Designing a Cellular
Manufacturing System:
A Materials Flow Approach
Based on Operation Sequences
By Asoo J. Vakharia & Urban
Wemmerlöv
Presented by Nuriye Kaptanlar
17/03/2003
Subject…
• Cell formation method integrating:
* cell formation
* within cell material flows
• Part families & cells (operation sequence)
• Within cell M/C sequence and M/C loads
Design of Cellular
Manufacturing Systems
• Selection of part families and grouping of parts
into families
• Selection of M/C and process populations and
grouping of these into cells
• Selection of tools, fixtures and pallets
• Selection of material handling equipment
• Choice of equipment layout
SIMULTANEOUSLY
[Prof. Selim Aktürk]
Advantages/Disadvantages
of Cellular Manufacturing
Advantages:
• Reduce material handling
• Reduce tooling
• Reduced set-up times
• Reduced expediting
• Reduced in-process
inventory
• Reduced pert makespan
• Improved human relations
• Improved operator
expertise
Disadvantages:
• Increased capital
investment
• Lower M/C utilization
• Labor resistance (need for
• cross training and
flexibility)
[Prof. Selim Aktürk]
Evaluation of Cell Design Decisions
•
•
•
•
•
•
•
Equipment and tooling investment (low)
Equipment relocation cost (low)
Inter- and intracell material-handling costs (low)
Floor space requirements (low)
Extent to which parts are completed in a cell (high)
Flexibility (high)
Production and scheduling related costs (low)
[Prof. Selim Aktürk]
Assign Machines to Groups
•
•
•
•
•
•
Production Flow Analysis
Binary Ordering Algorithm
Single-Pass Heuristic
Similarity Coefficients
Graph Partitioning
Assign Parts to Machines
[Prof. Selim Aktürk]
Objectives & Constraints
• Cell Independence
* primary objective
L
L
M
D
G
A
P
splitting
Receiving
L
M
L
M
M
G
G
Shipping
Objectives & Constraints
• Cell flexibility
• Internal routing flexibility
• External routing flexibility
• Process flexibility
• Cell system layout (incomplete independence)
L
L
M
D
G
A
Receiving
L
M
L
M
M
G
P
G
Shipping
Objectives & Constraints
• Cell flexibility
• Internal routing flexibility
• External routing flexibility
• Process flexibility
• Cell system layout (incomplete independence)
L
L
M
G
D
Receiving
L
M
L
M
M
G
A
P
G
Shipping
Objectives & Constraints
• Cell layout (within)
• Cell size
•
•
•
•
# of M/Cs or processes
# of M/C / process types
e.g. available space limits on the # of M/Cs in a cell
e.g manned cells
• Additional investment
• Existing M/C clusters broken up and reclustered.
Rearrangement may require additional equipment.
• Utilization levels
• Max (feasible routings)
• Min (economically justify to include the M/C)
To sum up
• Interdependencies and conflicts between these
objectives  Conceptually complex
• NP-Complete [Ballakur]
• Heuristics!
• Structural: link parts and M/C types based on routing
information alone.
• Operational: incorporate demand information, data on
part volume affects M/C util. and, therefore # of M/Cs of
each type req.in the cells.
To sum up
• Cell system and layout or cell layout problem
• Few procedures
• Completely ignored
• Can be dealt with once the part families and cells have
been established.
To sum up
• BUT relative positions of M/Cs in a cell, and
therefore, the materials flow pattern, should be a
controllable factor in the cell formation process.
• CM ‘s one of the foundations of JIT (simplifies internal
flows)
• Flow line cells have the advantages over job shop cells.
reduced mat’l handling
improved visible control of cell act.
easier use of conveyors in cells
more suited for the use of small transfer batches
easier monitoring of I/O flows
Basic Design Methodology:
1st Stage
• Data Collection
• Operation sequence for every part that is to be
processed in the system
• Avg. forecast demand per part
• Estimated processing time for a typical batch of each
part at each M/C type (current batch sizes and setup
times)
• Available equipment of each type
• Cost to acquire additional equipment
Basic Design Methodology:
1st Stage
• M: # of M/C types (i = 1,2,…,12)
• N: # of parts (j = 1,2,…, 19)
Table1 Data for Cell Formulation Problem
Machine Type(i)
1 2
3
4
5
6
7
8
9
10
11 12
No. Avail.
