designing a cellular manufacturing system: a materials flow approach based on operation sequences by...

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)


Assign Machines to Groups

• Production Flow Analysis• Binary Ordering Algorithm• Single-Pass Heuristic• Similarity Coefficients• Graph Partitioning • Assign Parts to Machines


Objectives & Constraints• Cell Independence

* primary objective

Receiving

Shipping

L

A

L M D G

L M G G

L MM

Psplitting

Objectives & Constraints• Cell flexibility

• Internal routing flexibility

• External routing flexibility

• Process flexibility

• Cell system layout (incomplete independence)

Receiving

Shipping

L

A

L M D G

L M G G

L MM

P

Objectives & Constraints• Cell flexibility

• Internal routing flexibility

• External routing flexibility

• Process flexibility

• Cell system layout (incomplete independence)

Receiving

Shipping

L

A

L M

D

G

L M G G

L MM

P

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 handlingimproved visible control of cell act.easier use of conveyors in cellsmore suited for the use of small transfer batcheseasier 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 12No. Avail. 2 1 1 2 1 4 5 1 2 7 3 1Total Load on M/C Type 450 96 288 696 240 504 1280 288 468 1170 1080 340(mins./day)

Basic Design Methodology:1st StageOperation Demand in Part(j) Sequence (ORj) Batches/day(dj)

1 (1,4,8,9) 2 2 (1,4,7,4,8,7) 3 3 (1,2,4,7,8,9) 1 4 (1,4,7,9) 3 5 (1,6,10,7,9) 2 6 (6,10,7,8,9) 1 7 (6,4,8,9) 2 8 (3,5,2,6,4,8,9) 1 9 (3,5,6,4,8,9) 1 10 (4,7,4,8) 2 11 (6) 3 12 (11,7,12) 1 13 (11,12) 1 14 (11,7,10) 3 15 (1,7,11,10,11,12) 1 16 (1,7,11,10,11,12) 2 17 (11,7,12) 1 18 (6,7,10) 3 19 (12) 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 StageOperation Demand in Part(j) Sequence (ORj) Batches/day(dj)

1 (1,4,8,9) 2 2 (1,4,7,4,8,7) 3 3 (1,2,4,7,8,9) 1 4 (1,4,7,9) 3 5 (1,6,10,7,9) 2 6 (6,10,7,8,9) 1 7 (6,4,8,9) 2 8 (3,5,2,6,4,8,9) 1 9 (3,5,6,4,8,9) 1 10 (4,7,4,8) 2 11 (6) 3 12 (11,7,12) 1 13 (11,12) 1 14 (11,7,10) 3 15 (1,7,11,10,11,12) 1 16 (1,7,11,10,11,12) 2 17 (11,7,12) 1 18 (6,7,10) 319 (12) 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 StageOperation Demand in Part(j) Sequence (ORj) Batches/day(dj)

1 (1,4,8,9) 2 2 (1,4,7,4,8,7) 3 3 (1,2,4,7,8,9) 1 4 (1,4,7,9) 3 5 (1,6,10,7,9) 2 6 (6,10,7,8,9) 1 7 (6,4,8,9) 2 8 (3,5,2,6,4,8,9) 1 9 (3,5,6,4,8,9) 1 10 (4,7,4,8) 2 12 (11,7,12) 1 13 (11,12) 1 14 (11,7,10) 3 15 (1,7,11,10,11,12) 1 16 (1,7,11,10,11,12) 2 17 (11,7,12) 1 18 (6,7,10) 3

Basic Design Methodology:3rd Stage

Group r Part j ORr2 4

1 2,10 (1,4,7,4,8,7) 2 15,16 (1,7,11,10,11,12)

Group p Part j OR p2 5

1 7-9 (3,5,2,6,4,8,9) 2 14 (11,7,10) 3 18 (6,7,10) 4 12,17 (11,7,12) 5 5 (1,6,10,7,9) 6 6 (6,10,7,8,9) 7 1,3,4 (1,2,4,7,8,9)

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 90 216 605-1 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.


