A New U-Shaped Heuristic for Disassembly Line Balancing Problems

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1 A New U-Shaped Heuristic for Disassembly Lie Balacig Problems Shweta Avial 1, ad P. K. Mishra 2 1,2 MED, M. N. Natioal Istitute of Techology, Allahabad, Idia s: 1 shweta@mit.ac.i, 2 pm@mit.ac.i Abstract: The product recovery operatios are fully based o disassembly lie balacig. The disassembly lie is a best chaise of automated disassembly or retured product. It is very difficult to fid the optimal balace of a disassembly lie because of its N-P hard ature. I this paper a ew U-shaped heuristic is proposed to assig the parts to the disassembly wor statios uder precedece costraits ad we compared the proposed heuristically obtaied solutios with the other heuristically solutios to see that this is performig well or ot. The heuristic tries to miimize the miimum umber of worstatios while addressig the hazardous, high demad ad low disassembly cost compoets. Examples are cosiders to illustrate the methodology of the proposed heuristics. For the problem tested, we observe that the heuristic described i this paper geerated sigificatly better result. Keywords: Disassembly, Heuristic, Lie balacig, U-shape assembly lie. I. INTRODUCTION Now a day s more ad more maufacturers are begiig to recycle ad remaufacturer their post-cosumed products due to isertio of ew product, more rigid eviromet legislatio, icreased public awareess ad exteded maufacturer resposibility. I additio, the ecoomic attractiveess of reusig product, subassemblies or parts istead of disposig of them has further fueled this effort. Recyclig is a process performed to retrieve the material cotets of used ad o-fuctioig products. Remaufacturig, o the other had, is also a idustrial process i which warm-out products are restored to lie-ew product s coditios. Thus, remaufacturig provides the quality stadards of ew product with used parts [18]. I order to miimize the amout of waste set to ladfills, product recovery sees to obtai materials ad compoet from old or outdated products through recyclig ad remaufacturig this icludes the reuse of compoets ad products. There are may attributes of a product that ehace product recovery; examples iclude: ease of disassembly, modularity, type ad compatibility of materials used, material idetificatio marigs, ad efficiet crossidustrial reuse of commo parts/materials. The first crucial step of product recovery is disassembly [14]. Ed-of life processig of complex products such as electroic product is becomig icreasigly importat, because they cotai a large variety of hazardous, useful as well as valuable compoets ad materials. Disassembly is ofte used to separate such compoets ad materials. A disassembly precedece graph (DPG) is frequetly used to describe a disassembly process. Box i this graph refer to operatios, typically the detachmets of compoets. Arcs represet the precedece relatioships. Both yield ad costs are associated with every operatio [19]. Disassembly is defied as the methodical extractio of valuable parts/subassemblies ad materials from discarded products through a series of operatios. After disassembly, reusable parts/subassemblies are cleaed, refurbished, tested ad directed to ivetory for remaufacturig operatios. The recyclable materials ca be sold to raw-material suppliers, while the residuals are set to ladfills [14]. Recetly, disassembly has gaied a great deal of attetio i the literature due to its role i product recovery. A disassembly system faces may uique challeges; for example, it has sigificat ivetory problems because of the disparity betwee the demads for certai parts or subassemblies ad their yield from disassembly. The flow process is also differet. As opposed to the ormal coverget flow i regular assembly eviromet, i disassembly the flow process is diverget (a sigle product is broe dow ito may subassemblies ad parts). There is also a high degree of ucertaity i the structure ad the quality of the retured product. The coditios of the products received are usually uow ad the reliability of the compoets is suspects. Some parts of the product may cause pollutio or may be hazardous. These parts ted to have a higher chace of beig damaged ad hece may require 21