2 1
1
2
1
4
5
1
2
7
3
1
Total Load on
M/C Type
450 96 288 696 240 504 1280 288 468 1170 1080 340
(mins./day)
Basic Design Methodology:1st Stage
Operation
Part(j)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Demand in
Sequence (ORj)
(1,4,8,9)
(1,4,7,4,8,7)
(1,2,4,7,8,9)
(1,4,7,9)
(1,6,10,7,9)
(6,10,7,8,9)
(6,4,8,9)
(3,5,2,6,4,8,9)
(3,5,6,4,8,9)
(4,7,4,8)
(6)
(11,7,12)
(11,12)
(11,7,10)
(1,7,11,10,11,12)
(1,7,11,10,11,12)
(11,7,12)
(6,7,10)
(12)
Batches/day(dj)
2
3
1
3
2
1
2
1
1
2
3
1
1
3
1
2
1
3
2
Basic Design Methodology:
2nd Stage
• Preliminary analysis of the collected data
• Single and Dual Operation Parts
Remove parts which only require processing on two or
less M/C types.  flexibility of allocating loads to cells
1: set of parts after removal of single/dual oper. Parts
(N1)
• Backtracks in Operation Sequences
2: set of parts that have backtracks in their oper. seq.
(N2)
3: set of parts consisting of the parts that have no
backtracks
(N3)
Basic Design Methodology:2nd Stage
Operation
Part(j)
1
 2
3
4
5
6
7
8
9
 10
 11
12
 13
14
 15
 16
17
18
19
Demand in
Sequence (ORj)
(1,4,8,9)
(1,4,7,4,8,7)
(1,2,4,7,8,9)
(1,4,7,9)
(1,6,10,7,9)
(6,10,7,8,9)
(6,4,8,9)
(3,5,2,6,4,8,9)
(3,5,6,4,8,9)
(4,7,4,8)
(6)
(11,7,12)
(11,12)
(11,7,10)
(1,7,11,10,11,12)
(1,7,11,10,11,12)
(11,7,12)
(6,7,10)
(12)
Batches/day(dj)
2
3
1
3
2
1
2
1
1
2
3
1
1
3
1
2
1
3
2
1:
1-10,12, 14-18
2:
2, 10, 15, 16
3:
1, 3-9, 12, 14,
17-18
Basic Design Methodology:
3rd Stage
• Part grouping
• Reduce the problem size by reducing the # of oper.
seq.s involved in the clustering process in Stage 4.
• 2 and 3 are treated separately.
• Step1: part groups, consisting of parts with identical
oper. seq.s are crated.
• Step2: combine these groups if the M/C types req. in
one group includes the M/C types req. in the other and
the M/C types common to both oper. seq.s appear in the
same order.
e.g. OR1= {1, 2, 3 } & OR2 ={1, 2, 4, 3, 5}can be
combined, new oper. seq. is OR2 .
Basic Design Methodology:
3rd Stage
• Part grouping (Continued)
• Criteria to merge groups:
* merge part groups to minimize the # of
non-common M/C types.
* if ties exist, select randomly
• 4: resultant set of groups after applying stage 4
identified from 2 (N4)
• 5: resultant set of groups after applying stage 4
identified from 3 (N5)
Basic Design Methodology:3rd Stage
Operation
Part(j)
1
2
3
4
5
6
7
8
9
10
12
13
14
15
16
17
18
Demand in
Sequence (ORj)
(1,4,8,9)
(1,4,7,4,8,7)
(1,2,4,7,8,9)
(1,4,7,9)
(1,6,10,7,9)
(6,10,7,8,9)
(6,4,8,9)
(3,5,2,6,4,8,9)
(3,5,6,4,8,9)
(4,7,4,8)
(11,7,12)
(11,12)
(11,7,10)
(1,7,11,10,11,12)
(1,7,11,10,11,12)
(11,7,12)
(6,7,10)
Batches/day(dj)
2
3
1
3
2
1
2
1
1
2
1
1
3
1
2
1
3
Basic Design Methodology:3rd Stage
Group r
1
2
Part j
2,10
15,16
ORr2
(1,4,7,4,8,7)
(1,7,11,10,11,12)
Group p
Part j
OR p2
7-9
14
18
12,17
5
6
1,3,4
(3,5,2,6,4,8,9)
(11,7,10)
(6,7,10)
(11,7,12)
(1,6,10,7,9)
(6,10,7,8,9)
(1,2,4,7,8,9)
1
2
3
4
5
6
7
4
5
Basic Design Methodology:3rd Stage
Table 2. Machine Load from Each Part Group (will be used for equip. util.)
