Proceedings of the 7th Asia Pacific Industrial Engineering and Management Systems Conference 2006 17-20 December 2006, Bangkok, Thailand

________________________________________

† : Corresponding Author

Genetic Algorithm Implementation for Solving Nesting Problem in Garment Industry

Bagus Arthaya† and Thedy Yogasara Parahyangan Catholic University, Bandung - 40141, INDONESIA

+62-22-2032700, Email: {bagusart, thedy}@home.unpar.ac.id

Soesilowati Alumni of Industrial Engineering Department Parahyangan Catholic University, Bandung

Jl. Wahidin 13, Rembang Jawa-Tengah, INDONESIA

Abstract. In order to quickly respond the fluctuating market demand, a company has to provide itself with an appropriate tool that leads to simplification of raw material supply, route of manufacturing process, high utilization of raw material, simple tooling system and so on. Garment industry includes manufacturing processes dealing with cutting a ply of long raw cloth according to the pattern defined in advanced. This kind of industry faces a lot of material preparation operations. The quantity of raw material to be prepared should be based on the variation of demand and combination of sizes. Order quantity for every size (i.e.: S, M, L or XL) in fact might never be the same and it is relatively unpredictable. Knowing the quantity of every size, placement of patterns on one ply of clothes is not a simple job. The objective is to minimize the waste (unused material) after nesting or placement of pattern is performed. This research focuses on developing an algorithm or technique for solving the nesting problem. As there are a number of pattern combinations to be placed on cloth’s ply, then Genetic Algorithm is formulated to find the best nesting and minimum waste of material. Solution offered by this technique is that roughly between 7 to 20% of waste is still produced. On the other hand, exact and appropriate pattern position on a ply of clothes is automatically determined. This feature leads to a simplified process in the next cutting operation. A case study has been performed on a local T-shirt factory in Bandung. The type of T-shirt is limited only for a plain type clothes and for T-shirt type without pocket and collar. Examples of pattern placement show the effectiveness of this algorithm. Keywords: genetic algorithm, nesting, pattern, ply, waste of materials.

1. INTRODUCTION

In the global market competition, a company has

always to speed up their processes and to improve its performance as well. There are many ways to do it, for instance by implementing the latest technology, eliminating unnecessary processes, decreasing operational costs or by reducing cost of materials. Competitive price of a product can be achieved by reducing the material’s cost. This can be done e.g. by minimizing the waste of raw material.

Garment industry is a good example area to explore how this idea can be implemented. In this business, market demand and combination of sizes are mostly unpredictable.

In a T-shirt fabrication, the order quantity for every size (i.e.: S, M, L or XL) in fact might never be the same. Knowing the quantity of every size, placement of patterns on one ply of clothes is not a simple job. The objective is to minimize the waste (unused material) while nesting or placement of patterns is being executed.

In the garment industry, the process starts with cut order planning which plan all cutting related activities. Afterward, order proceeds to marker making stage. This stage relates to pattern layout planning on a spread of cloth material. Optimal layout can yield an effective usage of raw material and turn into low operating cost.

The main focus of this research is to find the easiest

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Table 1: Possible combination of T-shirt sizes.

Size Combination Number of similar size in one section (j) No. Type 1 2 3 4 5 6 1 S 1S 2S 3S 4S 5S 6S 2 M 1M 2M 3M 4M 5M 6M 3 L 1L 2L 3L 4L 5L 6L 4 SM 1S 1M 2S 2M 3S 3M 4S 4M 5S 5M 6S 6M 5 SL 1S 1L 2S 2L 3S 3L 4S 4L 5S 5L 6S 6L 6 ML 1M 1L 2M 2L 3M 3L 4M 4L 5M 5L 6M 6L 7 SML 1S 1M 1L 2S 2M 2L 3S 3M 3L 4S 4M 4L 5S 5M 5L 6S 6M 6L

and fastest solution how to layout the patterns and to minimize the waste of material at once. After screening a lot of possibilities, genetic algorithm (GA) is chosen to solve this problem, as this technique promises a good heuristic solution. Some cases show the behavior of the algorithm and the features promised by this technique. 2. PROBLEM IDENTIFICATION

Some obvious problems that come up in this field can

be identified and stated as follows: 1. How do we determine the genetic symbols that

corresponds to all of the patterns (encoding process)?

