3696 LAYOUT PLAKNING MODELS AND DESIGN ALGORITHMS

67. Tompkins, J. A., and Reed, R., Jr., "An Applied Model for theFacilities Design Problem,"InternationalJournal ofProduction Research, vol. 14, no. 5, pp. 583-595, 1976.

68. Tretheway, S. J., and Foote, B. L., "Automatic Computation and Drawing of FacilityLayouts withLogical Aisle Structures," InternationalJournal ofProduction Research,vol. 32, no. 7, pp. 1545-1555, 1994.

69. "Vertical Conveyors Increase Plant's Efficiency 33%," Modern Materials Handling,vol. 40, Casebook Directory, p. 113, 1985.

70. "Vertical Reciprocating Conveyors; Flexible Handling Devices," MaterialHandling Engineering, vol. 45, no. 9, pp. 81-85, 1990.

71. Volvo: The EngineFactory ThatIs Different, a Volvo publication describing the VolvoSkovde plant, Gothenberg, Sweden.

72. White, J. A., "Layout: The Chicken or the Egg?," Modern Materials Handling, vol. 35,no. 9, p. 39, September 1980.

73. Wilhelm, M. R., and Ward, T. L., "Solving Quadratic Assignment Problems by SimulatedAnnealing," HE Transactions, vol. 19. pp. 107-119, 1987.

PROBLEMS

SECTION 6.1-6.2

6.1 What aresomeof the important factors thatshouldbe takenintoconsideration whenalayout is being designed?

6.2 In a manufacturing, environment, what is the impact of the material handling decisionson the effectiveness of a facility layout?

6.3 What kind of manufacturing environments are the following types of layout designsbest suited for?

a. Fixed product layoutb. Product layoutc. Group layoutd. Process layout

6.4 Compare die primary layoutdesign objectives for tlie following situations:a. Soda bottler

b. Printing shopc. Meat-processing plantd. Furniture manufacturing plante. Computer chip makerf. Shipyardg. Refinery plant

' h. College campus

SECTION 6.3

6.5 What are the basic differences between construction-type and improvement-typelayout algorithms?Contrast and compare the plant layout procedures proposed by Apple, Reed, andMuther.

Four departments are to be located in a building of 600' X 1000'. The expected personnel traffic flows and area requirements for the departments are shown in the tablesbelow. Develop a block layout using SLP.

6.6

6.7

6.8

6.9

370Part Two DEVELOPING ALTERNATIVES.- CONCEPTS AND TECHNIQUES

Dept. A B C D

A 0 250 25 240B 125 0 400 335C 100 0 0 225D 125 285 175 0

DepartmentA

B

C

D

Department Dimension200' X 200'

400' X 400'

600' X 600'

200' X 200'

XYZ Inc. has a facility with six departments (A. B, C, D, E, and F). A-summary of theprocessing sequence for 10 products and the weekly production forecasts for the products are given in the tables below.a. Develop the from-to chart based on the expected weekly production.b. Develop a block layout using SLP.

Product Processing Sequence Weekly Production1 ABCDEF 960

2 ABCBEDCF 1200

3 ABCDEF 720

4 ABCEBCF 2400

5 ACEF 1800

6 ABCDEF 480

7 ABDECBF 2400

8 ABDECBF 3000

9 ABCDF 96010 ABDEF 1200

Dept. Dimension

A 40' X 40'

B 45' X 45'

C 30' X 30'

D 50' X 50'

E 60' X 60'

F 50' X 50'

A toy manufacturing company makes 10 different types of products. There are 15equal-sized departments involved. Given the following product routings and production forecasts,a. Construct a from-to chart for the facility.b. Develop a block layout using SLP.

fj

fcSt

«tm-::^'•r/V.-:.

371

6 LAYOUT PLANNING MODELS AND DESIGN ALGORITHMS

Product Processing Sequence Weekly Production

1 ABCDBEFCDH 500

2 M G N O N O 350

3 HLHK 150

4 CFEDH 200

5 N O N 100

6 •IJHKL 150

7 G N O 200

8 ACFBEDHD 440

9 GMN 280

10 IHJ 250

6.10 Shown below is the activity relationship chart along with the space requirements foreach of the six cells in a small auto parts manufacturing facility.a. Construct relationship and space relationship diagrams.b. Design, the corresponding block layout using SLP.