2 special hadlig, which ca also ifluece the utilizatio of the disassembly worstatios. For example, a automobile slated for disassembly cotets a variety of parts that are dagerous to remove ad/or preset a hazard to the eviromet such as the battery, airbags, fuel ad oil. Various demaded sources may also lead to complicatios i disassembly lie balacig. The reusability of parts creates a demad for these parts, however, the demads ad availability of the reusable parts is sigificatly less predictable tha what is foud i the assembly process. Fially, disassembly lie balacig is critical i miimizig the use of valuable recourses (such as time ad moey) ivested i disassembly ad maximizig the level of automatio of the disassembly ad the quality of the parts (or material) removed [18]. I this paper a aalysis of U-shaped disassembly lie has bee carried out usig proposed heuristic. I sectio II, the relevat literature has reviewed, while sectio III depicts precise descriptio of the U-shaped ad traditioal straight-lie layout. I sectio IV, disassembly lie balacig problems has bee described ad i sectio V, the proposed heuristic has bee described ad i sectio VI a practical example ad computatioal results have bee show while the coclusio i sectio VII. II. LITERATURE REVIEW Product recovery ivolves a umber of steps [1]. The first crucial step is disassembly. Disassembly is a methodical extractio of valuable parts/subassemblies ad materials from post-used products through a series of operatios [2] [3]. After disassembly, re-usable parts/subassemblies are cleaed, refurbished, tested ad directed to the part/subassembly ivetory for remaufacturig operatios. The recyclable materials ca be sold to raw-material suppliers ad the residuals are disposed of [14]. The basic disassembly lie balacig problem (DLBP) ca be stated as the assigmet of disassembly tass to worstatios such that all the disassembly precedece relatios are satisfied ad some measure of effectiveess is optimized. Gugor ad Gupta preseted the first itroductio to the disassembly lie-balacig problem [4-6] ad developed a algorithm for solvig the DLBP i the presece of failures with the goal of assigig tass to worstatios i a way that probabilistically miimizes the cost of defective parts [7]. Tag et al. developed a algorithm to facilitate disassembly lie desig ad optimizatio []. McGover et al. first applied combiatorial optimizatio techiques to the DLBP [9], [14]. Gugor ad Gupta [11, 12] described the DLBP ad developed a heuristic algorithm for solvig the DLBP with the goal of miimizig the cost of defective parts [20]. McGover & Gupta [18] preseted a disassembly solutio ad that was foud first by greedy modal the improvig the solutio with the help of 2-opt heuristic. Gupta ad Lambert [3] provide a heuristically solutio for the disassembly lie balacig problems that icorporatig sequecig depedet part removal costs. McGover et al. [13] first proposed applyig combiatorial optimizatio techiques to the DLBP. Later, various combiatorial optimizatio techiques to solve DLBP were compared by McGover ad Gupta [14]. The fact that eve a simple disassembly lie balacig problem is NPcomplete was prove i literature [15], ad a geetic algorithm was preseted for obtaiig optimal solutios for DLBP. Ray et. al. [16] proposed a dyamic disassembly lie balacig algorithm that aims at smoothig the load of the shop floor. I order to solve the profit-orieted DLBP, Altei et. al. [17] developed the first mixed iteger programmig algorithm for the DLBP [20]. Dig et.al. [20] Proposed a multi objective disassembly lie balacig problem ad the solve this by a at coloy algorithm. The beefits of the U-lie as compared to a straight lie iclude reductio i the wasted movemet of operator, wor-i-process ivetory, ad improved productivity, easier implemetatio of zero-defects comparig, higher flexibility i worforce plaig i the face of chagig demad, ad improvemet i material hadlig. Several authors have provided a explaatio of U-shaped productio lies ad the way they operate, as well as the beefits realized by their implemetatio [15]. So a lot of research o U-shaped assembly lie balacig has bee doe but o research is available o U-shaped disassembly lie balacig. III. U-SHAPED AND TRADITIONAL STRAIGHT-LINE LAYOUT The traditioal straight lie layout allows to orgaize the tass sequetially i oe directio to form statios. A U-lie, however, permits tass located o both side of the lie to form statios. Fig. 1 (a, b) illustrate the fudametal differece betwee the straight lie ad U-lie layouts. Whe usig a straight lie layout, operator performs oe or more tass o a cotiuous portio of the lie. Whe usig a U-shaped layout, operators are allowed to wor across both legs of the lie, while partially assembled uits follow the U-shaped 22