2. How do we determine the orientation of all patterns that give the shortest length of cloth?

3. How do we define the number of ply of clothes more accurately so that it minimizes the waste of raw material?

In focusing the direction of this research, we introduce some limitations such as: the type of cloth is plain and pattern of pocket and collar are not included. 3. CUT ORDER PLANNING

This task starts from the number of demand to be cut.

The order consists of a variety of amount and sizes of T-shirt. This order number should be managed such that the cutting process can be accomplished precisely and efficiently.

Figure 1: Example of section on a long-wide cutting table.

The cutting process starts with laying the cloth material on a very long-wide table. This spread is divided into several sections. Every section consists of a combination of sizes and a certain ply height, as illustrated in Figure 1.

One specific section may consist of one or more similar size. The number of similar size in one section is tabulated in Table 1, with respect to 7 (seven) possible combination of sizes. Incoming order must be spread out into several sections that might have size combinations according to Table 1 and have different ply heights. . 4. DEVELOPMENT OF ALGORITHMS

Determining the number of section and ply height at once is not a simple job. It is an inter-related problems between the number of similar size, number of sections and layers in one ply. To solve this problem, three kinds of algorithm are developed and tested. 4.1 Algorithm for Configuring Section Group

This algorithm is used to determine the section

configuration that can minimize the waste of raw material, so it means to decrease the cost in general. This idea is realized by distributing the sizes of an order into several sections, where each section may have different size combination. An example of one T-shirt order that consists of 20 units S-size and 20 units L-size is listed in Table 2. This table shows two possible configuration that can fulfill the order. Table 2: Section group configuration for demand of 20-S

and 20-L T-shirt.

Size Combination Section Group

Section No. (i) No. Type

Unit to be Made

1 1 S 20 1 2 3 L 20

2 1 5 SL 20

Section 1 Section 2 Section 3 Length = 25 Length = 35 Length = 30 Ply = 5 Ply = 10 Ply = 15

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4.2 Genetic Algorithm (GA) This algorithm will determine the representation of the

T-shirt pattern and their possible placements. The development of algorithm is divided into three steps, i.e.:

1) Determination of the string representation, 2) Determination of the fitness function, 3) Determination of the genetic operator.

4.2.1 String Representation

The string representation is resulted from a coding

process of the T-shirt patterns (Figure 2) and is translated into a genetic string within a limited length. For each of the pattern, a specific number from 1 to 9 is assigned. These numbers that correspond to the type of pattern are listed in Table 3. Pattern of pocket is still listed and coded although it will not be included in the discussion. Each of T-shirt has two pairs type of pattern i.e. body and hands. The front and back body patterns have the same code as well as the left and right hands.

Figure 2: Example of T-shirt pattern (front and back bodies,

left and right hands and one pocket). Table 3: Pattern coding and value (number) of the gene.

Size Front body

Back body

Left hand

Right hand Pocket

S 1 1 2 2 3 M 4 4 5 5 6 L 7 7 8 8 9

Length of the string is calculated as follows: P = (jS + jM + jL) x A (1)

where P = string length, jS , jM , jL = number of similar size of S, M and L, A = number of pattern of each size, that is:

= ⎩⎨⎧

patternpocket one is thereif,5patternpocket no is thereif,4

All genes in the string have their own value in accordance with the pattern as shown in Figure 2. For p = size of {S: small, M: medium and L: large) and q = pattern of {B: body, H: hand and P: pocket), the number of gene value on one string can be calculated as follows:

Jpq = jp x gq (2) where:

Jpq = sum of gene value of size p, pattern q, jp = number of similar size of S, M and L, gq = number of pattern q for one T-shirt, that is:

= ⎩⎨⎧

othersfor ,2pocketfor ,1

For instance, a string of [2 1 1 2 3 1 2 1 3 2] represents a layout of S size combination with size similarity of 2 and the T-shirt has a pocket. Length of string is calculated from equation (1):

P = (2 + 0 +0) x 5 = 10 And number of gene value (Jpq) is calculated from equation (2) as follows: JSB = 2 x 2 = 4 (4 genes for body) JSH = 2 x 2 = 4 (4 genes for hand) JSP = 2 x 1 = 2 (2 genes for pocket) where (jS, jM, jL) = (2, 0, 0), A = 5 since pocket is included, and (gB, gH, gP) = (2, 2, 1). 4.2.2 Fitness Function

Fitness in GA is a measure of goodness of an objective

function whether it has reached a certain quality. The higher the fitness, the more probable a string to survive in their life or in the next generation. In the case of minimizing the length of layout, section with less length has a higher chance to survive (to be chosen as new candidate). The fitness is then calculated as follows:

Fitness =length

1 (3)

where: length = length of section after performing the pattern

placement algorithm.

