 f9;6;9 f4;3

f6;4 f10;6 f9 90 0 f9;8 7

266666666666666664

377777777777777775

4.3. Contact constraint matrix for fasteners

A contact constraint matrix for fasteners (CF) records contactconstraints for each fastener. Constrained fasteners, for examplebolts, only have one disassembly direction. Unconstrained fasten-ers, for example washers, can be removed in any disassemblydirection. A fastener must be removed from a component. A com-ponent cannot be removed from a fastener.

For a 3D product with nf fasteners and six part disassemblydirections, the DF matrix has nf rows and one column. For eachconstrained fastener fi, CFi = d_dir(fi) = 1, 2, 3, 4, 5, or 6, which rep-resents a disassembly direction, +x, �x, +y,�y, +z, and�z. For Fig. 1,CF1 = 3 and CF7 = 1. For each unconstrained fastener fi, CFi = ‘0’. Theapproach chooses d_dir(fi), in Section 5.2.

4.4. Motion constraint matrix for components

A motion constraint matrix for components (MC) records mo-tion constraints for each component. Each row element contains‘first-level parts’, parts that intersect with a part’s projection inany given direction. The MC matrix for Fig. 1 is.

MC ¼

MC1

MC2

MC3

MC4

MC5

MC6

MC7

MC8

MC9

266666666666666664

377777777777777775

¼

f1; f8;4 f1; f8 0 6f1; f3; f10;4;7 f1; f3 f2 f2

f3; f4; f5 f3; f4; f5 6;8 0f5 f5;1;2;6;7;9 f6; f7 f6; f7

f8 f8 f7 f7; f9;8f4;4;9 f4 f2; f10;1 f2; f10;3f4; f8;4 f4; f8;2 8 0

f9 f9 f6; f10;5 f6; f10;3;7f9;4 f9;6 0 0

266666666666666664

377777777777777775

4.5. Motion constraint matrix for fasteners

A motion constraint matrix for fasteners (MF) records motionconstraints for each fastener. Each row element contains ‘first-levelparts’, parts that intersect with a part’s projection in any givendirection. For Fig. 1, MF9 = [0050]. MF10 = [0200].

4.6. Projection matrix for components

A projection matrix for components (PC) counts blocking com-ponents for each component. Each row element contains the num-ber of components, at all levels, that block a component, in thegiven direction. A PC matrix can also count fasteners. The DSSG ap-proach uses the PC matrix to choose optimized part disassemblydirections. The PC matrix for Fig. 1 is.

PC ¼

PC1

PC2

PC3

PC4

PC5

PC6

PC7

PC8

PC9

266666666666666664

377777777777777775

¼

1 0 1 45 0 1 10 0 8 00 7 0 11 0 0 63 1 2 21 1 5 11 2 1 31 2 2 2

266666666666666664

377777777777777775

4.7. Optimized part disassembly directions

A single target component can only be removed in one disas-sembly direction. A target cannot change directions during disas-sembly. The best PC matrix direction for removing a single targetcomponent is generally the direction with the least number ofobstacles. For Fig. 1, the best PC matrix direction for removing com-ponent 4 is either the +x or +y direction.

For a single target component that has two ‘best’ directions, theapproach can choose one of the directions, or create two single-tar-get DSSGs and choose the best DSSG, (Section 5.2). The best DSSGcontains a minimum number of parts. For multiple target compo-nents, the best DSSG contains a minimum number of parts and amaximum number of target components.

Multiple targets can be removed in different ways. Targets canbe removed in their best individual directions. Alternatively, tar-gets can be removed in their best common directions. The ap-proach can consider individual directions, common directions, orcommon obstacles by removing targets from the PC matrix, sum-ming and comparing matrix rows, or both.

Smith and Smith used similar techniques to find the best partorders for assembling products [29]. The approach summed rowsor columns in contact and motion constraint matrices, used thecounts to order parts in assembly sequences, and used the assem-bly sequences to create initial populations for a genetic algorithm-based assembly planner.

For Fig. 1, the best common PC matrix direction for removingcomponents 4, 7, and 9 is the +x direction. For multiple target com-ponents that have more than one best direction, the approach canchoose a direction for each target or create more than one DSSG foreach target and choose the best DSSG for each target, (Section 5.4).

Most prior method search for solutions in a DG that contains alldirections, or they do not consider part disassembly directions. TheDSSG approach chooses optimized part disassembly directions be-fore searching for solutions. Choosing directions before searchingreduces model complexity and searching time.

