designing a cellular manufacturing system with incremental cell formation

Amirkabir University

of Technology

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International Industrial Engineering Conference 13&14th July 2004

Advanced Manufacturing Systems 1- 126 ��

and Technology

Designing a Cellular Manufacturing System

with Incremental Cell Formation

Iraj Mahdavi1, Javad Rezaeian2, Ashkan Rahimian3

1, 2, 3- Mazandaran University of Science & Technology, Babol, Iran 1- [email protected]

2- [email protected] 3- [email protected]

Abstract

In the past several years, many studies have been carried out on cellular manufacturing. Some have used binary data, while others have used sequence-based

production data for cell formation. In practice, it has been observed that cellular systems

are designed with incremental cell formation by considering most important part-family

first and designing cell for this part-family. Subsequently, cells are added for other part-

families in an incremental fashion. The objective of this paper is to design such a cell for

a given part-family. Effort has been made to minimize cycle time for a fixed number of

workstations. Approach used in this paper is to identify a combination of the operations,

which can be done on same workstation, and partition the problem in two sub-problems

with respect to this combination. Process is repeated recursively. This approach is

computationally fast and gives solutions, which are as good as or better than the other

methods. Four examples from the literature have been solved to demonstrate the advantages of this algorithm

Keywords: Group Technology, Part-family, Incremental Cell Formation, Multistage

Programming, Cycle Time, Branch and Bound

1. Introduction

Group technology (GT) is a manufacturing philosophy for improving productivity in batch production systems. GT is best suited to a batch-flow production system where many

different parts having relatively low annual volumes, are produced in small lot sizes (Carrie 1973).

It involves the grouping of parts into part-families and machines into machine-cells so that a family of parts can be produced within a group of machines. The problem of

determining machine-groups and part-families is called the machine-cell formation (MCF) or machine-component grouping (MCG) problem.

The application of GT promises a reduction in material handling cost, set-up time, lead


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time and work-in-process, etc.

In Production flow analysis approach, the machine route for every part is noted and transferred into a machine-component incidence matrix (MCIM). This matrix provides the main data for the formation of part-families and machine cells. There exist many

algorithms in the GT literature based on this approach. These algorithms can broadly be classified as: Array-based methods (Kings 1980, King and Nakornchai 1982 ); Clustering

methods ( McAuley 1972, Carrie 1973 , Chandrasekharan and Rajagopalan 1986, 1987, Srinivasan and Narendran 1991, Gupta and Seifoddini 1990, Nair and Narendran 1998 ,

1999); Mathematical programming-based method ( Kusiak 1987 , Srinivasen et al . 1990, Shutb 1989, Choobineh 1988 and Adil et al. 1996 ); Graph theoretic methods (

Rajagopalan and Batra 1975, Kumar et al.1986 , Askin et al.1991, Srinivasan 1994 , Mukhopadyay et al. 2000 ) ; Neural network-based methods (Kaparthi and Suresh 1992

,1993 , Venugopal and Narendran 1994 , Kamal and Burke 1996 , Venugopal 1999 ); Search methods (Boctor 1991 , Sofianopoulou 1997 , 1999 , Gupta et al. 1996 , Su and Hsu

1998 , Zhao and Wu 2000 , Lee-Post 2000 , Logendran et al. 1994 and Baykasoglu et al. 2000).

All the above methods assume that the conversion of a job shop to cellular manufacturing (CM) is performed comprehensively rather than incrementally. However,

planning and implementation of most cell conversions in industry are incremental ones, not comprehensive.

This paper presents the incremental cell-formation problem where the cells are formed and implemented incrementally. When incremental cells are formed for high-volume

items, there are no inter-cell moves. Once cells are formed, operations and machines are allocated to the cell with an objective of minimizing cycle time. The motivation for this

approach is from the work of Marsh et al. (1999) and Mahesh and Srinivasan (2002). The present paper considers this problem of minimizing the cycle time of an

equivalent part of a part-family for a fixed number of workstations. The proposed method is compared with two other approaches, branch and bound

technique and multistage programming, presented by Mahesh and Srinivasan (2002). It is superior to both the methods either in computational time or in cycle time.

2. Incremental Cell Formation Problem (Mahesh and Srinivasan (2002))

The cells are formed one after the other. To form the first cell, a product or family that

has the highest volume or which has the highest profit contribution, is selected. The next cell is then constructed for the next highest volume product or family, and the process is

repeated (Marsh et al.1999). The following assumptions are made to solve the problem.