4.2.3 Genetic Operator Genetic operator functions to generate population

from one to the next generation. The basic operators used here are:

1) Reproduction, is a process in which individual strings

left hand right hand

front bodyback body

pocket

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are reproduced (copied) according to their objective values. String with higher fitness will have higher probability of contributing one or more offspring in the next generation. Reproduction method used here is the biased roulette wheel.

2) Crossover, is the most important operator in GA to produce new strings by exchanging some information between string pairs. This is done by shuffling some genes of two string pairs on a random position. The order crossover (OX) is implemented in this case.

3) Mutation, is a process in which a structure of individual chromosome (string) converts into albino. This string shows a very much different form from its population, so this will prevent solution from being trapped in a local optima.

4.2.4 Layout Optimization of Basic Pattern

Implementation of GA for layout optimization of T-

shirt basic patterns can be summarized as follows: 1. Define the string of initial population randomly

according to the size combination and number of initial population,

2. Apply the pattern placement algorithm for determining pattern layout and total placement. Calculate the fitness of all possible layout using equation 3,

3. Randomly select the strings to be reproduced and take the new strings based on proportion of string fitness. The higher the fitness, the bigger probability of them to be reproduced,

4. Apply crossover operation in which random marriage between strings occurs and strings with variety sequences are generated,

5. Perform mutation operation to select the most possible candidate for the next generation and they are completely new.

6. Repeat step 2 to 5 until the number of generation has been reached.

4.3 Pattern Placement Algorithm

In this research, some improvements have been

introduced based on previous works done by Susanti (1999), and Martinus (1999). For instance: hand patterns can be placed in opposite direction as shown in Figure 3, or shifting patterns to left or right to expose hidden space by the previous methods.

In this algorithm, strings resulted from GA are converted into a certain layout. It is done by placing the pattern representing a gene starting from the first in a string. For example, a string of [1 7 8 8 2 2 1 7] will be placed on

a ply of cloth, then this procedure will put the first string (1 = S-back) taking the width of cloth (flat) as a consideration. Afterward, the second pattern (7 = L-front) is placed and so on until all string has been positioned. Some conventions are declared before the placement as depicted in Figure 4. This relates the variables of pattern and the x, y coordinates on the cloth. Figure 3: Example of possible hand patterns placement. Figure 4: Some convention for positioning the patterns. 4.3.1 Modified String Formation

This step aims at re-arranging the sequence of a gene

in string resulted from a GA process. A string is re-arranged starting from gene representing a body pattern, then hands and finally pocket if any. An example of initial string has a sequence as follows:

2 1 5 5 4 4 2 1

hp bp hp hp bp bp hp bp where:

hp = hand pattern, bp = body pattern,

and then the modified string becomes as follows: 1 4 4 1 5 5 2 5

body pattern hand pattern

Lpost-1 to be placed Lpost-2

flat 1

Y

X

xStart flat 2 flat 2xP

JaL2L1

xEnd flat 2

L-front (7)

Spost-1 (2)

Lpost-1 (8)

Lpost-2 (8)

width of cloth width of pattern placement L-front

heig

ht o

f pat

tern

pl

acem

ent L

-fro

nt

leng

th o

f clo

th =

hei

ght o

f pa

ttern

pla

cem

ent S

post

-1

S-back (1)

And so on

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This step will decrease the total length of cloth and reduce computation time as well as speed up the achievement of optimal solution.

4.3.2 Flat Definition

The position where to place a pattern is identified by a

horizontal line called flat. The flat is numbered when one pattern is placed onto a spread of cloth as shown in Figure 5. Placement of the next pattern must be done along the flat free of a pattern.