Machine Type (i)
Part Group 1 2
3
4
5
6 7
8
9
10 11 12
4-1
36 0 0 480 0
0 60 48 0
0
0
0
2
30 0 0
0 0
0 140 0
0
90 216 60
5-1
0 48 288 108 240 216 0 144 144 0
0
0
2
0 0 0
0 0
0 180 0
0 360 288 0
3
0 0 0
0 0 108 180 0
0 360 0
0
4
0 0 0
0 0
0 300 0
0
0 384 160
5
96 0 0
0 0
72 120 0 72 240 0
0
6
0 0 0
0 0
36 60 24 36 120 0
0
7
288 48 0 108 0
0 240 72 216 0
0
0
Basic Design Methodology:
4th Stage
• Clustering process
•
•
•
•
•
The composite oper. seq.s from stage 3 containing no
backtracks are merged in descending order of similarity.
Stops when the measure of materials flow pattern
exceeds its critical value.
Resulting part groups are called “part families”
Single and dual oper. parts and part groups with
backtracks are then assigned to the part families.
M/Cs are allocated to the part families to form
candidate cells.
Basic Design Methodology:
4th Stage
• Clustering process (continued)
• SOpq : similarity btw part groups ‘p’ & ‘q’
* is used to identify pair of part groups for potential
merging.
* measures the proportion of M/C types used by two
groups ‘p’ & ‘q’ in the same order.
* first part of the index measures for part group ‘p’ and
the second part for ‘q’
* the multiplier .5 is used to standardize this index so
that it has a lower bound of 0 and upper bound of 1.
Basic Design Methodology:4th Stage
•
P
1
2
3
E.g.
ORp2
{1, 6, 10, 7, 9, 8}
{6, 10, 9,2}
{6, 10, 9, 8, 7}
C12: {6, 10, 9}
C13: {6, 10, 7}, {6, 10, 8}, {6, 10, 9}, {6, 10, 9, 8}
C23: {6, 10, 9}
Cpq, not uniquely defined, the set with the largest # of M/Cs is
chosen
Basic Design Methodology:4th Stage
• SO matrix for groups in 5
SO= 1
2
3
4
5
6
7
1
2
3
4
5
6
0
0 0,67 0 0,67 0
0,34 0 0,53 0
0,51 0
0,53 0 0,80 0,62 0
0
0 0,37 0,55
• Combine group 5 & 6.
7
-
Basic Design Methodology:
4th Stage
• Clustering process (continued)
• The composite oper. seq. for the candidate merging
groups, OR2p1+p2 is computed using the heuristic
suggested by Hollier.
• Note: although the resulting oper. seq. does not contain
backtracks, the individual parts included in group
‘p1+p2’ might experience backtracking.
Basic Design Methodology:4th Stage
• Composite oper. seq. [Hollier]
From
1
6
10
7
9
8
1
0
0
0
0
0
Table 3. Travel Chart
To
6 10 7 9 8
2 0 0 0 0
- 3
0 0 0
0 3 0 0
0 0
- 2 1
0 0 0 - 0
0 0
0 1 -
Table 4. A Matrix
To
From 1
6 10
1
2
0
6
-2
3
10
0 -3
7
0
0
-3
9
0
0
0
8
0
0
0
Pos k 0
2
3
Neg k 2
3
3
zk
0
2
3
• OR2(5+6) : {1, 6, 10, 7, 8, 9}
7
0
0
3
-2
-1
3
3
3
9
0
0
0
2
1
3
0
0
8
0
0
0
1
-1
1
1
1
Basic Design Methodology:
4th Stage
• Clustering process (continued)
• The stopping rule in Clustering:
*  is calculated and for each composite oper. seq.and
compared to its critical value
: ratio of the # of backtracks per unit of time to the # of
forward moves of batches per unit of time
*  differs from SOpq by considering the # of batches
per unit time which flow btw equip.
*  is more stringent, but using it while determining the
merging groups req. great computational effort.
Basic Design Methodology:
4th Stage
• Clustering process (continued)
• The stopping rule in Clustering:
* Therefore:
To identify candidates for merging SOpq is used.
The flow parameter  is used to approve or
disapprove the merger of the candidate groups.
• The merging terminates when all SOs are 0.
• The parts associated with each final part group are
referred to as a part family.
Basic Design Methodology:4th Stage
• The flow parameter  is calculated for the
composite oper. seq. 5+6.