3 cofiguratio. By allowig operators to wor across both legs of the lie, the U-shaped layout i fig. 1 requires fewer worstatios the the comparable straight lie layout [24]. The U-lie balacig problem is to assig tass to statios arraged i a U-shaped productio lie [13]. The U-shaped assembly lie balacig problem may be defie as: assigig all the tass o the U-lie to form a miimal umber of wor statios while the wor cotets i each statio should ot be greater tha the give cycle time. 6. Each part is assiged to oe ad oly oe worstatio, 7. The sum of the part removal times of all the parts those are assiged to a worstatio must ot exceed CT. 8. The precedece relatioships amog the parts must ot be violated. 9. Ay part ca be assig to ay worstatio. The mai objective of the wor is to Miimizig the sum of the worstatio idle times, which will also miimize the total umber of worstatios. This objective is represeted as: Fig 1.a. Traditioal straight assembly lie layout Miimize NWS Z CT WS j 1 j 2 Fig 1.b. U-shaped assembly lie layout Notatios: J = 1,2,3,4 NWS = Number of Worstatios CT = Cycle Time WS = Wor Load Z = Total Idle Time K = 1,2,3, = Number of Parts to Remove PRT = Total Part Removal Time NWS = Miimum No of Worstatios mi NWS max = Maximum No of Worstatios h = Part s Hazardous or ot (0, 1) H = Part Hazardousess PS = Positio of Part i Removal Sequece D D C T = Demad of Part K = Demad of Total Parts = Part Removal Cost = Part Removal Times IV. DISASSEMBLY LINE BALANCING PROBLEM DESCRIPTION Problem assumptios iclude the followig: 1. Part removal times are determiistic, 2. Part removal times are costat, 3. Each product udergoes complete disassembly, 4. All products cotai all parts with o additios, deletios, or modificatios, 5. All the parts are assiged, The perfect lie balace, Z 0 Lie balacig sees to achieve Perfect Balace (all idle times equal to zero). Whe this is ot achievable, either lie Efficiecy (IE) or the Smoothess Idex (SI) is used as a performace evaluatio tool for disassembly lie balacig, Elsayed ad Boucher [3]. I additio, we fid: The maximum umber of worstatios ca be calculated as: NWS max The miimum umber of worstatios ca be calculated as: PRT 1 NWSmi CT A hazardous measure has developed to quatify each solutio sequece performace, with a lower calculated value beig more desirable. This measure is based upo biary variables that idicates whether the part is cosidered to cotai hazardous material (the biary variable is equal to oe if hazardous, otherwise zero) ad its positio is the sequece. A give solutio sequece hazard measure is defie as the sum of hazard biary variables multiplied by their positio i the sequece, thereby rewardig the removal of hazardous part early i the part removal sequece [18]. The positio i sequece is calculated as the umber of predecessors of the compoet or the umber of compoets which are ecessary to remove earlier to the hazardous compoet. This measure is represeted as: H h * PS 1 1, hazardous h 0, otherwise If idividual hazardous measure of a compoet is required the it ca be calculated as H h* PS A demad measure has developed to quatify each solutio sequece performace, with a lower 23

4 calculated value beig more desirable. This measure is based upo positive iteger values that idicate the quatity required of this part after it is removed (or zero if ot desired) ad its positio i the sequece. Ay give solutio sequece demad measure is defied as the sum of the demad value multiplied by their compoet s positio i the sequece. Positio i sequece is calculated as the umber of predecessors of the compoet or the umber of compoets which are ecessary to remove earlier to refer compoet, rewardig the removal of high demad parts early i the part removal sequece [18]. D d * PS 1 If idividual demad measure of a compoet is required the it ca be calculated as D d * PS V. PROPOSED HEURISTIC The heuristic is developed to achieve followig objectives: 1. Miimize the total miimum umber of disassembly wor statios to decrease total idle time, 2. Balace the disassembly lie, 3. Remove hazardous parts/compoets early i the disassembly sequece, 4. Remove high demad compoets before low demad compoets, 5. Remove low disassembly cost compoets before high disassembly cost compoets, 6. Remove the parts which have large part removal time before the parts which have small part removal time ad 7. Assig same type of parts at same worstatios (e.g. hazardous compoet at same wor statios, high demad compoet at same worstatios). The proposed heuristic is a U-shaped heuristic where the parts are assiged to the worstatios which are arraged i U-shaped. The product comes from oe directio to disassemble ad the parts are removed at each worstatio. The proposed heuristic is based o some simple priority rules that are based o owledge. The first priority rule assig the parts which are hazardous, the secod rule assig the part to the worstatio, that have highest demad ad the i decreasig order, the third rule is based o pert removal cost, ad it assig the