1. Cellular Manufacturing Group Technology
OST: Chapter 5
Cellular Manufacturing
Group Technology
(c) Prof. Richard F. Hartl
OST

2. Introduction Review of the introductory example
Production and assembly of 4 parts (A, B, C, D)
A: saw -> turn -> mill -> drill
B: saw -> mill -> drill -> paint
C: grind -> mill -> drill -> paint
D: weld -> grind -> turn -> drill
(c) Prof. Richard F. Hartl
OST

3. Group Technology (GT)
Observation already in 1920ies: product-oriented departments to manufacture standardized products in machine companies lead to reduced transportation
Can be considered the start of Group Technology (GT): Parts with similar features are manufactured together with standardized processes  small "focused factories" are created as independent operating units within large facilities.
More generally, GT can be considered a “theory of management” based on the principle "similar things should be done similarly“
"things" .. product design, process planning, fabrication, assembly, and production control (here); but also other activities, including administrative functions.
(c) Prof. Richard F. Hartl
OST

4. When to use GT?
Pure item flow lines are possible, if volumes are very large.
If volumes are very small, and parts are very different, a functional layout (job shop) is usually appropriate
In the intermediate case of medium-variety, medium-volume environments, group configuration is most appropriate
(c) Prof. Richard F. Hartl
OST

5. Cellular Manufacturing
Principle of GT: divide the manufacturing facility into small groups or cells of machines  cellular manufacturing
Each cell is dedicated to
a specified family of part types (or few “similar” families).
Preferably, all parts are completed within one cell
Typically, it consists of
a small group of machines, tools, and handling equipment
(c) Prof. Richard F. Hartl
OST

6. Different Versions of GT
The idea of GT can also be used to build larger groups, such as for instance, a department, possibly composed of several automated cells or several manned machines of various types.
GT flow line (closest to flow shop)
classical GT cell
GT center (closest to job shop)
(c) Prof. Richard F. Hartl
OST

7. GT flow line
All parts assigned to a group follow the same machine sequence and require relatively proportional time requirements on each machine.
Automated transfer mechanisms may be possible.
 mixed-model assembly line (Chapter 4)
fräsen
(aus)bohren
drehen
schleifen
bohren
(Askin & Standridge,
1993, p. 167).
(c) Prof. Richard F. Hartl
OST

8. classical GT cell
Allows parts to move from any machine to any other machine. Flow is not unidirectional.
Since machines are located in close proximity  short and fast transfer is possible.
(Askin & Standridge,
1993, p. 167).
(c) Prof. Richard F. Hartl
OST

9. GT center Machines located as in a process (job shops)
But each machine is dedicated to producing only certain Part families  only the tooling and control advantages of GT; increased material handling is necessary
When large machines have already been located and cannot be moved, or
When product mix and part families are dynamic  would require frequent relayout of GT cell
(Askin & Standridge, 1993, p. 167).
(c) Prof. Richard F. Hartl
OST

10. Cellular manufacturing
Group technology
Parts with similar features are manufactured
Small "focused factories" are created as independent operating units within large facilities.
Divide the manufacturing facility into small groups
Each cell is dedicated to a specified family or set of part types
A cell is a small group of machines, tools, and handling equipment
Since machines are located in close proximity  short and fast transfer is possible
(c) Prof. Richard F. Hartl
OST

11. Cellular manufacturing
Often u-shaped for short transport
Often typical material flow
(c) Prof. Richard F. Hartl
OST

12. Cellular manufacturing
Example with 3 workers
Also u-shaped
(c) Prof. Richard F. Hartl
OST

13. Cellular manufacturing
Advantages:
Short transportation and handling (usually within cell)
Short setup times because often same tools and fixtures can be used (products are similar)
High flexibility (quick reaction on changes)
Clear arrangement, few tools/machines  easy to control
High motivation and satisfaction of workers (identification with “their" products)
Small lot sizes possible
Short flow times
(c) Prof. Richard F. Hartl
OST

14. Cellular manufacturing
How to build groups?
Similiar parts (similiar process flow/machine usage, same materials,…) are grouped
Visual inspection
Classification and coding based on design and production data (time consuming, no universally applicable system is available)
Production Flow Anlaysis (PFA), i.e. mathematical models
(c) Prof. Richard F. Hartl
OST

15. Production Flow Analysis
Many clustering methods have been developed
Can be classified into:
Part family grouping: Form part families and then group machines into cells
Machine grouping: Form machine cells based upon similarities in part routing and then allocate parts to cells
Machine-part grouping: Form part families and machine cells simultaneously
(c) Prof. Richard F. Hartl
OST

16. Machine-part grouping
Construct matrix of machine usage by parts
sort rows (machines) and columns (parts) so that a block-diagonal shape is obtained
(c) Prof. Richard F. Hartl
OST