• Only one machine can be allocated to each workstation.

• Any number of operations can be carried out at each workstation without violating precedent constraints.

• At least one operation should be carried out at each workstation.

• No operation is split across the workstations (or machines).

• All operations should be carried out within the cell; or no operation should be left out.

• Workflow should be unidirectional.

• A set of common operations across the parts of a part-family exists. Although processing times of these operations may vary across parts, they are performed in


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the same station.

• Parallel stations are not allowed.

• Sequence of operations of parts in a part-family does not contradict with one another.

3. Equivalent Part of a Part-family (Mahesh and Srinivasan (2002))

In an equivalent part, not only should all the operations of a part-family exist in it, but

also they should be processed in such a way that a unidirectional flow is ensured. We use the following notations to explain this concept:

Let tji denote the processing time of jth operation on ith machine of equivalent part and Nk denote the volume of the kth part of a part-family (k = 1, 2…k) and tjik as the

processing time of the jth operation on the ith machine of the kth part;

tji = tjikN1

k∑=

K

k

.

Assume that there exist three parts in a part-family. Their production volumes for a particular period are 5, 4 and 3 respectively. The sequence of operations and the processing

times with alternative machines for each part are given in Table 1.

Operation Alternative machine Processing times

Part 1

1

2

3

4

Part 2

1

3

4

5

Part 3

1

2

5

6

1,2

3,4,5

2

4,5

1,2

2

4,5

3,4

1,2

3,4,5

3,4

4

6,3

8,2,1

4

5,6

4,3

5

7,8

6,7

5,6

8,3,2

8,9

10

Table1. Data for parts 1-3.

Using the above data, data for a part that represents the entire part-family are

determined. This part is called the equivalent part of a part-family. The processing times for the equivalent part of a part-family are determined thus:

t11 = (5�6+4�4+3�5) = 61 t12 = (5�3+4�3+3�6) = 45.

Likewise, processing times for all operations are calculated. Data for equivalent part are shown in Table 2. These data are used to group operations and machines to different

workstations.


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1

2

3

4

5

6

1,2

3,4,5

2

4,5

3,4

4

61,45

64,19,11

40

53,62

48,55

30

Table2. Data for the equivalent part of a part family.

4. Heuristic Based on Cutting Approach The proposed algorithm is based on the cutting of workstations or operations. After

assigning one feasible combination to a cell, the process of allotment of operations to the remaining cells are designed corresponding with lower number of workstations or

operations at the left and right sides of assigned cell respectively. The present algorithm is illustrated in the following flowchart and the program is

written in Delphi 7 and tested on a PC (Pentium III processor) running Windows XP Home Edition.


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4.1. Algorithm Step1: Determine NC as smallest integer larger than or equal to ratio of number of

operations to the workstations. (This number denotes the minimum number of operations

to be assigned at least to one workstation) Step 2: Determine initial cycle time (CT).

This is equal to minimum total operation times of the NC size as obtained at step 1. Step 3: Determine the combinations of the NC size.

Step 4: Select a feasible combination such that it could be assigned at one workstation. Step 5: Find the cell in which the current combination can be placed after taking into

consideration previous unassigned operations. Step 6: Place the current combination in the current cell.

Step 7: Check if all cells are filled. If yes stop, otherwise go to the next step. Step 8: Cut the operation matrix, based on current feasible combination. The cutting

approach is designed on the basis of creating new operation matrix at the left and right sides of the assigned cell.

Step 9: Repeat step 3 to 9 for each cut. If the process is infeasible, go to step10. Step 10: Calculate combinations of NC+1 operation. Step 11: Determine the minimum of the CT and new CT.


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Step 12: Increase the CT value by one (CT+1).

4.2. Numerical Illustration

The numerical illustration takes the following example (Example 1). In this problem there exist 8 numbers of operations (NO) for an equivalent part of a part-family. Each

operation can be done by more than one machine, but processing times will vary, as given in Table 3. There exist six machines, from which five are to be chosen for five numbers of

workstations (NS), such that the cycle time is minimized and the unidirectional flow is maintained. The data for the problem are shown in Table 3.


1

2

3

4

5

6

7

8

5,2

5,3

1,4

6

6,1,2

2

3,2

1

3,6

7,2

1,4

2

5,2,7

6

1,6

10

Table 3. Data for example 1.

