Perancangan Tata Letak Fasilitas
- Design or Optimization?
Perancangan Tata Letak Fasilitas www.aeunike.ub.ac.id
Layout Problems
Aesthetics Aesthetics Aesthetics Aesthetics
Aesthetics Aesthetics Aesthetics Aesthetics Aesthetics Facility Layout Process
- Combination of art and
engineering
- Many techniques available
- – Muther’s SLP Approach (1973)
- – Optimization based approaches
- Phase I - Determination of the location of the
5. Space Available
Source: John S. Usher class notes Systematic Layout Planning
10. Evaluation
A
N
A
LY
ZE
S
E
A
R
C
H
S
E
L
E
C
T
9. Develop Layout Alternatives
7. Modifying Considerations
8. Practical Limitations
3. Relationship Chart
4. Space Requirements
6. Space Relationship Diagram
2. Activity Relationships
1. Flow of materials
Systematic Layout Planning Input Data and Activities
- Phase II - Establishing the general overall
layout
area where departments are to be laid out
Systematic Layout Planning
- Phase III - Establishing detailed layout plans
- Phase IV - Installing the selected layout
- P Product: Types of products to be produced
- Q Quantity: Volume of each part type
- R Routing: Operation sequence for each part type
- S Services: Support services, locker rooms, inspection stations, and so on
- T Timing: When are the part types to be produced? What machines will be used during this time period?
SLP SLP
COPYRIGHT 2005. RICHARD MUTHER & ASSOCIATES – SLP OVERVIEW
5 COPYRIGHT 2005. RICHARD MUTHER & ASSOCIATES – SLP OVERVIEW
Packaging Ruang Assembly
1 Lantai 2 : Office Room Jalan
6
Office
6
1
6
5
2 Power Entry
2
2 Tool Cabinet
R a k Rak
down
MQC
MQC P P P P P P
4 2,5
Daerah Pengiriman
Ruang Perkakas
Sample relationship diagram
3 m 3 m 4 m 4 m 3 m 3 m 3 m 2.5 m 2.5 m 2 m 6 m 2 m 4 m 3 m 2 m 4.5 m 4.5 m 6 m
Up Elevator
Ruang Kesehatan
Ruang Ganti Wanita Ruang Ganti Pria L P
Toilet Pria Toilet Wanita
T. Wudhu Pria T. Wudhu Wanita
Mushollah Pria Mushollah Wanita 1.0e-2 m. x 1.0e-2 m.
1.0e-2 m. x 1.0e-2 m. 1.0e-2 m. x 1.0e-2 m.
Kantin
Ruang Receptionist Pos Satpam
3
9
5
1.0e-2 m. x 1.0e-2 m. Parkir Mobil
1
2
4
3
Level 0 (Overall Layout) DIRECTOR ROOM MEETING ROOM
Level 1 Detail Layout
1 Lantai 2 : Office Room
3
4 2,5
5
6
1
6
5
9
3
4
5
4
4
6
1
1
4
4
5
4
3
B B A D D A A REST AREA Jalan Raya Rungkut Industri 18 m
PLANT KANTOR
FP FP FP FP FP FP
Parkir Sepeda Motor
8
4
Office Office
1
1
4
4
6
1
6
5
7
KM ( WANITA)
KM ( PRIA)
PRIA MARKETING MANAGER PRODUCTION MANAGER R & D MANAGER HRD MANAGER ADMINISTRATION AND FINANCE MANAGER LOGISTICS WANITA MUSHOLLA TEMPAT WUDHU STAF MARKETING STAF OF ADMINISTRATIO N AND FINANCE TEMPAT WUDHU
down
6 SECRETARY RECEPTIONIST
INSPECTION STAFF & OPERATOR OF PRODUCTION ENGINEER, OPERATOR AND STAFF OF MAINTENANCE’S
4
8
Jalan Jalan
PUNCH 25 TON
24 m 4 m Receiving Area Delivering Area 14 m
Raw Material Storage Warehouse
8 m 6 m Daerah Penerimaan
Press machine Ruang Supply Mesin
PARKIR DIRECTOR ROOM MEETING ROOM
INSPECTION STAFF & OPERATOR OF PRODUCTION ENGINEER, OPERATOR AND STAFF OF MAINTENANCE’S
6 SECRETARY RECEPTIONIST