4.8. Time complexity for creating the disassembly graph

Overall time complexity for creating the five DG matrices isO(nd � np

2). Time complexity for choosing optimized part disassem-bly directions is O(nt � nd). Therefore, overall time complexity forcreating the DG is O(nd � np

2). Minimum time complexity for creat-ing a complete DG is O(nd � np

2) [4]. Therefore, the DSSG approachcreates a DG in minimum time.

310 S. Smith et al. / Advanced Engineering Informatics 26 (2012) 306–316

5. The DSSG model

The DSSG model used in this study is an inverted tree. Rootnodes represent target components. Leaf nodes represent partsthat constrain the target components. The tree contains a mini-mum set of parts that must be removed to remove the target com-ponents. Nodes are arranged and ordered in constraint levels. Eachnode has an assigned disassembly direction.

For Fig. 1, Fig. 2 shows a single-target DSSG for removing targetcomponents 4 and 7, in the +x direction. The DSSG contains twotargets, one other component, and six fasteners (9 parts). Squaresrepresent components. Circles represent fasteners.

Component 4 is connected to component 7 by a motion con-straint. Fasteners f4 and f9 are connected to component 7 by fas-tener constraints. Boundary component 5 is connected tofastener f9 by a motion constraint. Fasteners f5–f8 are connectedto components 4 and 5 by fastener constraints. Fasteners f4–f8 donot have any constraints; they can be removed.

The approach creates a DSSG by adding nodes from root nodesto leaf nodes. Removing nodes, in reverse order, gives a disassem-bly sequence optimized for number of removed parts, part order,and part disassembly directions. Removing leaf nodes, in order,also reduces reorientations. Removing nodes in different valid or-ders may further reduce reorientations.

5.1. An approach for creating a single-target DSSGs

The approach for creating a single-target DSSG gets parts fromthe DG, arranges and orders the parts in levels, and adds the partsto a DSSG. The process creates a root node for target component t,assigns a disassembly direction to t, puts t in a queue, and removesa part p from the queue (Fig. 3).

The approach gets the part’s constraint-level parts (p0 = c0 or f 0)from the DG, assigns disassembly directions to all p0, adds all p0 tothe DSSG, and adds all new p0 (that are not in the DSSG or thequeue) to the queue. (For simple stacked structures, the processadds all p0 to the queue.) The process repeats, until all p are addedto the DSSG.

5.2. Expert rules

The approach uses expert rules to improve solution quality,minimize graph complexity, and reduce searching time. The ruleschoose parts, part order, and part disassembly directions, fromthe DG, based upon physical constraints. The rules were derivedfrom disassembly planning case studies. The rules use the PC ma-trix to choose part disassembly directions.

From case studies, the best disassembly direction for removing tis the direction d_dir(t) with the least number of obstacles, all f0

that constrain c must be removed before c, all c0 that constrain p

nt = 2

nc = 3

nf = 6

np = 9

disassembly sequence

target component

f5 f6

4

7

f4

Fig. 2. Single-target DSSG f

in d_dir(p) must be removed before p, and the best direction forremoving all p0 is d_dir(p), unless the p0 have pre-assigned disas-sembly directions.

In this study, the approach chooses the best direction forremoving each target component, creates one single-target DSSGfor each target component, and selects and merges the best DSSGsto create one multiple-target DSSG. The best DSSGs contain a max-imum number of target components n0t and a minimum number ofparts n0p.

For Fig. 1, the best directions for removing components 4, 7, and9 are all the +x direction. Figs. 4 and 5 show the +x-direction DSSGsfor components 4, 7, and 9. The DSSGs for components 7 and 9 con-tain the DSSG for component 4. Therefore, the approach merges theDSSGs for components 7 and 9 to create one multiple-target DSSGfor the three components.

Different rules can be used for different applications. The ap-proach can choose the best individual directions for removing eachtarget. The approach can choose the best common direction forremoving all targets. The approach can also choose more direc-tions, create more single-target DSSGs, and select and merge thebest DSSGs.

For component 7, in Fig. 1, the +x-direction DSSG in Fig. 5 hastwo targets, one other component, and six fasteners. The �x-direc-tion DSSG in Fig. 6 has one target, two other components, and se-ven fasteners. The �y-direction DSSG in Fig. 6 has one target, twoother components, and six fasteners. The +x-direction DSSG is thebest solution, by both techniques.

In general, choosing directions before creating DSSGs reducesoverall time complexity. If the rules choose optimal directions,the approach finds optimal DSSGs. If the rules choose optimized(but not optimal) directions, the approach finds optimized DSSGs(that may not be optimal). However, the DSSGs are always optimalfor the selected directions.