17. Machine-part grouping
How can this sorting can be done systematically?
Various heuristic and exact methods have been developed. The simplest one is binary ordering, also known as “rank order clustering” or “King’s algorithm“
(c) Prof. Richard F. Hartl
OST

18. Binary Ordering Example: 5 machines; 6 parts:
Interpret rows and columns as binary numbers
Sort rows w.r.t. decreasing binary numbers
Sort columns w.r.t. decreasing binary numbers
part
machine 1 2 3 4 5 6 A - B C D E
(c) Prof. Richard F. Hartl
OST 18

19. Binary Ordering Sort rows w.r.t. decreasing binary numbers
New ordering of machines: B – D – C – A - E
part
value
machine 1 2 3 4 5 6 A - B C D E
= = 20
= 43
= 29
= 35
= 6
25 32
24 16
23 8
22 4
21 2
20 1
(c) Prof. Richard F. Hartl
OST

20. Binary Ordering Sort columns w.r.t. decreasing binary numbers
part
machine 1 2 3 4 5 6
value B - 43 D 35 C 29 A 20 E
24 = 16
23 = 8
New ordering of parts:
22 = 4
21 = 2
20 = 1 =7
= 24
= 6
= 20
=25
=28
(c) Prof. Richard F. Hartl
OST

21. Result of Binary Ordering
No complete block-diagonal structure
Remaining items: 6, 5, and 3 produced in both cells
Or machines B, C, and E have to be duplicated
part
machine 6 5 1 3 4 2 B - D C A E
value 28 25 24 20 7
2 groups:
Group 1: parts {6, 5, 1 }, machines {B, D}
Group 2: parts { 3, 4, 2}, machines {C, A, E}
Parts 1, 4, and 2 can be produced in one cell
(c) Prof. Richard F. Hartl
OST

22. Repeated Binary Ordering
Binary Ordering is a simple heuristic  no guarantee that „optimal“ ordering is obtained
Sometimes a better better block-diagonal structure is obtained by repeatingthe Binary Ordering until there is no change anymore
(c) Prof. Richard F. Hartl
OST

23. Example Binary Ordering (contd.)
part
machine 6 5 1 3 4 2
value B - 60 D 56 C 39 A E 18 28 25 24 20 7  6
Example Binary Ordering (contd.)
After sorting of rows and columns:
part
machine 6 5 1 3 4 2
value B - 60 D 56 C 39 E 18 A 28 26 24 20 7  5
No change of groups in this example
(c) Prof. Richard F. Hartl
OST 23

24. Single-Pass Heuristic
Considering capacities (Askin and Strandridge):
All parts must be processed in one cell (machines must be duplicated, if off-diagonal elements in matrix)
All machines have capacities (normalized to be 1)
Constraints on number of identical machines in a group
Constraints on total number of machines in a group
(c) Prof. Richard F. Hartl
OST

25. Single-Pass Heuristic - Example
7 parts, 6 machines
Given matrix of processing times (incl. set up times) for typical lot size of parts on machines
Entries in matrix not just 0/1 for used/not used)
All times as percentage of total machine capacity
Maximal number of machines per cell: here at most 4 machines in a group
Not more than one machine of each type in a group
(c) Prof. Richard F. Hartl
OST

26. Single-Pass Heuristic
part
machine 1 2 3 4 5 6 7
sum
min. # machines A
0.3 -
0.6
0.9 B
0.1
0.7 C
0.4
0.5
1.2  D
0.2
1.4  E F
 1.1 1 1 2 2 1 2
 = 9 machines
(c) Prof. Richard F. Hartl
OST

27. Single-Pass Heuristic
At least 9 machines are needed
Not more than 4 machines in a group
 at least 9/4 = 2,25 groups, i.e. at least 3 groups
Step 1: acquire block diagonal structure e.g. using binary sorting
Step 2: build groups
(c) Prof. Richard F. Hartl
OST

28. Single-Pass Heuristic
Step 1:
For binary sorting treat all entries as 1s.
Result:
part
machine 1 5 7 3 4 6 2 D
0.2
0.3
0.5
0.4 - C A
0.6 F B
0.1 E
(c) Prof. Richard F. Hartl
OST

29. Single-Pass Heuristic
Step 2:
Assign parts to groups (in sorting order)
Necessary machines are also included in group
Add parts to group until either
the capacity of some machine would be exceeded, or
the maximum number of machines would be exceeded
(c) Prof. Richard F. Hartl
OST