part from miimum part removal cost to high part removal cost or i icreasig order of part removal cost ad i the last the forth rule assig the part to the worstatio i order of decreasig part removal time. The priority rules o which the proposed heuristic is based are as follows: 1. Maximum part hazardous 2. High part demad 3. Low disassembly cost 4. Maximum part removal time The heuristic raig procedure is as follows: 1. Fid the hazardous parts ad ra them accordig to their decreasig order of hazardousess, 2. Fid the parts that have demad ad list them i decreasig demad order, 3. List the parts i order of their icreasig part removal cost order, ad 4. List the parts i order of their decreasig part removal time The assig a ra to all the parts, based o above priority rules. Assig the first ra to that part that is hazardous ad have high demad, low part removal cost ad have highest part removal time i case of tie. It meas if two parts have property of same hazardous the it is a case of tie, so ow chec for their demad, if oe of them have more demad tha other oe, assig it at first ra but if the demads of both parts are same the chec for their part removal cost, if oe of them have lower cost tha other oe, assig it at first ra ad if the part removal cost is agai same ad it is agai case of tie, so chec for their part removal time ad assig them ra i order of their part removal time. After assigig ra to all parts, start the assigmet of parts to the worstatios i order of decreasig their ra ad their precedece costraits. If a tas has first ra but it caot be assiged to worstatios because of precedece costraits, the chec for ext part i the ra list ad agai chec for assigmet. If tas is eligible for assigmet but the time available at the curret worstatio is ot eough the chec ext assigable tas ad o if part ca be assig o curret worstatios, start a ew worstatio with full of cycle time ad repeat the same till all parts get assiged to worstatios. VI. COMPUTATIONAL EXAMPLE The developed algorithm has bee ivestigated o a variety of test cases to cofirm its performace ad to optimize parameters. The proposed U- shaped heuristic has bee used to provide a solutio to the disassembly lie balacig problem based o the disassembly sequecig problem preseted by Kogar ad Gupta [25] where the objective is to completely disassemble a give product (see Figure 1) cosistig of = compoets ad several precedece relatioships (e.g., parts 5 ad 6 eed to be removed prior to part 24

5 7). The problem ad its data were modified with a disassembly lie operatig at a speed which allows CT = 40 secods for each worstatio to perform its required disassembly tass. This provided a applicatio to a previously explored disassembly problem. This practical ad relevat example cosists of the data for the disassembly of a product as show i Table 1. It cosists of te subassemblies with part removal times of T = {14,, 12, 18, 23, 16, 20, 36, 14, }, hazardousess as h = {0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, part demad d = {0, 500, 0, 0, 0, 750, 295, 0, 360, 0}, ad part removal cost as C = {27, 63, 48, 62, 24,18, 83,77, 93, }, The disassembly lie is operated at a speed that allows 40 secods for each worstatio [18]. Fig. 2: example of product precedece relatioships Table 1: Kowledge based of the example from literature Part Time Hazardous Demad Cost After applyig proposed heuristic a raig is provide to all the tass ad the assig them accordig to their ra from higher to lower order ad accordig to their precedece costraits. The fial raig of the parts removal is as follows: Table 2. Raig of tass Ta s No Ra I this list the part umber 7 is raed first because it has hazardous property ad it also have some demad, after this part umber 6 is assiged at ra 2 cause of it has o hazardous property but it have maximum demad over demad of all the parts. The part umber 2 is assiged at ra 3 ad part umber 9 at ra 4, because of part umber 2 have much more demad ad it require miimum 8 removed parts to remove it ad part umber 9 do ot require ay removed part to remove it. Part umber ad 5 are also assiged at ra 5 ad 6, these tass do ot have hazardous property ad demad also, so here, there part removal cost is cosider as decisio variable ad accordig to their part removal cost they are assiged raig. This process is also repeated for the part umber 1,3,4,8 ad they got assig their respective ra. After assigig ra to all the parts to remove, the assigmet of part to the worstatios is started. Start first worstatio with the cycle time as CT=40, ad chec the ra list for the assigmet of parts to the worstatios that are arraged i U-shaped. Tas umber 7 hast first ra i the list but it caot be