Variables used to define a flat are xStart and xEnd to define the start and end point position of a pattern, L-flat and T-flat define the pattern width and height, while Blocked-List shows whether there are or not a free area blocked beneath a flat. Figure 5: Flat definition according to the pattern position. 4.3.2 Hinders Initialization

A horizontal segment line that hinders a pattern

placement is called hinders. This segment becomes a hurdle when pattern height is bigger than the distance between T-flat and hinders. The existence of hinders will decrease the length of flat and as the consequence, there will be more waste of material. Example of hinders is shown in Figure 6. 4.3.3 Block Inspection

A block is an empty space that blocked unintentionally

caused by the placement of pattern (Figure 7). The block has some variables. i.e.:

1. xBlock, position in x-axes that determines the starting point where it exists,

2. L-block, shows the width of the block, 3. Fit height, shows the height of the block, 4. F-block, determines the flat where the block resides.

To utilize a block, one can just check whether the

pattern height is smaller than the fit height. If it is not the case, then find the next flat to place the coming pattern. If it is so, then the width of this block has to be match to the width of the pattern, by using the width inspection step. Figure 6: Hinders development that may reduce flat length. Figure 7: Block existence caused by pattern placement. 4.3.4 Width Inspection

Inspection is simply done by comparing width of flat

to pattern width, within a certain conditions such as:

flat 1 Y

X

xStart flat 2

flat 2

xEnd flat 2

S-front

xEnd flat 1

xStart flat 1

L-flat 2 L-flat 1

T-fla

t 1

Y

Xflat 2

S-front

L-hinders 1

T-hi

nder

s 1

L-front

flat 1

xStart hinders 1

xEnd hinders 1

hinders 1

Y

Xflat 2

S-front

L-block

fit h

eigh

t

L-front

flat 1

xBlock

S-front

L-front

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1. if the flat width is smaller than pattern width then check for any other available area or free space,

2. if not, then follow the left-side shifting of a flat procedure prior to position the pattern.

4.3.5 Available Area Inspection

Concerning the possible free space around a pattern,

there are four possible available areas, i.e.: 1. Available area just next to the right side (DAT-r), 2. Another available area in the right side (DAL-r), 3. Available area just next to the left side (DAT-l), 4. Available area just above the flat (DAT-a).

This inspection is performed to make sure whether a

certain pattern can still be placed in a flat although its width is higher than L-flat. By doing so, pattern should no be placed immediately in the lower area, but maximally utilizing the free areas around of the previous patterns.

4.3.6 Left-side Shifting of a Flat

Left-side shifting of a flat is done by moving a pattern

to the most left position on a flat in order to minimize the width of placement. There are two conditions to do this shifting, i.e.:

1. There is available free space exactly in the left side of a pattern (DAT-l),

2. Fit height of DAT-l must be higher or equal to the pattern height.

4.3.7 Forced Placement Procedure

Forced placement is a specific procedure to place a

hand pattern with position 2 (Figure 3) and it is forced to move up from bottom side when placed between two previous pattern (Figure 8). Some conditions for this procedure are:

1. When flat starts from left end of cloth then xStart flat is equal to that left end,

2. When flat finishes at right end of cloth then xEnd flat is equal to that right end,

3. When the lower edges of the left and right patterns are equal then forcedly place the hand pattern position 2 in the middle of the free space in between,

4. When the lower edge of pattern in the left side of the flat is lower than that in the right side then the left side of hand pattern is placed parallel to the right edge of the left side pattern,

5. When the lower edge of pattern in the right side of the flat is lower than that in the left side then the right side of hand pattern is placed parallel to the left edge of the right side pattern.

4.3.8 Flat Upper-side Shifting

Shifting operation to the upper side is performed to reduce the total length of the cloth. In this case, an available free spaced come up just above the pattern (Figure 9). Some conditions for this procedure are:

1. When there is a free space (L-avail) exactly above the pattern and the flat (DAT-a),

2. Width of DAT-a must be higher or equal to the pattern width.

Figure 8: Force placement of hand pattern. Figure 9: Existence of free space above pattern.