30. Single-Pass Heuristic
table
Iteration
part chosen
group
assigned machines
remaining capacity 1 2 5 3 7 4 6 1
D, C, A
D (0,8), C (0,6), A (0,7) 1
D, C, A
D (0,5), C (0,6), A (0,1) 2
D, F, B
D (0,5), F (0,8), B (0,9) 2
D, F, B
D (0,1), F (0,5), B (0,9)
D (0,1), F (0,1), B (0,6), C (0,5) 2
D, F, B, C 3
C, E
C (0,7), E (0,5)
C (0,7), E (0,1), F (0,8), B (0,7) 3
C, E, F, B
(c) Prof. Richard F. Hartl
OST

31. Single-Pass Heuristic
Machines used:
One machine each of types: A, E
Two machines of types: B, D, F
Three machines of type: C
Single-pass heuristic of Askin und Standridge is a simple heuristic  not necessarily optimal solution (min possible number of machines)
Compare result with theoretical min number of machines
(c) Prof. Richard F. Hartl
OST

32. Single-Pass Heuristic
Maybe reduction possible?!
part
machine 1 2 3 4 5 6 7
sum
min. #
heuristic A
0.3 -
0.6
0.9 B
0.1
0.7 C
0.4
0.5
1.2 D
0.2
1.4 E F
1.1
(c) Prof. Richard F. Hartl
OST 32

33. BIP Model
Minimize total (or weighted) number of machines used when the number of groups is given
Previous example:
At least 9 machines necessary
Every group has at most M = 4 machines
 at least 3 groups (try 3)
(c) Prof. Richard F. Hartl
OST

34. BIP Model ajk ... capacity of machine k needed for part j
i  I groups (cells)
j  J ... parts
k  K machines
M maximum number of machines per group
(c) Prof. Richard F. Hartl
OST

35. BIP Model 1, if part j is assigned to group i 0, otherwise =
1, if machine of type k is assigned to group i = =
(c) Prof. Richard F. Hartl
OST

36. BIP Model objective: constraints:
each part must be assigned to one group
respect capacity of machine k in group i
not more than M machines in group i
binary variables
(c) Prof. Richard F. Hartl
OST

37. Solution group parts machines remaining capacity 1 2, 4, 6 B, C, E, F
1, 5
A, C, D
A (0.1), C (0.6), D (0.5) 3
3, 7
B, D, F
B (0.9), D (0.1), F (0.5)
Optimal solution with 10 machines
Theoretical minimum number was 9 machines (not reached because of constraints)
Single pass heuristic used 11 machines
(c) Prof. Richard F. Hartl
OST

38. Similarity Coefficients
Also a clustering method (machine grouping)
Define
ni Number of parts visiting machine i
nij Number of parts visiting machines i and j
Similarity coefficient between machines i and j
Proportion of parts visting machine i that also visit machine j
(c) Prof. Richard F. Hartl
OST 38

39. Similarity Coefficients
Hierarchical Clustering Heuristic:
Calculate Similarity Coefficients (SC) for all combinations of machines
Group that combination leading to the highest SC. Stopping criteria: e.g. SC have to reach a given lower bound, only machines (no clusters) can be grouped, etc.
Update SC: e.g. maximum of the SC of the machines that are to be combined (this is some kind of lower bound, determining the new coefficients exactly could lead to higher values.
e.g. A: 0 1 1
B: 1 1 0
C: 1 0 1
(c) Prof. Richard F. Hartl
OST 39

40. Similarity Coefficients
Machine-Part-Matrix: 1 2 3 4 5 6 7 8 A B C D E F ni 3 3 4 4 2 2
(c) Prof. Richard F. Hartl
OST 40

41. Similarity Coefficients
Calculate SC: ni
nij  A B C D E F - 3 1 0   1 3  1  -  2  3 3 4 4 2 2
sij  A B C D E F 1
0,333 0 
0,75  0
0,5 1 
Combine: A-B
(c) Prof. Richard F. Hartl
OST 41

42. Similarity Coefficients
Bild Cluster und Update SC:
sij  AB C D E F 1
0,333 0 
0,75  0
0,5 1 
sij  AB C D EF 1
0,333
0,75  0
0,5 0 
sij  AB CD EF 1
0,333
0,5 0 
 0,5
(c) Prof. Richard F. Hartl
OST 42

43. Similarity Coefficients
Dendogram:
Graphical illustrations of possible groupings per threshold
(c) Prof. Richard F. Hartl
OST 43

44. Graph Partitioning Machines with common parts should be in same group
Graph illustrating common parts
Group forming can be seen as special case of graph partitioning
(c) Prof. Richard F. Hartl
OST

45. Graph Partitioning
Given a graph with nodes and edges, find a partitioning of the node set into a (given) number of disjoint subsets of approximately equal size, such that the total cost of edges that connect nodes of different subsets is minimized.
NP-hard optomization problem
Various methods have been developed
Simple and well-known heuristic by Kernighan and Lin
(c) Prof. Richard F. Hartl
OST