assig to the worstatio because of its precedece costraits, so move to ext oe ad the ext part i.e. part umber 6, ad it ca be assig to the wor statio. After this, agai chec the list from startig ad the part umber 7 is agai ot assigable, so move to ext oe. The ext part is part umber 2 ad it ca be assig to same worstatio, ad the ext part that is part umber 9, ca also be assig to the same worstatio. Now first worstatio has bee completed because it has o idle time so o more parts ca be assig o this worstatio, so start a ew worstatio with CT=40, ad start the assigmet procedure agai. For this ew worstatio, chec the ra list from start, ad tas umber 7 is agai ot assigable, so agai move to ext part ad assig part umber 5, ad agai chec the ra list because of same part umber 7 caot be assig so assig the part umber 1 at secod worstatio. The idle time left o secod worstatio is 3 secods ad o tas ca be assig i this worstatios, so agai start a ew worstatio with CT=40, ad repeat the procedure of parts assigmets. Now at this third worstatio, part umber 7 is assiged which was ot earlier assiged because of its precedece relatios, ad the chec for the ext ot assiged 25

6 parts i the ra list, ad assiged the part umber at the same worstatio. Now the idle time of third worstatio is secods ad o part i the list ca be assiged o this worstatio, start a ew forth worstatio with CT=40 sec, ad agai chec for assigmet ad assig the part umber 4 & 3 at this worstatio ad idle time left at forth worstatio is sec, here o tas ca be assig o forth worstatio, so start a ew oe with CT=40, ad assig the last part i.e. part umber 8 at fifth worstatio ad the remaiig idle time o this worstatio is 4 sec ad there is o more tas available i the ra list to be assig, so the procedure of assigmet of parts o the worstatios is ow completed ad the assigmet of parts to the wor statio has show i Fig. 3. Fig. 3: Assigmet of parts o the worstatios Table 3: Solutio by Proposed Heuristic W/S No. Part assiged Part removal time Idle time The problem solved by proposed heuristic is also solved by 2-opt heuristic by Mc.Gover & Gupta. The compariso of results of this problem, with result of Mc.Gover & Gupta is give as: Table 4: Compariso of Solutios S. No. Bases Mc.Gover & Gupta Proposed 1. Number of Worstatio Five Five s 2. Cycle Time 40 Secods 40secods 3. Lie Efficiecy 73% 73% Worstatio s Efficiecy Heuristic Based o % 2. 85% 3. 80% 4. 90% 5. 80% 1. Hazardous Part 2. Part Demad 3. Part Removal 1. 0% % 3. 75% 4. 75% 5. 90% 1. Hazardous Part 2. Part Demad 3. Part Removal Cost 4. Part Removal Time Time 1. Miimize The No. of 1. Miimize Worstatios The No. of 2. Balace The Worstatio Lie s 3. 3.Remove 2. Balace Hazardous Part The Lie First 1. 3.Remove 4. Remove High Hazardous Demad Parts 6. Objectives Part First Before Low 3. Remove Demad Parts High 5. Remove Same Demad Parts At Same Parts Before Worstatio Low (Hazardous Demad Part At Same, Parts High Demad Parts At Same Worstatio) 7. Lie Type Straight Lie U-Shaped Lie VII. CONCLUSION A efficiet, ear optimal, multi objective heuristic is preseted for U-shaped determiistic disassembly lie balacig. The proposed heuristic is able to achieve all of the objectives ad provide a efficiet solutio with miimum umber of worstatios. It disassemble all high demads parts at the same worstatio the try to remove hazardous part at the same worstatios the assig the part to the worstatios with respect to their miimum part disassembly costs ad the accordig to their part removal time. The comparisos shows that the proposed heuristic performs better the the heuristic provided by M. McGover ad Gupta while achievig oe more objective i.e. assig the same parts at same worstatios (high demaded parts at same ad hazardous parts at same worstatios). It is because of its U-shape ad arragemet of its priority rules. The U-shape of the lie allows the assigmet of parts o both sides of the lie. If we compare this U-shaped lie to straight lie the, i U-shaped, parts are assiged from both directios ad it ca be see that tas o 8 that is assiged at fifth worstatio caot be possible at straight lie because of precedece resectios ad it ca oly possible i U-shaped lie. So because of U-shaped ad arragemet of priority rules the proposed heuristic performs better ad provides optimal/ear optimal sigificat solutios. This proposed heuristic provides a additioal advatage i.e. the worers are allowed to move to ay worstatios, so that they ca wor freely. REFERENCES [1] A. Gugor, ad S. M. Gupta, Issues i Evirometally Coscious Maufacturig ad Product Recovery: A Survey, Computers ad Idustrial Egieerig, Vol. 36, No. 4, pp ,

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