4.3.10 Minimum Length Calculation

Every time one pattern has been placed, a minimum

length of cloth can be determined. As depicted in Figure 9, after placing the S-front pattern, 1st minimum length is calculated. Finally, after all patterns have been placed (after S-back is placed), then the last minimum length will determined the total minimum length of the cloth.

flat 3

S-front L-front

flat 1 L-post 2flat 2

S-back

S-front

fit h

eigh

t = D

AT-a

flat 2

L-front

L-avail

1st m

in. l

engt

h

2nd

min

. len

gth

last

min

. len

gth

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5. RESULTS AND ANALYSIS

To observe the behavior of this algorithm, some cases are worked out and compared to the previous works done by Martinus (1999). The most important features introduced in this stage is that there are modification in the string representation to maximize the available area, giving free orientation for the hand pattern, shifting and forcing operation of pattern when there are possible area to be used.

5.1 The First Case Order with size combination of S, M and L is tested and there are some specifications related to this order listed as follows:

a) Size combination : S, M, L b) Cloth width : 63 inch (160 cm) c) Type of section : starting section d) Number of sim. size (j) : 1 e) String by Martinus : 3 1 2 9 4 5 9 7 8 8 6 3 f) Improved string : 1 2 2 7 5 5 7 8 4 8 4 1 g) Rearranged string : 1 7 7 4 4 1 2 2 5 5 8 8

Comparison between the two placement procedures is figured out in Figure 10 and 11 and the detailed are listed in Table 4. Table 4: Comparison between two procedures (first case).

Previous

Algorithm [Martinus]

Improved Algorithm

Savings (%)

Cloth length 235 cm 205 cm 12.77 Material used 29898.5 cm2 29898.5 cm2 Waste of material 7,706.2cm2 2,905.6cm2 62.30 Percentage of waste 20.49% 8.86%

In figure 10 can obviously seen that free form of string allows the position of hand pattern come early in the placement procedure. This results in wasting a lot of material while re-arranging the body patterns to come earlier makes the total length of the cloth smaller (Figure 11).

Figure 10: Pattern placement using Martinus procedure for

the first case. Figure 11: Pattern placement using improved procedure for

the first case.

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5.2 The Second Case Order with size combination of S and M is tested and there are some specifications related to this order listed as follows:

a) Size combination : S, M b) Cloth width : 54 inch (137,16 cm) c) Type of section : final section d) Number of sim. size S : 2 e) Number of sim. size M : 1 f) String by Martinus : 3 3 6 6 3 3 5 2 1 4 2 1 g) Improved string : 1 1 4 4 1 1 5 2 2 5 2 2

Comparison between the two placement procedures is depicted in Figure 12 and 13 and the detailed are listed in Table 5.

We will see that final section (after A-A) in Figure 12 gives quite some waste materials since available area next to the body patterns can not be utilized for anything. While in Figure 13, this section can be reduced by adjusting the orientation of the hand patterns. This results from defining hand patterns to the same gene value and using opposite orientation in pattern placement procedure. Figure 12: Pattern placement using Martinus procedure for the second case.

Figure 13: Pattern placement using opposite hand

orientation in the second case. Table 5: Comparison between two procedures (second case).

Previous

Algorithm [Martinus]

Improved Algorithm

Savings (%)

Cloth length 283 cm 255cm 9.89 Used material 28344.5cm2 28344.5cm2 Waste of material 10,471.8cm2 6,631.3cm2 36.67 Percentage of waste 26.98% 18.96%

5.3 The Third Case (Layout Optimization)

The last case shows how this algorithm works when encountering demand of all the same size but the total number is not a factor of similar size number (j = 6) in Table 1. In here, layout optimization method is used to determine the number and type of section group that may exist to fulfill the demand. Number of unit to be made in one section is defined based on the similar sizes (j) and then as the consequence, the ply height is determined.

The demand specifications of this case are listed as

follows: a) No. of demand : 13 units

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b) Size combination : S c) Cloth width : 63 inch (160 cm) d) Type of section : first and last section e) Number of sim. size (j) : 6 f) String : 1 1 1 2 2 1 2 1 2 2 1 2 2 2 2 1 2 1 1 1 1 2 1 2 g) Rearranged string : 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2

2 2 2 2 2 2 2

The first method (Martinus) uses very similar way to solve this problem, but the difference is that it results in only one section group. In this section one ply height of three layer is made in which six similar sizes are placed. On the other hand, the current method divides the demand in two section in order to exactly fit the desired amount. Figure 14: Pattern placement for the third case.