5.3. Time complexity for creating single-target DSSGs

Time complexity for extracting nt single-target DSSGs from a DGis O(nt � np

2), for general three-dimensional structures, andO(nt � np), for simple stacked structures.

5.4. An approach for creating a multiple target DSSG

The approach for creating a multiple-target DSSG merges sin-gle-target DSSGs to create one multiple-target DSSG. The approachmerges single-target DSSGs by merging identical nodes within theDSSGs. The approach creates a disjoint multiple-target DSSG forsingle-target DSSGs that do not have any identical nodes.

The approach merges DSSGs until n0t , for the merged DSSG, isequal to nt. If the merged nodes have different directions, the ap-proach uses rules to choose a direction. The final multiple-target

target component

constraint-level parts

boundary components

constraints

constraints

constraints

constraint-level parts f7

5

f9

f8

or target component 7.

Rule 2Get c from the DG Choose d_dir(c )

Add c to the DSSG Add c to the queue

Start

Get p from the queue

p = c or f ?

Finish

Parts in the queue?

p = c p = f

yes

no

Rule 1Get t from the DG Choose d_dir(t)

Put t in the DSSG Put t in a queue

Rule 4Get c from the DG Choose d_dir(c )

Add c to the DSSG Add c to the queueRule 3

Get f from the DG Choose d_dir(f )

Add f to the DSSG Add f to the queue

Fig. 3. An approach for creating a single-target DSSG.

f5 f6 f7

4

nt = 1

nc = 1

nf = 3

np = 4

Fig. 4. Single-target DSSG for component 4.

S. Smith et al. / Advanced Engineering Informatics 26 (2012) 306–316 311

DSSG represents a high quality, practical, realistic, physically feasi-ble solution that is optimized for number of removed parts, part or-der, and part disassembly directions.

If the approach chooses optimal disassembly directions, theDSSG is optimal. If the approach chooses other directions, the DSSGmay not be optimal. However, the DSSG is always optimal, for theselected directions. The DSSG contains a minimum set of parts thatmust be removed to remove the target components, in the selecteddirections.

The DSSG improves solution quality and reduces model com-plexity, compared to prior approaches. Nodes are also ordered to

reduce reorientations and searching time. Nodes are removed withrealistic part motions. Links represent contact, motion, and fas-tener constraints.

For Fig. 1, the approach merges the +x-direction DSSGs for com-ponents 7 and 9, to create one multiple-target DSSG for compo-nents 4, 7, and 9. All of the parts in the single-target DSSGs areidentical, except components 7 and 9, and fastener f4. The finalDSSG contains ten parts. The DSSG reduces model complexity bynine parts, compared to the DG.

5.5. Time complexity for creating a multiple-target DSSG

Time complexity for creating nt single-target DSSGs isO(nt � np

2), for general 3D structures, and O(nt � np), for simplestacked structures. Time complexity for merging nt single-targetDSSGs is O(nt � np). Therefore, overall time complexity for creatinga multiple-target DSSG is O(nt � np

2), for general 3D structures,and O(nt � np), for simple stacked structures.

Minimum time complexity for creating a DG, for one direction,is O(np

2), for general 3D structures, and O(np), for simple stacked

f5 f6 f7

4 5

7

f9 f4

f5 f6 f7

4 5

9

f8

f9 f4

7

nt = 3

nc = 4

nf = 6

np = 10

nt = 2

nc = 3

nf = 6

np = 9

f5 f6 f7

4 5

9

f8

f9 nt = 2

nc = 3

nf = 5

np = 8

f8

Fig. 5. Optimized DSSGs for Fig. 1.

f7

5

7

f8

f9

3

f4 f5 f3 f7

5

7

f8

f9 f4

2

f1 f2 f3

nt = 1

nc = 3

nf = 7

np = 10

nt = 1

nc = 3

nf = 6

np = 9

Fig. 6. Single-target DSSGs for component 7.

312 S. Smith et al. / Advanced Engineering Informatics 26 (2012) 306–316

structures. Minimum time complexity for creating nt single-targetDGs is O(nt � np

2), for general 3D structures, and O(nt � np), for sim-ple stacked structures. Therefore, the DSSG approach creates amultiple-target DSSG in minimum time.

6. Methods for searching DSSGs

The methods for searching DSSGs remove nodes from the DSSG,to find solutions optimized for number of parts, part order, partdisassembly directions and reorientations. In this study, methodsfor searching DSSGs include rules, heuristic algorithms, and othergraphs searching techniques. Similar methods can be used to opti-mize solutions for other optimization criteria.