46. Kernighan and Lin Input: A weighted graph G = (V, E) with
Vertex set V. (|V| = 2n)
Edge Set E. (|E| = e)
Cost cAB for each edge (A, B) in E.
Output: 2 subsets X & Y such that
V = X  Y and X  Y = { } (i.e. partition)
Each subset (group) has n vertices
Total cost of edges “crossing” the partition is minimized.
(c) Prof. Richard F. Hartl
OST

47. Kernighan and Lin
Complete enumeration (brute force) is not possible (np-hard):
Try all possible bisections. Choose the best one.
If there are 2n vertices  number of possibilities = (2n)! / (n!)2 = nO(n)
For 4 vertices (A,B,C,D), 3 possibilities
1. X = {A, B} & Y = {C, D}
2. X = {A, C} & Y = {B, D}
3. X = {A, D} & Y = {B, C}
For 100 vertices  5  1028 possibilities
(c) Prof. Richard F. Hartl
OST

48. Kernighan and Lin
(c) Prof. Richard F. Hartl
OST

49. Kernighan and Lin V(G) = { a, b, c, d, e, f }.
Start with any partition of V(G) into X and Y, e.g.,
X = { a, c, e } Y = { b, d, f }
The cut value is the sum of all edge costs
between the 2 sets:
cut-size = = 16
Try to improve this partitioning using KL a c b d e f 3 1 2 4 6
(c) Prof. Richard F. Hartl
OST

50. Kernighan and Lin
For each node x  { a, b, c, d, e, f } compute the gain values of moving node x to the others set:
Gx = Ex - Ix where
Ex = cost of edges connecting node x with the other group (extra)
Ix = cost of edges connecting node x within its own group (intra)
This gives:
Ga = Ea – Ia = 3 – 4 – 2= – 3
Gc = Ec – Ic = – 4 – 3 =0
Ge = Ee – Ie = 6 – 2 – 3 = + 1
Gb = Eb – Ib = –2 = + 2
Gd = Ed – Id = 2 – 2 – 1 = – 1
Gf = Ef – If = – 1 = + 9
(c) Prof. Richard F. Hartl
OST

51. Kernighan and Lin Cost saving when exchanging a and b is essentially
Ga + Gb
Calculate: gab = Ga + Gb - 2cab
gab = Ga + Gb – 2wab = –3 + 2 – 23 = –7
gad = Ga + Gd – 2wad = –3 – 1 – 20 = –4
gaf = Ga + Gf – 2waf = –3 + 9 – 20 = +6
gcb = Gc + Gb – 2wcb = – 21 = 0
gcd = Gc + Gd – 2wcd = 0 – 1 – 22 = –5
gcf = Gc + Gf – 2wcf = – 24 = +1
geb = Ge + Gb – 2web = – 20 = +1
ged = Ge + Gd – 2wed = +1 – 1 – 20 = 0
gef = Ge + Gf – 2wef = – 26 = –2
(c) Prof. Richard F. Hartl
OST

52. Kernighan and Lin Maximum gain by exchanging nodes a and f
new cut-size = 16 – 6 = 10
X’ = { c, e } Y’ = { b, d } a c b d e f 3 1 2 4 6
(c) Prof. Richard F. Hartl
OST

53. Kernighan and Lin gcb = Gc + Gb – 2wcb = gcd = Gc + Gd – 2wcd =
G’c = Gc + 2cca – 2ccf = 0 + 2(4 – 4) = 0
G’e = Ge + 2cea – 2cef = 1 + 2(2 – 6) = –7
G’b = Gb + 2cbf – 2cba= 2 + 2(0 – 3) = –4
G’d = Gd + 2cdf – 2cda = –1 + 2(1 – 0) = 1
gcb = Gc + Gb – 2wcb =
gcd = Gc + Gd – 2wcd =
geb = Ge + Gb – 2web =
ged = Ge + Gd – 2wed =
new cut-size = 10 – (-3) = 13
X’ = { e } Y’ = { b } a d b c e f 3 1 2 4 6
(c) Prof. Richard F. Hartl
OST

54. Kernighan and Lin G’e = Ge + 2ced – 2cec = G’b = Gb + 2cbd – 2cbc=
geb = Ge + Gb – 2ceb = –1 – 2 – 20 = –3
Summary of the gains
g1 = +6
g1 + g2 = +6 – 3 = +3
g1 + g2 + g3 = +6 – 3 – 3 = 0
Maximum gain is g1 = +6  Exchange only nodes
a and f. End of 1 pass.
This pass must be repeated until no changes are observed any more.
(c) Prof. Richard F. Hartl
OST

55. Kernighan and Lin Group formation with KL-Algorithm: See XLS
(c) Prof. Richard F. Hartl
OST

56. Grouping without binary ordering
„Key machine“
See XLS
(c) Prof. Richard F. Hartl
OST