The step-by-step procedure of the proposed algorithm for the above problem to form

six workstations is given below:

For calculation of NC there is NO = 8 and NS = 5, then NS

NO=5

8 = 1.6

SO, NC takes the value of 2.

Construction of two activities in each feasible combination is shown in Table 4. Table 4. Construction of two activities.

The initial cycle time is the minimum of combination time that is equal to value of

7.The corresponding combination (4,5) cannot be placed at the first cell, because it does not include the first operation in that combination. Therefore, the second cell will be

selected for that combination. In this situation the operations of 1, 2 and 3 should be assigned to the first cell which it

is not possible due to over-sizing of the first cell (size 3) than NC size (size 2); it will be automatically shifted to the next cell (cell 3).

In this cell the combination of (4, 5) can be assigned to this cell and on the basis of cutting approach, the cells are cut as shown in Figure 1.

At the left section, there are three operations (1, 2, and 3) and two workstations.

Combinations Machine Combination time

1,2

4,5

5,6

6,7

5

6

2

2

10

7

13

12


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At the right section, there are three operations (6, 7, and 8) and two workstations.

Both the sections have equal value of NC, which are 2. It means that the algorithm proceeds to the next step for assigning the operations.

Left section Right section

(4, 5)

Figure 1. Cells in first cut.

At the right section, two activities of combination should be determined (as the NC size for this section is value of 2). The combinations are tabulated in Table 5.

Table 5. Construction of two activities for right section.

Since the combination time for Table 5 is greater than initial cycle time, the route of current assignment is cancelled.

In this situation the cycle time will be increased by 1 (CT = 8). Increase NC value by 1(NC = 3) and determine combination of new NC activities as

shown in Table 6.

Table 6. Construction of new NC activities.

Since the combination time is 19, which is more than CT, then on the basis of step 3, determine the combination of the NC size with combination time equal to CT.

Referring to Table 4, we find that there is no combination with CT= 8, there will come increment CT by 1 value (CT + 1). The new CT is less than 19 (Table 6).

The above procedure will be continued to up the cycle time of 10. The combination of (1, 2) on the basis of Table 1 is assigned to the first cell.

Then, after cutting there will be six operations (3, 4, 5, 6, 7 and 8) with 4 workstations. By referring to Table 1 the combination of (4, 5) can be placed in cell III and after

Combination Machine Combination time

6,7 2

12

Combination Machine Combination time

5,6,7

2

19


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second cutting the cells at the left and right of assigned cell are shown in Figure 2.

Left section Right section

Cell II Cell III Cell IV Cell V

(4, 5)

Figure 2. Cells in second cut.

At the right side of the assigned cell, there are two cells (cell IV & cell V) with three operations (6, 7, and 8). The only combination of two activities for those cells using Table

4, would be combination (6,7) with time 12, which is more than CT = 10. Then, omit the above route of assigning.

Increment CT by 1 (CT= 11). Since the cycle time is not available in the two activities of combination from Table 4, increment CT by 1 (CT = 12) will occur .The only

combination is (6, 7) with value of 12 on machine 2. This combination can be placed at cell 4 due to feasibility of assigning.

By cutting, there are three cells at the left side and one cell at the right side of the fourth cell. The operation 8 is assigned to cell 5 on machine 1.

The algorithm is continued with three remaining cells and five operations (1, 2, 3, 4 and 5).

Calculate NC for remaining cells and operations:

NC = 3

5 = 1.67 therefore NC = 2.

By using Table 4, the feasible combinations are (1, 2) on machine 5 and (4, 5) on machine 6. Assign combination (1, 2) at cell I and cut the cells and continue assigning

combination (4, 5) at cell III. Finally, only operation 3 will be assigned to cell II on machine 4.

The result of whole assigning process is shown in Figure 3.

Cell I Cell II Cell III Cell IV Cell V

1, 2*5*10 3*4*4 4, 5*6*7 6, 7*2*12 8*1*10

Operation(s)*machine*time

Figure 3. Result of whole assigning process.

The data and the comparative cycle time and computational time for example numbers

2, 3 and 4 are shown respectively in the Tables 7, 8, 9, 10, 11 and 12.