6.1. Rules

In this study, the DSSG approach builds a DSSG by adding nodesand links from root nodes to leaf nodes. The approach removes leafnodes, in reverse order, to find solutions optimized for number of

removed parts, part order, and part disassembly directions. The ap-proach removes leaf nodes in other valid orders to find solutionsoptimized for reorientations.

6.2. Heuristic algorithms

In this study, the DSSG approach uses heuristic algorithms, suchas genetic algorithms (GAs) to find solutions optimized for reorien-tations. For Fig. 1, the approach uses a rule to find solutions opti-mized for number of removed parts, part order, and partdisassembly directions. The approach uses a GA to find solutionsoptimized for reorientations.

The DSSG approach can also use other graph searching tech-niques to search DSSGs.

6.3. Time complexity for searching a DSSG

The DSSG approach builds a DSSG by adding nodes and linksfrom root nodes to leaf nodes. The approach finds a solution that re-

S. Smith et al. / Advanced Engineering Informatics 26 (2012) 306–316 313

moves leaf nodes, in reverse order, in zero time. Therefore, the DSSGapproach finds solutions optimized for number of removed parts,part order, part and part disassembly directions in minimum time.

The approach removes leaf nodes, in other valid orders, to findsolutions optimized for reorientations. Time complexity for search-ing a DSSG, by directions stored in the DSSG, is O(nd � np

2). Mini-mum time complexity for removing all nodes from a DG isO(nd � np

2). Therefore, the DSSG approach finds solutions optimizedfor reorientations in minimum time.

7. Overall time complexity

The DSSG approach is an optimal approach. The approach cre-ates a DG in minimum time. The approach creates a minimum-sizemultiple-target DSSG in minimum time. The approach finds solu-tions optimized for number of parts, part order, and part disassem-bly directions, in minimum time. The approach finds solutionsoptimized for reorientations, in minimum time.

Tables 1 and 2 compare the DSSG approach for general 3Dstructures (DSSG) to the DSSG approach for simple stacked struc-tures (DSSG-S), enumeration with a disassembly graph (DG),Smith’s method [8], enumeration with a disassembly constraintgraph (DCG), searching a DCG, wave propagation [12], and Garcia’smethod [11].

Table 1 shows time complexities. Table 2 shows time complex-ities for Fig. 1, with nd = 6, nt = 3, nb = 13, np = 19, in number ofoperations � 1 ls. In Table 1, nb,t = max(nb,nt). In Tables 1 and 2,blank cells indicate that an approach does not use the given step.Cells with a ⁄ indicate that an approach describes the given step,but does not report time complexity for the step.

Table 1 shows that the DSSG approach is the only optimal ap-proach. Table 1 shows that the DSSG approach finds solutions opti-mized for number of parts, part order, part disassembly directions,and reorientations in O(nd,t � np

2), minimum time. Table 2 showsthat the DSSG approach finds high quality solutions in practicaltime.

Table 1 shows that the DSSG approach is faster than the wavepropagation approach. Table 1 shows that the DSSG-S approachis faster than Garcia’s method. The DSSG approach also improvessolution quality, compared to both approaches. The wave propaga-tion approach and Garcia’s method may produce unrealistic, infea-sible solutions.

The DSSG approach uses rules to find solutions optimized fornumber of parts, part order, and part disassembly directions, inzero time. The DSSG approach uses rules, GAs, or other graphsearching techniques to optimize solutions for reorientations, inO(nd � np

2) time. Rules can find solutions within the limit. GA runtimes may be greater than the limit.

8. A GA method for searching DSSGs

This study uses a GA method to find solutions optimized forreorientations. The study uses the GA to find optimized solutionsfor Fig. 1 and two case studies. The GA creates an initial population,

Table 1Time complexities for methods, paths.

Method Create DG Create DCG Create DSSG o

Enumeration DG O(nd � np2)

Smith’s method [8] O(nd � np2)

Enumeration DCG O(nd � np2) O(nd � np

2)Search DCG O(nd � np

2) O(nd � np2) O(nb,t � np

3)Wave propagation [12] O(nd � np

2) O(nd � np2) ⁄

Garcia’s method [11] O(nd � np2) O(nd � np

2) O(nb,t � np � log(DSSG approach O(nd � np

2) O(nt � np2)

DSSG-S approach O(nd � np2) O(nt � np)

finds feasible solutions in the initial population, finds the best solu-tions, modifies the best solutions, and repeats the process.

8.1. Create an initial population

The GA creates an initial population by randomly selecting partsfrom a DSSG. For Fig. 5, the GA created disassembly sequenceS1 = (f4 f7 f8 5 9 7 f5 f9 4 f6).