Table 5. Modified Travel Chart
To
From In 1
6 10 7
In
- 2
1
0
0
1
0
2
0 0
6
0 0
3 0
10
0 0 0
3
7
0 0
0
0
8
0 0
0
0
0
9
0 0
0
0
0
Out
0
0 0
0 0
8
0
0
0
0
1
0
0
9
0
0
0
0
2
1
0
Out
0  =
(5+6)
0 0/(2+2+3+3+1+1+3)
0
0 Merge 5 & 6
0
0
3
-
Basic Design Methodology:4th Stage
• OR25 = {1, 6, 10, 7, 8, 9}; OR26 = {0};
SO6p=0 for p = {1, 2,…, 7}
• Several more iterations are carried out and:
• Family1: 1, 3-9 with OR13= {1, 3, 5, 2, 6, 10, 4, 7, 8, 9}
• Family2: 12-14, 17-18 with OR13= {11, 6, 7, 10,12}
Table 6. Loads on Machine Types from Part Families 1 and 2
Machine Types (i)
Part Family (f) 1
2
3
4
5
6
7
8
9
1
384 96 288 216 240 324 420 240 468
2
0
0
0
0
0 108 660 0
0
10
360
720
11
0
672
12
0
160
Basic Design Methodology:
4th Stage
• Clustering process (continued)
• Allocation of single and dual oper. parts s.t.
* the composite oper. Seq. for the family contains the
M/C req. to process part.
* the load on the M/C type in this family’s oper. seq.
is the lowest among all oper. seq.s in which the M/C
types occur.
Basic Design Methodology:4th Stage
• Parts 11 (6), 19 (12) and 13 (11, 12) are the single-dual
oper. parts.
• The load on M/C 6 to process part 11 is 72 min. (daily)
• The load on M/C 12 to process part 19 is 40 min . (daily)
• The load on M/C 11 & 12 to process part 13 is 192 min. &
80 min. (daily)
• Part 11 could be allocated to both family 1 or 2.
* since M/C type 6 is in these two families.
* but allocated to family 2 since the total load on the
same M/C type 6 in this family is < the total load on the
same M/C type in family 1. (108 vs. 324)
• Parts 13 and 19 are allocated to family 2 since M/C types
11 and 12 are only included in OR23
Basic Design Methodology:
4th Stage
• Clustering process (continued)
• Allocation of part groups with backtracks (4) s.t.
* the M/Cs included in the oper seq. of part group
with backtracks are also included in the oper. seq. of
family group
* flow value is not violated. (composite oper seq. for
the combined group of parts is computed)
* a separate family F1- Remainder Cell- is created
from 4 which cannot be allocated to any of the
families identified (composite oper seq. is specified by
Hollier’s heuristic)
Basic Design Methodology:4th Stage
Group r
1
2
Part j
2,10
15,16
4
ORr2
(1,4,7,4,8,7)
(1,7,11,10,11,12)
• Since the allocation of these part groups to any of
the part families violate the critical , a separate
family is created.
• OR33 = {1, 11, 4, 8, 10, 7, 12}
Table 7. Load on Machine Types from Part Family 3
Machine Types (i)
Part Family (f) 1
2
3
4
5
6
7
3
66 0
0
480 0
0
200
8
48
9
0
10
90
11
216
12
60
Basic Design Methodology:
4th Stage
• Candidate cells are created
• Each family is allocated to a separate cell
• c: index of the cells
• Unconstrained allocation of equipment to each
candidate cell to ensure load feasibility
• mic: # of M/Cs of type ‘i’ allocated to cell ‘c’
• no-load cell: M/Cs originally available in the system
that have not been allocated to any of the cells
identified.
Basic Design Methodology:4th Stage
Table 8. Candidate Cells
Parts
Machine Number
Cell Included
Type
Allocated
1
1,3-9
1
1
3
1
5
1
2
1
6
1
10
1
4
1
7
2
8
1
9
2
2 11-14,17-19
11
3
6
1
7
2
10
2
12
1
3 2,10,15,16
1
1
11
1
4
2
8
1
10
1
7
1
12
1
4
None
6
2
10
3
Av. Utilization
per machine(%)
80,00
60,00
50,00
20,00
67,50
75,00
45,00
43,75
50,00
48,75
60,00
37,50
68,75
75,00
58,33
13,75
45,00
50,00
10,00
18,75
41,67
12,50
0,00
0,00
•
•
•
•
•
Ai = 480 min/day, Ui = .8
4 candidate cells (1 no-load)
IN: receiving
OUT: shipping
Fig3
Extensions
• Additional restrictions
• The utilization of cell equip. must be above an
acceptable level.
• The cell flexibility must exceed a certain level
and so on…
• Can be imposed in different ways
• Successively relax the critical  and generate new
solutions
• Perturb the candidate cell system solution (intracell
mov. Instead of intercell ones)
Summary & Conclusions
• Cell design method using a clustering.
• SOpq index to deal with similarity (1st in the literature)
• Consider the within-cell M/C seq. in the cell formation
• Can create alternative solutions by selecting different
values of  or by imposing constraints wrt investment,
utilization or cell size.
• Future research to investigate the impact on the
candidate cell solution
• From imposing constraints on the design process.
• Additional stopping rules.