PRIA MARKETING MANAGER PRODUCTION MANAGER R & D MANAGER HRD MANAGER ADMINISTRATION AND FINANCE MANAGER LOGISTICS WANITA MUSHOLLA TEMPAT WUDHU STAF MARKETING STAF OF ADMINISTRATION AND FINANCE TEMPAT WUDHU
1
KM ( PRIA)
KM ( WANITA)
Forming machine
Rolling machine Welding machine
Injection molding Grinding machine
Cutting machine x y x y x y x y x y x y x y x y x y
7
5
MQC
4.5 m 4.5 m 6 m
Detail Layout R ECEPT
Jalan Office
8 m 6 m Daerah Penerimaan Daerah Pengiriman
Level 1
Detail Layout
Level 2
Detail Layout
FP FP FP FP FP FP
STAF O F AD MINISTRAT
IO N AND FI NANC E
7
ST A F MA R K ETIN G
6
5 Level 2
PUNCH 25 TON
IST
IO N
5
6
1 ENGI N EER , O PERA TO R AN D ST AF F OF MA
INTE NA NC E’ S
6
Detail Layout
4
5
4 MEETING ROOM
6
4 0,52
STA FF & OPER A TOR OF PR O D U C TIO N
4 m 3 m 2 m
4 m Receiving Area
Delivering Area 14 m 3 m 3 m 4 m 4 m 3 m 3 m 3 m 2.5 m 2.5 m 2 m 6 m 2 m
Press machine Ruang Supply Mesin
Office
Cutting machine x y x y x y x y x y x y x y x y x y
Injection molding Grinding machine
Rolling machine Welding machine
Forming machine
2 Power Entry
2
2 Tool Cabinet
R a k
Rak
MQC
Packaging Ruang Assembly
MQC P P P P P P
Ruang Perkakas
B B A D D A A REST AREA 18 m 24 m
MQC
Raw Material Storage Warehouse
Up Elevator
Ruang Kesehatan
Ruang Ganti Wanita Ruang Ganti Pria L P
Toilet Pria Toilet Wanita
T. Wudhu Pria T. Wudhu Wanita
Mushollah Pria Mushollah Wanita 1.0e-2 m. x 1.0e-2 m. 1.0e-2 m. x 1.0e-2 m. 1.0e-2 m. x 1.0e-2 m.
Kantin
Ruang Receptionist Pos Satpam
Jalan Jalan
1.0e-2 m. x 1.0e-2 m.
Parkir Mobil Parkir Sepeda Motor
6
TEMPAT WUDHU TEMPAT WUDHU
Operations Review
6 Special Considerations in Office Layout
4 KM PRIA KM WANITA PRIA WANITA MUSHOLLA
4 Level 2
- Is the company outgrowing available space?
- Is the available space too expensive?
- Is the current building not in the proper location?
- How will a new office layout affect the organization?
- Are office operations too centralized or decentralized?
- Does the office structure support the strategic plan?
- Is the office layout in tune with the company's image?<
- Minimizing distance traveled by employees
- Permitting flexibility so that the current layout can be changed, expanded or downsized easily
- Providing a safe and pleasant atmosphere for people to work in
- Minimizing capital and operational costs of the facility
Cubicles layout Albany International Airport layout
Operations Review for MortAmerica, Inc.SLP for MortAmerica, Inc.
- Is there a significant increase in mortgage lending operat
- Evaluation
of MortAmerica, Inc.?
- Are the costs of leasing and refurbishing interior space too • Planning h>Site selec
- Is there a problem with the current location? For example:
- – There is not enough space for expansion
- Design and layout
- – Major attorneys’ offices, other related financial institutions and restaurants, are not located within a reasonable distance of MortAmerica, Inc.
- – Adequate parking space is not available
- – Traffic is too congested
- Will a change in office location improve business?
Current and Future Space Requirements SLP for MortAmerica, Inc.