8.2. Find feasible solutions

The GA finds feasible solutions by removing parts, in order,from the DSSG. The approach represents a DSSG, in matrix form,as a constraint level (CL) matrix. Each row in the CL matrix rep-resents a part in the DSSG. Each row element CLi contains linksto the part’s constraint-level parts. Parts with ‘0’ elements can beremoved.

CL ¼

CL4

CL5

CL7

CL9

CLf4

CLf5

CLf6

CLf7

CLf8

CLf9

26666666666666666664

37777777777777777775

¼

f5; f6; f7

f7; f8

4; f4; f9

4; f9

000005

26666666666666666664

37777777777777777775

!

f5; f6

04; f9

4; f9

000005

26666666666666666664

37777777777777777775

!

f5; f6

04; f9

4; f9

000000

26666666666666666664

37777777777777777775

For the DSSG in Fig. 5, S1 = (f4 f7 f8 5 9 7 f5 f9 4 f6) is not fea-sible. Fasteners f4, f7, and f8 can be removed. After removing f4,f7, and f8, component 5 can be removed. After removing compo-nent 5, component 9 cannot be removed, because CL9 – ‘0’. Bythe same process, disassembly sequence S2 = (f6 f7 f8 5 f5 f4 4 f9

7 9) is feasible.

8.3. Find the best solutions

The GA finds the best solutions by removing parts, in order,from the CL, CC, MC, and MF matrices, choosing disassembly direc-tions, and calculating the fitness of each feasible solution. The GAprocess chooses feasible part disassembly directions from the DGmodel.

For each c in a feasible solution, there is at least one CCc,j [MCc,j = ‘0’. For each fi in a feasible solution, MFi,j = ‘0’. For S2 = (f6 f7

f8 5 f5 f4 4 f9 7 9), after removing f6, f7, and f8, CC5 [ MC5 = [4 0 01, f8, f9]. Component 5 can be disassembled in the �x or the +ydirection.

A reorientation is needed if d_dir(p0) – d_dir(p), for p removedbefore p0. For S2, f6 and f7 can be disassembled in the +x direction.Fastener f8 can only be disassembled in the +y direction. A reorien-tation is needed to remove f8. Overall, four reorientations areneeded for S2.

r partial DCG Optimize number of parts Optimize reorientations

O((nd � np)!) O((nd � np)!)Oðnt � ðnd � npÞnp Þ Oðnt � ðnd � npÞnp ÞO(np!)⁄

Oð2nt � n2pÞ

np)) O(np2)

O(nd � np2)

O(nd � np2)

Table 2Time complexities for methods, (number of operations � 1 ls).

Method Create DG Create DCG Create DSSG or partial DCG Optimize number of parts Optimize reorientations

Enumeration DG 2 ms 10173 years 10173 yearsSmith’s method [8] 2 ms 1026 years 1026 yearsEnumeration DCG 2 ms 2 ms 4000 yearsSearch DCG 2 ms 2 ms 89 ms ⁄

Wave propagation [12] 2 ms 2 ms ⁄ 3 msGarcia’s method [11] 2 ms 2 ms 1 ms 0.4 msDSSG approach 2 ms 1 ms 0 ms 2 msDSSG-S approach 2 ms 0.06 ms 0 ms 2 ms

314 S. Smith et al. / Advanced Engineering Informatics 26 (2012) 306–316

The GA uses a fitness function Ft = 1/(1 + R), to calculate the fit-ness of each feasible solution R = (reorientations, in degrees/90), tocalculate the fitness of each feasible solution. Fitness varies from 0to 1. For S2, number of reorientations = 4, R = 540/90 = 6, and Ft = 1/7 = 0.143. The GA uses genetic operators to randomly modify thebest solutions.

8.4. Repeating the process

The process repeats for a maximum number of generations(iterations), or until average fitness stops improving. For Fig. 1,the GA ran until the process found an optimized solution S3 =(f4 f5 f6 f7 4 f8 5 f9 7 9), with R = 3 and Ft = 1/4 = 0.25.

The GA reduced R (reorientations, in degrees) by 50%. S3 con-tains the same number of removed parts as S2. However, S3 has adifferent part order, may use different disassembly directions,and requires fewer reorientations (in degrees).

9. Case studies

To demonstrate using a GA to find solutions optimized for reori-entations, the study also completed two case studies: a 19-partdrive assembly and a 36-part gear reducer assembly.

9.1. Drive assembly

Fig. 7 shows a 19-part drive assembly, from [28]. Fig. 8 shows amultiple-target DSSG for components 3 and 6.