• 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

• E.g.P ORp

2

1 {1, 6, 10, 7, 9, 8}2 {6, 10, 9,2}3 {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


• SO matrix for groups in 5

1 2 3 4 5 6 7SO= 1 - 2 0 - 3 0 0,67 - 4 0 0,67 0 - 5 0,34 0 0,53 0 - 6 0,51 0 0,53 0 0,80 - 7 0,62 0 0 0 0,37 0,55 -

• Combine group 5 & 6.


• 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.


• Composite oper. seq. [Hollier]

Table 3. Travel Chart ToFrom 1 6 10 7 9 8 1 - 2 0 0 0 0 6 0 - 3 0 0 0 10 0 0 - 3 0 0 7 0 0 0 - 2 1 9 0 0 0 0 - 0 8 0 0 0 0 1 -

Table 4. A Matrix ToFrom 1 6 10 7 9 8 1 - 2 0 0 0 0 6 -2 - 3 0 0 0 10 0 -3 - 3 0 0 7 0 0 -3 - 2 1 9 0 0 0 -2 - -1 8 0 0 0 -1 1 -Pos k 0 2 3 3 3 1

Neg k 2 3 3 3 0 1

zk 0 2 3 3 0 1

• OR2(5+6) : {1, 6, 10, 7, 8, 9}


• 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.


• 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.


• The flow parameter is calculated for the composite oper. seq. 5+6.

Table 5. Modified Travel Chart ToFrom In 1 6 10 7 8 9 Out In - 2 1 0 0 0 0 0 1 0 - 2 0 0 0 0 0 6 0 0 - 3 0 0 0 0 10 0 0 0 - 3 0 0 0 7 0 0 0 0 - 1 2 0 8 0 0 0 0 0 - 1 0 9 0 0 0 0 0 0 - 3 Out 0 0 0 0 0 0 0 -

(5+6)= 0/(2+2+3+3+1+1+3)

Merge 5 & 6


• OR25 = {1, 6, 10, 7, 8, 9}; OR2

6 = {0};

SO6p=0 for p = {1, 2,…, 7}

• Several more iterations are carried out and:• Family1: 1, 3-9 with OR1

3= {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 2Machine Types (i)

Part Family (f) 1 2 3 4 5 6 7 8 9 10 11 12 1 384 96 288 216 240 324 420 240 468 360 0 0 2 0 0 0 0 0 108 660 0 0 720 672 160


• 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 OR2

3


• 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)


• 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}

Group r Part j ORr2 4

1 2,10 (1,4,7,4,8,7) 2 15,16 (1,7,11,10,11,12)

Table 7. Load on Machine Types from Part Family 3Machine Types (i)

Part Family (f) 1 2 3 4 5 6 7 8 9 10 11 12 3 66 0 0 480 0 0 200 48 0 90 216 60


• 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.


• Ai = 480 min/day, Ui = .8• 4 candidate cells (1 no-load)• IN: receiving• OUT: shipping• Fig3

Table 8. Candidate Cells Parts Machine Number Av. UtilizationCell Included Type Allocated per machine(%) 1 1,3-9 1 1 80,00

3 1 60,00 5 1 50,00

2 1 20,00 6 1 67,50 10 1 75,00 4 1 45,00 7 2 43,75 8 1 50,00 9 2 48,75 2 11-14,17-19 11 3 60,00 6 1 37,50 7 2 68,75 10 2 75,00 12 1 58,33 3 2,10,15,16 1 1 13,75 11 1 45,00 4 2 50,00 8 1 10,00 10 1 18,75 7 1 41,67 12 1 12,50 4 None 6 2 0,00 10 3 0,00

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.

designing a cellular manufacturing system: a materials flow approach based on operation sequences by...

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