Department Name Current/Future Categories of Employees and Number in Each Category Requirements Senior Senior Staff Clerical/Secretary Net Gross Executive Staff Space Space, Required 150%
- Review current space utilization
of Net Space Current space/employee 150 100
75 Number of employees
1
4
1 Current total 150 400 75 625 938
- Determine space projections
Customer Service (CS) space/category Future space/employee 120
75 Number of employees
6
1 Future space/category 720 75 795 1,193
- Determine level of interaction between Current space/employee 200 100
75 Number of employees
2
10
2 Current total 400 1,000 150 1,550 2,325 Mortgage processing/marketing space/category departments
(MP/M) Future space/employee 250 200 100
75 Number of employees
1
1
15
1 Future space/category 250 200 1,500 75 2,025 3,038 Current space/employee 100
75 Number of employees
10
1
- Identifying special consideration
Current total 1,000 75 1,075 1,613 Credit check (CC) space/category Future space/employee
80 Number of employees
5 Future space/category 400 400 600 Current space/employee 200 100
90
75 Number of employees
2
4
15
5 Current total 400 400 1,350 375 2,525 3,788 Operations Audit (O/A) space/category Future space/employee 250 100 100
75 Number of employees
3
4
20
2 Future space/category 750 400 2,000 150 3,300 4,950 Current space/employee 250 200 100 Top management (TM) Number of employees
5
2
5 Current total 1,250 400 500 2,150 3,225 space/category Future space/employee 250 200 100 Current and Future Space Requirements Relationship diagram for MortAmerica, Inc.
Customer service (CS) Current net Current gross space150% of Future gross space 150% of
Support service area Future net space E space net space net space
Mortgage processing (MP)
I E
I O Credit check (CC) E
O Copying/Printing Area (C/P) 300 450 465 700
I I
I Closing/underwriting (C/U) O E
I I O
I A File Storage Room (FS)
Top Management (TM)
I O
I 300 450 80 120
I U A O
I I
X U O Operations/audit (O/A) U
U O U U A Customer Waiting Lounge (CW) 300 450 800 1200
I U U
X O Copying/printing (C/P) A
U O U A U
I U Files storage (FS) O U
Conference Rooms (CR) 500 750 1000 1500 U
I I U U
X Customer waiting (CW) U U U
Employee Break Room (EBR) A 200 300 850 1275
U Conference room (CR)
X X A Employee break room (EBR)
X Rest Rooms (RR) 200 300 500 750
I Rest rooms (RR) Total 1800 2700 3695 5545
Activity relationship diagram for Space relationship diagram for MortAmerica, Inc. MortAmerica, Inc.
TM TM CC
CC MP MP
O/A O/A
RR RR
C/U C/U
CS CS CW CW
FS FS CR CR C/P EBR
C/P EBR
Pre-architectural layout for MortAmerica, Engineering design approach Inc.
TM
1. Identify the problem
2. Gather the required data CC MP
3. Formulate a model for the problem RR RR
O/A
M W C/U
4. Develop an algorithm for the model and solve it CS CW
5. Generate alternative solutions, evaluate, and select FS CR EBR
C/P
7. Implement the solution
8. Continuously review after implementation
- 1 per 200
1 per room 1 per room - 1 service sink Dormitories 1 per 8 1 per 10 1 per 10 1 per 100 1 service sink
3. Hybrid (composite) algorithms; algorithms that
the starting solution and evaluate the resulting modified solution. If it is better, the modification is made permanent. If not, the systematic modification is continued until it is n longer possible to produce better solutions
2. Improvement algorithms; systematically modify
empty layout, they add one department (or a set of departments) after another until all the departments are included in the layout
1. Construction algorithms: starting with an
Introduction (2)
Basic Algorithms for The Layout Problem Introduction (1)
Hospitals 1 per 15 1 per room 1 per room 1 per 100 1 service sink Prisons 1 per 15 1 per cell 1 per cell 1 per 100 1 service sink Hotels 1 per room
411 1 per 100 1 per 100 1 per 1000 1 service sink
Schools - 1 per 50 1 per 50 1 per 100 1 service sink Airports - 1 per 750 1 per 500 1 per 1000 1 service sink Factories Section
Churches - 1 per 200 1 per 150 (male); 1 per 75 (female) 1 per 1000 1 service sink
(male); 1 per 150 (female) 1 per 120 (male); 1 per 60 (female) 1 per 1000 1 service sink
Others Restaurants - 1 per 200 1 per 75 1 per 500 1service sink Arenas (capacity more than 3000)
Organization Showers Lavatories Water Closets Water Fountain
OSHA, ADA and Local Codes OSHA, ADA and Local Codes Service and Manufacturing Facilities
- The heuristic algorithms are devided into tree classes:
- A model by itself does not provide a solution to a problem, however, algorithms or solution techniques have to be developed to solve model
- An algorithm is a step-by-step procedure that finds a solution to a model, and hence to the problem, in a finite number of steps
- A number of algorithm have been proposed and these may be classified as: (a) Optimal algoritms and (b) Heuristic algorithms
- All optimal algorithms developed for the layout problem require extremly high memory and computational time, and they increase exponentially as the problem size increases.