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Operation Alternative machines Processing times

1

2

3

4

5

6

7

8

9

10

11

12

1,7,6,9

9,10,1

4,10,1

10,2

2,6,5,10,3,9,4

10,8,6

7,3,10

7

9,10,4,6,8,1,7

3,6,9,10,2,1,8

8,2

5,7,1,2

3,8,6,7

2,3,3

8,2,6

3,10

2,4,1,6,10,7,7

2,1,3

8,5,10

2

6,1,4,3,7,9,1

8,7,7,9,8,1,6

3,4

4,9,5,10


Number of

workstation

Branch and bound algorithm

Cycle time Computational time

Multistage programing approach


Cutting approach


4

5

6

7

22 0.49

12 0.99

11 1.48

9 1.48

22 0.06

22 0.06

22 0.05

22 0.05

22 0.02

12 0.02

11 0.02

9 0.02

Table 8. Comparative analysis for example 2.


1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

11,5,4,3,8,1,12

2,6,1,8,10,3,12,9,4,5

1,12,11

8,10,7,4,2,6,9,5,1,3

8,7,9,2,12,1,10,4

8,2,10

7,1,8,3,9,5,11,6,12

5,1,6,10,4,3,12,7,9

1,10,5,7,11,6,2,4,8

8,1,10,7,3,4,12

6,12

3,5,12,9,11,2,7,8,1

1,4,5,8,10,7

3,12,4,11,8,9

6,3,2,10

2

3,8,6,2,3,2,8

1,5,2,7,2,1,2,7,7,6

7,3,10

7,1,6,1,4,3,9,9,1,3

7,7,10,8,2,1,8,8

4,5,7

1,5,10,1,2,6,5,7,1

8,9,6,4,10,5,1,2,4

2,2,3,5,6,4,6,4,1

3,8,7,6,4,5,2

10,4

5,4,8,7,6,6,7,7,9

8,7,9,9,2,10

1,3,7,7,7,4

10,10,1,10

2



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Number of

workstation





Cutting approach


6

7

8

9

10

11

12

14 9.56

13 15.88

12 20.49

8 20.60

8 16.04

8 9.67

8 4.34

14 0.06

14 0.06

14 0.06

14 0.06

14 0.05

13 0.05

12 0.05

14 0.03

13 0.03

12 0.03

8 0.03

8 0.03

8 0.03

8 0.03



1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1,7,6,9,5,2,3

2,8,1

10,2,7,6,5

6,3,9,5,4,10,8,7,2,1

10,3,8,9

7,3,8,9,10,2,6,1,4

2,4,7

1,5,10,2,6,7,9

9,7,1,8,4,10,3,2,5,6

4,3,2

3,5,6

3,6,10,7

10,1,4,9

7,8,6,4

10,2,4,5,7

8,3,6,9,5,7,2,4

1,9,3

7,9

2,4,3,6,1,7,5,10,9

7,10

3,8,6,7,9,10,1

4,10,6

3,10,2,4,1

2,10,7,3,7,2,1,8,1,4

6,4,7,1

1,3,6,7,9,8,2,1,8

4,5,9

5,2,7,3,4,5,5

6,6,4,5,6,4,10,2,3

9,2,2

3,9,10

7,6,4,10

8,7,3,8

6,5,9,4

2,2,9,5,4

3,7,4,1,7,7,10,7

6,6,8

5,2

2,7,10,9,6,3,6,7,8

7,7


Number of

workstation





Cutting approach


7

8

9

10

18 86.18

16 160.16

15 240.14

13 294.13

18 0.06

18 0.05

17 0.05

17 0.06

18 0.03

16 0.03

15 0.03

13 0.03



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5. Conclusions

In this paper we have presented a method for solving problem of assigning operations and machines to workstations for a cell for a part-family with the objective of

minimizing cycle time (maximizing output). The approach recursively solves the problem by partitioning operations and workstations with respect to a selected set of operations. The

algorithm is compared for the four problems with two other methods, proposed by Mahesh and Srinivasan (2002).

For the four problems solved, both the Cutting method and Branch & Bound method provided optimal solutions. The cycle times obtained by the Multistage Programming

method are much higher than the best cycle time. Further, as the number of workstations increase, the error margin increases. Computational time for Cutting method and

Multistage Programming method does not seem to be affected much by the increase in the number of workstations, while for Branch and Bound method time is dependent on the

number of workstations. Hence, it is observed that Cutting method has advantage of both the methods.

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Acknowledgements

The authors express their gratitude to Prof. A.K. Mittal and Prof. S.M. Waseem for going through the manuscript.

designing a cellular manufacturing system with incremental cell formation

Engineering

machinecell formation

technology time

cell conversions

incremental cells

machine cells

family of parts

incremental ones

incremental fashion