The approach set GA population size to 20, crossover rate to70%, mutation rate to 10%, reproduction rate to 20%, andmaximum number of generations to 50. Average R in the initialpopulation was 8.25. After 12 generations, the GA found a solution

f12

2

f9 f10

3

1

f11

f7

f8

y z

x

Fig. 7. Drive ass

S1 = (f7 f8 f3 f4 5 2 f9 f1 f2 4 3 f5 f6 6), with R = 3. The GA reducedR by 63.6%.

9.2. Gear reducer assembly

Fig. 9 shows a 36-part gear reducer assembly, from [12]. In [12],the wave propagation approach was used to remove targetcomponents 5 and 7. The approach found solutions optimized fornumber of removed components. The approach did not find solu-tions optimized for part order, part disassembly directions or reori-entations. The approach did not consider motion or fastenerconstraints. The approach found two solutions S1 = (1 2 3 4 5 6 7)and S2 = (11 10 9 8 7 6 5).

Smith et al. [8] completed a case study for the same structure.The approach found solutions optimized for number of parts, partorder, part disassembly directions, and reorientations. The ap-proach also considered motion and fastener constraints. However,run time was relatively high. Users also had to choose part orderfor target components. The approach found one solution S3 = (f1

f2 f3 1 2 3 4 5 6 7).In this study, the DSSG approach was used to remove compo-

nents 5, 7, 18, and 21. The study added components 18 and 21, be-cause they cannot be disassembled in the same direction ascomponents 5 and 7. Fig. 10 shows the disjoint DSSG for compo-nents 5, 7, 18, and 21.

The approach set GA population size to 20, crossover rate to70%, mutation rate to 10%, reproduction rate to 20%, and maximumnumber of GA generations to 100. Average R in the initial popula-tion was 9. The DSSG approach found solutions optimized for num-ber of parts, part order, part disassembly directions, andreorientations. The approach also considered motion and fastenerconstraints. The GA found a solution S4 = (f1 f2 f3 1 2 3 4 5 6 7 f8

f9 23 22 21 20 15 16 17 18), with R = 1. The GA reduced R by 88.9%.

f2

f13

f5

5

f4

f3

6

4

f6 f1

embly [28].

f7 f8 f3

2 4

6

f4

f5 f6

3

f9 nt = 2

nc = 5

nf = 9

np = 14

f1 5 f2

Fig. 8. Multiple-target DSSG for components 3 and 6.

f6 f7

22

f1 f2

2

3

f3

20

15

17

16

4

5

7

6

1 23

21 nt = 4

nc = 15

nf = 5

np = 20

S. Smith et al. / Advanced Engineering Informatics 26 (2012) 306–316 315

S4 corresponds to the wave propagation solution S1 = (1 2 3 4 56 7) and Smith et al.’s solution S3 = (f1 f2 f3 1 2 3 4 5 6 7), for remov-ing target components 5 and 7. The DSSG approach eliminatedsolutions corresponding to the wave propagation solutionS2 = (1110 9 8 7 6 5), because they require removing four fasteners,f4–f7, rather than three fasteners, f1–f3.

18

Fig. 10. Multiple-target DSSG for components 5, 7, 18, and 21.

Table 3Directions and parts for case studies.

Case study nd nb nt nc nf np

Fig. 7 6 9 2 6 13 19Fig. 9 6 17 4 23 13 36

9.3. Time complexities for the case studies

Table 3 shows number of disassembly directions and number ofparts for the case studies. Table 4 shows time complexities for thecase studies, in (number of operations � 1 ls).

The results show that the DSSG approach can find high quality,practical, realistic, physically feasible multiple-target selective dis-assembly sequence solutions, for general 3D structures. The resultsshow that the DSSG model represents a solution that is optimizedfor number of parts, part order, and part disassembly directions.The results show that a DSSG can be searched to find solutions thatare optimized for reorientations.

The DSSG approach reduces model complexity and searchingtime, compared to Smith et al.’s approach [8]. The DSSG approachimproves solution quality, model complexity, and searching time,compared to the wave propagation approach. The DSSG approachcan find solutions for general 3D structures. The DSSG-S approachis also faster than Garcia’s method.