One section where six similar sizes are placed has a

ply height of two layers and one final section to fulfill the rest has only one complete set of S pattern. By doing so, whatever the number of demand, this method will always find an exact amount of T-shirt to be produced. Result of re-arranging the body pattern and the consequences of using Table 1 is shown in Figure 14 and 15. The detailed comparison is shown in Table 6 and the general data is in Table 7. Figure 15: Pattern placement for the 13th unit placed in last

section for the third case. Table 7: Comparison between two procedures (third case).

Previous

Algorithm [Martinus]

Improved Algorithm

Savings (%)

Cloth length 1110 cm 806.5 cm 27.34 Used material 11,9762cm2 11,9762cm2 Waste of material 57,859.7cm2 9,294.1cm2 83.94 Percentage of waste 32.58% 7.20%

6. CONCLUSIONS

In order to minimize the waste of raw material in cutting process of T-shirt, good method should be used in dealing with variation in order quantity as well as the size combination. The simulation results show that genetic algorithm is one possible method to solve combinational problems like the one come up in the T-shirt cutting process. The problem consists of variation in the number of unit and a number of difference sizes to be made.

To optimize the use of material, pattern placement procedure should be developed. Some specific actions involved are utilizing trapped spaces (called block) between patterns, orienting a pair of hand patterns in opposite direction, shifting patterns to the left, the right or to the upper sides whenever possible after checking for available space around previous patterns.

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Table 6: Detailed comparison between Martinus and current method (third case).

Method Section Similar size (j)

Min. layout length (cm)

Ply height

Total produced

Exceeded units

Total length of cloth (cm)

Martinus First 6 370 3 18 5 1,110 First 6 370 2 12 Current Final 1 66.5 1 1

0 806.5

The number of similar size on one ply will much

influence the flexibility in placing the pattern and finding the best pattern layout. The total number of order can be grouped into several sections, one of each may have different ply height. To maximize the usage of material, the highest number of similar sizes is the priority to determine the ply height. This results in much saving material as shown in Table 7.

REFERENCES Chan, K.C.. and Djohari, S. (1995) Layout of

Facilities of Unequal Areas Using Genetic Algorithm, 6th International Conference on Manufacturing Engineering, Melbourne, 1995.

Goldberg, D.E. (1989) Genetic Algorithm in Search, Optimization and Machine Learning, Reading Massachusetts: Addison Wesley Publishing Co. Inc.

Martinus, A. (1999) Development of Pattern Algorithm and GA Model for Optimizing T-shirt Basic Pattern Layout, Thesis, University of Parahyangan Bandung (in Indonesian).

Soesilowati (2000) Development of Layout Optimization Algorithm of T-shirt Basic Pattern on Plain and Stripes Material using Genetic Algorithm, Thesis, University of Parahyangan Bandung (in Indonesian).

Susanti, F. (1999) Optimization of T-shirt Basic Pattern Layout using Genetic Algorithm, Thesis, University of Parahyangan Bandung (in Indonesian).

AUTHOR BIOGRAPHIES Bagus Arthaya is a senior lecturer in Industrial Engineering Department, Parahyangan Catholic University, Bandung - Indonesia. He received a doctorate degree from Mechanical Engineering Department at the Katholieke Universiteit Leuven, Belgium in 1995. He has some experiences in mechatronics and robotics related to welding process. He also implemented smart mechatronics instrumentation in land surveying tools to promote more accurate and fast measurement system. His teaching and research interests include robotics and mechatronics, reverse engineering, planning and scheduling, expert systems, ergonomics and image processing with special emphasis on ergonomics and product inspections. His email address is <bagusart@home.unpar .ac.id>. Thedy Yogasara is a lecturer in Industrial Engineering Department, Parahyangan Catholic University, Bandung - Indonesia. He started teaching in 1998 and obtained his master degree in Manufacturing Engineering and Management from the School of Mechanical and Manufacturing Engineering, UNSW, Australia in 2003. His teaching and research field are human factors/ergonomics, plant layout, product design and development and optimization methods. He can be reached at < thedy@home.unpar .ac.id >.

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