use two or more types of solution techniques
- Starting with an empty layout, they add one department (or a set a departments) after another until all the departments are included in the layout
- Tha main difference among the various construction algorithms relate to the criteria used to determine the:
- – quantitative flow data
- – maximizing an adjacency score
- – First department to enter the layout
- – Subsequent department or departments added to the layout
- – Location of the first and subsequent departments in the layout
- – continuous representation
- – layout construction
- Example: Modified Spanning Tree Algorithm for Single-row Layout Problem, Graph Theoritic Approach
- 0.5(l
- l
- Consider multirow layout problem in which the departments are all squeres with equal area.
- Assume that the number of departments in every row and column is equal to m and n
- The number of location in which the departments will be located is also equl to mn and is known
- 2-Opt algorithm is used to solve the same model (QAP or
1
. . . mn . . . . m+1 m+2 . .
ABSModel 2) heuristically
2-Opt Algorithm
Modified Spanning Tree (MST) Modified Spanning Tree (MST)
= - Step 4: Repeat step 3 until all machine are connected. The sequence of machines obtained determines the arragement of machines
= f’ j*i*
] and set j*=l. Set f’ i*j*
] and set i*=k. otherwise, connect l to j*, remove row j*, column j* from matrix [f’ ij
, connect k to i*, remove row i*, column i* from matrix [f ij
≥ f’ j*l
]. If f’ i*k
, f’ j*l in row i*, j* of matrix [f’ ij
Denote this pair of i, j, as i*, j*. Connect machines i*, j*. Set f’ i*j* = -
Step 3: Find the largest element f’ i*k
j )) Step 2: Find the largest element in [f’ ij ], and the corresponding i, j.
i
) (d ij
= (f ij
] where f’ ij
, compute an adjacency weight matrix [f’ ij
Modified Spanning Tree (MST) Step 1: Given the flow matrix [f ij ], clearance matrix [d ij ] and machine lengths l i
Construction Algorithms • Construction algorithms generate a facility layout from scratch.
Their primary function; layout improvement
Format they use for layout representation; discrete
Objective functions; minimizing of the sum of flows time distance
Type of input data; qualitative flow data
Algorithmic Approaches Layout algorithms can be classified according to:
2 … m
2-Opt Algorithm 2-Opt Algorithm
Step 1: Let S be the initial solution provided by the user and z its OFV. Set i=1; j=i+1=2 Step 2: Consider the exchange between the position of department i and j in the solution S. If the exchange results in a solution S’ that has an OFV z’<z, set z=z’ and S=S’. If j<mn, set j=j+1; otherwise, set i=i+1, j=i+1. If i<mn, repeat step 2; otherwise, go to step 3
Step 3: If set S=S*, z=z*, i=1, j=i+1=2 and go to step 2.
1(2) 2(1) 1(2)
Otherwise, return S* as the best solution to the user. Stop
3-Opt Algorithm 3-Opt Algorithm
Step 1: Let S be the initial solution provided by the user and
- The 3-Opt algorithm is similar to the 2-Opt algorithm z its OFV. Set S*=S, z*=z, i=1; j=i+1; k=j+1 except that is considers exchanging the position of three departments at a time. Step 2: Consider changing the position of department i to that of j, j to that of k, and k to that of i,
- If the layout problem with mn departments, 2-Opt simultaneously. If the resulting solution S’ has OFV consider mn(mn-1)/2 pairwise exchange for each layout z’<z, set z*=z’ and S*=S’.
and 3-Opt considers (mn)!/[(mn-3)!3!] exchange.
Step 3: If k<mn, set k=k+1, and repeat step 2. Otherwise,
- Because we are searching and evaluating more layouts in set j=j+1 and check if j<mn-1.