10. Design rules

Study results show that disassembly planning can be used toimprove product designs. Study results also show that product de-sign impacts disassembly planning solution quality, model com-plexity, and searching time. The results were used to developeight new design rules for green product design:

23

1420

1321

119 1

22

10

8 7f5

f6

f7

f4

f8

f9

Fig. 9. Gear reducer

DR1: Design for easy disassemblyDR2: Design for single-translation motionsDR3: Design boundary components that can be removed easilyDR4: Design boundary components that can be removed in the

same direction as targetsDR5: Place target components close to boundary componentsDR6: Place multiple targets close to each other in the structureDR7: Design to remove all targets in the same directionDR8: Design to access and remove components and fasteners from

a single direction

The design rules can be used to make products that are easier tobuild and easier to disassemble. The design rules can also be used

12

6

5

5

43

2 1

1618

19f10

f11

f12

f13

f3

f1

f2

17

assembly [16].

Table 4Time complexities for case studies, (number of operations 1 lsec)

Case Study Method DG DCG PDCG DSSG Optimize np Optimize R

Fig. 8 DSSG 2 msec 0.7 msec 0 msec 2 msecFig. 10 DSSG 8 msec 5.0 msec 0 msec 8 msecFig. 10 Wave 8 msec 8 msec ⁄ 170 secFig. 10 DCG 8 msec 8 msec 793 msec ⁄

Fig. 10 Smith’s 8 msec 1071 years 1071 years

316 S. Smith et al. / Advanced Engineering Informatics 26 (2012) 306–316

to improve disassembly planning solution quality, reduce modelcomplexity, and reduce searching time.

11. Conclusions

Modern green products must be easy to disassemble. Duringtheir life cycle, specific parts must be selectively disassembledfor repair, reuse, recycling, or remanufacturing. Prior studies de-scribe methods for removing multiple targets from a product.However, solution quality, model complexity, and searching timehave not been considered thoroughly.

The goal of this study is to improve solution quality, minimizemodel complexity, and reduce searching time. To achieve the goal,this study introduces a new disassembly sequence structure graph(DSSG) model for multiple-target selective disassembly sequenceplanning, an approach for creating DSSGs, and methods for search-ing DSSGs.

The DSSG model contains a minimum set of parts that must beremoved to remove target parts, and the best directions for remov-ing each part. The approach uses expert rules to choose parts, partorder, and part disassembly directions, based upon physical con-straints. The searching methods use expert rules to remove allparts, in order, from the DSSG.

The DSSG approach is an optimal approach. The approach findshigh quality, practical, realistic, physically feasible solutions. Theapproach creates a high quality minimum-size model, in O(nd � np

2)time, minimum time for nd directions and np parts. The approachfinds solutions, in O(max(nt,nd) � np

2) time, minimum time for nt

targets, nd directions, and np parts.The solutions are optimized for number of parts, part order, part

disassembly directions, and reorientations. The solutions removeparts in practical order. The solutions remove parts with realisticpart motions. The solutions consider contact, motion, and fastenerconstraints. The solutions remove obstructed parts in sub-assemblies.

The study also presents eight new design rules for green prod-uct design. The DSSG approach and design rules can be used to cre-ate products that are easier to build, easier to use, and easier todisassemble. The study results can be used to improve the productdesign process, increase product life-cycle value, and reduce prod-uct environmental impact.

Acknowledgement

The Taiwan National Science Council provided support (NSC 97-2221-E-002-158-MY2).

References

[1] S. Behdad, M. Kwak, H. Kim, D. Thurston, Simultaneous selective disassemblyand end-of-life decision making for multiple products that share disassemblyoperations, J. Mech. Des. 132 (4) (2010) 041002.

[2] J. Xu, Research on recycling economy oriented product disassembly sequenceplanning approach, Int. Conf. Manage. Sci. Ind. Eng. MSIE 2 (2011) 1112–1116.

[3] T. Dong, L. Zhang, R. Tong, J. Dong, A hierarchical approach to disassemblysequence planning for mechanical product, Int. J. Adv. Manuf. Technol. 30 (5–6) (2006) 507–520.

[4] R. Wilson, J. Latombe, Geometric reasoning about assembly, Artif. Intell. 71 (2)(1994) 371–396.

[5] H. Srinivasan, R. Gadh, Complexity reduction in geometric selectivedisassembly using the wave propagation algorithms, in: IEEE Int. Conf. onRobotics and Automation, Leuven, Belgium, 1998, pp. 1478–1483.

[6] S. Chen, Assembly Planning – A Genetic Approach, 24th ASME DesignAutomation Conf., Atlanta (1998) Paper No. DETC98/DAC-5798.

[7] S. Smith, G. Smith, Automatic stable assembly sequence generation andevaluation, J. Manuf. Syst. 20 (4) (2001) 225–235.

[8] S. Smith, W. Chen, Rule-based recursive selective disassembly sequenceplanning for green design, Adv. Eng. Inform. 25 (1) (2011) 77–87.