3-Opt than in 2-Opt, 3-Opt should yield better results, but it also takes significantly more computation time If j<mn-1, set k=j+1, and repeat step 2. Otherwise, set i=i+1, j=i+1, k=j+1, and check if i<mn-2. If i<mn-2, repeat step 2. Otherwise, go to step 4
Step 4: If set S=S*, z=z*, i=1, j=i+k, k=j+1 and go to step
2. Otherwise, return S* as the best solution to the user. Stop
Modified Penalty Algorithm Modified Penalty Algorithm
- MP algorithm involve transforming the contrained • The constrained model is transformed into an
ABSModels into an unconstrained one using the penalty unconstrained model using penalty parameters ,
1
2 method.
dan
3
- The square of each constraint is multiplied by a penalty
Minimize c x c x c x
n n
11
11
12
12
3
3
parameter and placed in the objective function
b a x a x a x
max , n n
1
1
11
11
12
12
1 1 Minimize c x c x c x
n n
11
11
12
12
3
3
2 a x a x a x b
max ,
n n
2
21
21
22
22
2
2
n n
2 Subject to a x a x a x b
11
11
12
12
1
1
1
2
a x a x a x b
max , n n a x a x a x b 3
21
21
22
22
2
2 3
n n
21
21
22
22
2
2
2 a x a x a x b
n n
31
31
32
32
3
3
3 x x x
, , , n
21
22
3 Modified Penalty Algorithm
Step 0: Obtain values for from the user. Set S=initial solution vector and z=corresponding OFV Step 1: Transform the constrained model into an unconstrained one Step 2: Solve the unconstrained minimization model using the Powel algorithm. If the OFV of the resulting solution is less than or equal to z, set S*=new solution vector and z*=OFV corresponding to S*
10
=10(1) + 15(1) + 20(2) + 10(2) + 5(3) + 5(1) = 105
TC 2134
Since all departments areas are assumed to be of equal size, the feasible exchanges of iteration 1 are 1-2, 1-3, 1-4, 2-3, 2-4, and 3-4 Select the pair 1-3 and perform the exchange in the layout
Step 3: Modify solution vector S* so that a feasible solution obained Step 4: Improve the solution using greedy 2-Opt. Stop
5
3
5
10
2
20
15
1
=10(1) + 15(2) + 20(1) + 10(1) + 5(2) + 5(3) = 95 TC
4
3
2
1
4 Pairwise Exchange Method (2) To From
3
2
1
The existing layout is shown
Example: Consider 4 department of equal size.
Pairwise Exchange Method (1) It is an improvement-type layout algorithm Its implementation with unequal-area departments will be shown later via CRAFT, MULTIPLE
TC 3214
4 The objective function value for the existing layout:
4231
TC 2134
Pairwise Exchange Method (5)
Since the lowest total cost is 95, which worse than the total cost value of 90 in the second iteration, the procedure terminated. The final layout arrangement is 2-3-1-4
TC 3214
=10(1) + 15(2) + 20(1) + 10(1) + 5(2) + 5(3) = 95 TC
1324
=10(2) + 15(1) + 20(3) + 10(1) + 5(1) + 5(2) = 120
TC 3421
=10(1) + 15(3) + 20(2) + 10(2) + 5(1) + 5(1) = 125
=10(1) + 15(1) + 20(2) + 10(2) + 5(3) + 5(1) = 105
TC 4213
TC 3142
=10(2) + 15(1) + 20(1) + 10(3) + 5(1) + 5(2) = 100
TC 4123
=10(1) + 15(2) + 20(1) + 10(1) + 5(2) + 5(3) = 95
2
3
1
4
=10(1) + 15(1) + 20(1) + 10(2) + 5(1) + 5(2) = 105
=10(1) + 15(2) + 20(1) + 10(3) + 5(2) + 5(2) = 105
=10(2) + 15(1) + 20(3) + 10(1) + 5(1) + 5(2) = 120
TC 3124
TC 1324
=10(2) + 15(1) + 20(3) + 10(1) + 5(1) + 5(2) = 120
TC 1432
=10(3) + 15(2) + 20(2) + 10(1) + 5(2) + 5(1) = 105
TC 1243
TC 1234 =10(1) + 15(2) + 20(3) + 10(1) + 5(2) + 5(1) = 125 Pairwise Exchange Method (3)
Pairwise Exchange Method (4)
For the next iteration, we consider all feasible exchange which consist of the same set as in iteration 1 The pair 2-3 is selected with a total cost value of 90. Continuing on, the third iteration
=10(1) + 15(1) + 20(2) + 10(1) + 5(1) + 5(3) = 95
3412
TC 1234
=10(1) + 15(2) + 20(3) + 10(1) + 5(2) + 5(1) = 125
TC 3241
=10(2) + 15(1) + 20(3) + 10(1) + 5(1) + 5(2) = 120
TC 1324
=10(2) + 15(3) + 20(1) + 10(1) + 5(1) + 5(2) = 110
TC 2314
=10(2) + 15(1) + 20(1) + 10(1) + 5(3) + 5(2) = 90 TC
=10(1) + 15(3) + 20(2) + 10(2) + 5(1) + 5(1) = 125
Pairwise Exchange Method (6) Graph-based Method (1)
The pairwise exchange procedure is not guaranted to The graph-based method is a construction-type layout yield the optimal layout solution because the final outcome algorithm (its root graph theory) is dependent on the initial layout, that is, a different initial layout can result in another solution (local optimality)
It is often used with an adjacency-based objective It may have observed that it is possible to cycle back to
To find a maximally weighted block layout is equivalent to one of the alternative layout arrangements from a previous iteration obtaining an adjacency graph with the maximum sum of
It can be easily accomplished only if the pair of arc weights departments considered are of equal size
Graph-based Method (3) Graph-based Method (2) Procedure Step 1 : Select department pair with the largest weight.