[9] C. Pan, S. Smith, G. Smith, Determining interference between parts in CAD STEPfiles for automatic assembly planning, J. Comput. Inf. Sci. Eng. 5 (1) (2005) 56–62.

[10] C. Pan, S. Smith, G. Smith, Automatic assembly sequence planning from STEPCAD files, Int. J. Comput. Integr. Manuf. 19 (8) (2006) 775–783.

[11] M. García, A. Larré, B. López, A. Oller, Reducing the complexity of geometricselective disassembly, in: Proc. of the 2000 IEEE/RSJ Int. Conf. on IntelligentRobots and Systems, Japan Takamatsu, 2000, pp. 1474–1479.

[12] H. Srinivasan, R. Gadh, Efficient geometric disassembly of multiplecomponents from an assembly using wave propagation, J. Mech. Des. 122(2000) 179–184.

[13] S. Min, X. Zhu, X. Zhu, Mechanical product disassembly and/or graphconstruction, Int. Conf. on Meas. Tech. Mechatron. Automation 2 (2010)(2010) 627–631.

[14] S. Gupta, E. Erbis, S. McGovern, Disassembly sequencing problem: a case studyof a cell phone, Proc. of SPIE 5583 (2004) 43–52.

[15] I. Aguinaga, D. Borro, L. Matey, Parallel RRT-based path planning for selectivedisassembly planning, Int. J. Adv. Manuf. Technol. 36 (11–12) (2008) 1221–1233.

[16] M. Johnson, M. Wang, Planning product disassembly for material recoveryopportunities, Int. J. Prod. Res. 33 (11) (1995) 3119–3142.

[17] A. Lambert, Linear programming in disassembly/clustering sequencegeneration, Comput. Ind. Eng. 36 (1996) 723–738.

[18] A. Lambert, Optimal disassembly sequence generation for combined materialrecycling and part use, in: Proc. of the 1999 IEEE Int. Symposium on Assemblyand Task Planning, Porto, Portugal, 1999, pp. 146–151.

[19] R. Rai, V. Rai, M. Tiwari, V. Allada, Disassembly sequence generation: a Petri netbased heuristic approach, Int. J. Prod. Res. 40 (13) (2002) 3193–3198.

[20] J. Wang, J. Liu, S. Li, Y. Zhong, Intelligent selective disassembly using the antcolony algorithm, AIEDAM 17 (4) (2003) 325–333.

[21] X. Fang, Q. Hua, Z. Feng, Disassembly sequence planning based on ant colonyoptimization algorithm, Proc. IEEE Int. Conf. Bio-Inspired Comput.: Theor.Appl., BIC-TA (2010) 1125–1129.

[22] Y. Tseng, F. Yu, F. Huang, A green decision support system for integratedassembly and disassembly sequence planning using a PSO approach, ICSOFT 2(2010) 444–449.

[23] C. Chung, Q. Peng, Evolutionary sequence planning for selective disassembly inde-manufacturing, Int. J. Comp. Integ. Manuf. 19 (3) (2006) 278–286.

[24] Y. Shimizu, K. Tsuji, M. Nomura, Optimal disassembly sequence generationusing genetic programming, Int. J. Prod. Res. 45 (18–19) (2007) 4537–4554.

[25] Y. Tseng, H. Kao, F. Huang, Integrated assembly and disassembly sequenceplanning using a GA approach, Int. J. Prod. Res. 48 (20) (2010) 5991–6013.

[26] X. Zhang, S. Zhang, Product cooperative disassembly sequence planning basedon branch and bound algorithm, Int. J. Adv. Manuf. Technol. 51 (9–12) (2010)1139–1147.

[27] S. Zhao, Y. Li, Disassembly sequence decision making for product recycling andremanufacturing systems, ISCID (2010) 44–48.

[28] G. Boothroyd, P. Dewhurst, W. Knight, Product Design for Manufacture andAssembly, Marcel Dekker, New York, 1994.

[29] G. Smith, S. Smith, Automated initial population generation for geneticassembly planning, Int. J. Comput. Integr. Manuf. 16 (3) (2003) 219–228.

Shana S. Smith is a Professor in the Department of Mechanical Engineering atNational Taiwan University. Dr. Smith’s research interests include product lifecycledesign, product assembly and disassembly planning, user-centered design, virtualreality, and engineering graphics.

Greg Smith is a research scientist. Dr. Smith’s research interests include artificialintelligence, disassembly planning, and engineering design.

Wei-Han Chen is an M.Sc. of Mechanical Engineering. Mr. Chen’s research focus isdisassembly planning.