Ties, if any, are broken arbitrarily Step 2 : Select the third department to enter. The third department is selected based on the sum of the weights with respect to selected departments in Step 1
Step 3 : Pick the fourth department to enter by evaluating the value of adding one of the unassigned departments represented by a node on a face of the graph. A face of a graph is a bounded region of a graph
Graph-based Method (5) Graph-based Method (4) Step 4 : The remaining task is to determine on which face to insert the remaining department. The optimal solution can be found with a minimum total sum of arch weights
Step 5 : Having determined an adjacency graph, the final step is to construct a corresponding block layout. A block layout based on the final adjacency graph is made. The manner by which we constructed the block layout is analogous to the SLP method. We should note that in constructing the block layout, the original department shapes had to be altered significantly in order to satisfy the requirements of the adjacency graph Graph-based Method (6) Graph-based Method (7)
CRAFT Computerized Relative Allocation of Facilities
Technique (Armour, Buffa, and Vollman, 1963) Input data : from
- – to chart An improvement-type layout algorithm Departments represented in a discrete fashion It begins by determining the centroids of the departments in the initial layout, then calculates the rectilinear distance between pairs of department centroids and stores values in a distance matrix CRAFT next considers all-possible two-way (pairwise) or three-way department exchanges and
identifies the best exchange ( maximal reduction in layout cost) CRAFT
The next iteration starts with CRAFT once again identifying the best exchange by considering all- possible two-way or three-way exchanges in the (update) layout. The process continuous until no further reduction in layout cost can be obtained The final layout obtained in such a manner is also known as a two-opt (three-opt) layout
CRAFT Initial CRAFT Layout (z = 2974 x 20 = 59,480 units)
Intermidiate CRAFT Layout (z = 2953 x 20 = 59,060 units) Final CRAFT Layout (z = 2833.50 x 20 = 56,670 units)
Final “massaged” layout obtained with CRAFT BLOCPLAN Departments arranged in bands which the number of bands is determined by the program and limited to two or three bands All the departments are rectangular in shape
Input data: a relationship chart anda a from-to chart, the two charts can be used only one at a time when evaluating a layout Layout cost can be measured either by the distance-based objective or the adjacency-based objective
BLOCPLAN uses the continuous representation BLOCPLAN may be used both as a construction algorithm and an improvement algorithm
LOGIC Layout Optimization with Guillotine Induced Cuts (Tam, 1991) Input data: a from-to chart The layout is represented in a continuous fashion A construction and improvement algorithm LOGIC is based on dividing the building into smaller and smaller portions by executing successive “guillotine” cuts (straight lines that run from one end of the building to the other). Each cut is either a vertical cut or a horizontal cut
LOGIC LOGIC
LOGIC
Facilities Planning (4th Ed.). New York: Wiley.
=4, A
CRC Press.
REFERENCES • Heragu, S. (2008). Facilities Design (3rd Ed.).
=12
6
=8, and A
5
=16, A
4
3
MULTIPLE MULTI-floor Plant Layout Evaluation (Bozer, Meller, and Erlebacher, 1994) is similar to CRAFT Input data: a from-to chart It was originally develop for multiple-floor facilities
=8, A
2
A
1 =16,
Suppose the following area values are given for six departments: A
MULTIPLE
MULTIPLE’s use of “spacefilling curves” (SFC) for exchange any two departments whether they are adjacent or not
(It can also be used in single-floor facilities) The layout is represented in a discrete fashion An improvement-type layout algorithm
- Tompkins, White, Bozer and Tanchoco. (2010).