CELL A 2,100

CELLB 2,100

CELLC 2,100

CELLD 2,800

CELLE 1,500

CELLF 1,500

CELLG 2,900

,6.11 Anactivity relationship chart is shown below for the American Mailbox Company. Construct a relationship diagram for the manufacturing facility. Given the space requirements (in ft^), construct a block layout using SLP.

RECEIVING 2,500

PUNCH PRESS 5,500

PRESS BENDING 2,500

PRESS FORMING 2,500

RIVETING 1,500

POWER SAWING .2,500

POWER DRAW, 2,000

WELDING ROBOT 1,000

SECnON6.4

6.12 Suppose five departments labeled A through E are located as shown in the layoutbelow. Giventhe correspondingflow-between chart, compute the efficiency rating forthe layout.

572Part Two DEVELOPING ALTERNATIVES; CONCEPTS AND TECHNIQUES

A B

C

D - E

A B C D . E

A— 5 0 4 -3

B — 6 -1 2

C — -6 0

D — 3E

—

6.13 Inanassembly plant, material handling between departments is performed using a unidirectional closed-loop conveyor. The figure belowshows the layout for the modular

A

P/D#3

B •

P/D#2Warehouse

module

; P/D#l

E

/ ^ ^ s( Conveyor flow j :^^ •'

P/D#4

D

P/D#5

C

facility, which consists of three equal-sized assembly modules (A, B, and C), one administrative module (D), and one warehouse module (E). P/D points for each module arealso shown in the figure. The administrative and warehouse activities are not to bemoved; however, assembly areas A, B, C can be relocated. The distance between P/Dpointsand the number of palletloads moved betweendepartments are givenbelow.

Distance between P/Ds Pallet Flow per Day

From To Distance From/To A B C D E

P/D 1 P/D 2 60' A 0 0 5 0 30P/D 2 P/D 3 90' B 10 0 25 0 0

P/D 3 P/D 4 30' C . 25 5 0 0 0

P/D 4 P/D 5 90' D 0 0 0 0 0

P/D 5 P/D 1 60' E 5 20 5 0 0

Using the pairwise exchange method, determine new locations for assembly modulesA, B, and C that minimize the sum of the products of palletflows and conveyortraveldistances.

6.14 Four equal-sized machines are served by an automated guided vehicle (AGV) on alinear bidirectional track, as shown in the figure below. Each machine block is 30' X30'. The product routineinformation and required production rate are givenin the table

•below. Determine a layout arrangement based on the pairwise exchange method. As-sume that the pickup/delivery stations are located at the midpoint of the machine edgealong the AGV track.

A B• ^

D

-m'M-j

ilvSi

e.

6.15

6.16

3Z36 LAYOUT PIANNING MODELS AND DESIGN ALGORITHMS

Product Processing Sequences Weekly Production

• 1 BD CAC 300 units

2 BDAC 700 units

3 D BD CAC 900 units

4 AB C A 200 units

Using the data from Problem 6.14 but assuming that the locations of the P/D pointsformachines A and B are 5 feet from the lower righthand corner of each machine and theP/D points for machines C and D are 10 feet from the lower-lefthand corner of machines C and D, develop an improved layout using the pairwise exchange method.A mobile robot is serving two cells located at eidier sides of the AGV track, as shownby the figure below. There are three machines placed in each cell. Given the from-tochart in the table below, find the best machine arrangements for both cells. Rearrangement is limited only to machines within each cell. Assume that the P/D point of eachmachine is located at the midpoint of the machine edge along the AGV track,

V y AGV TRACK

M/C A B C D E F

A — 10 50 30 . 0 60

B 5 — 45 40 30 0

C 40 30 — 35 5 20

D 40 25 50 — 40 50

E 0 55 40 50 —0

F 20 . 0 60 20 10 —

wc Distance M/C Distance

A-B 30 D-E 30

A-C 60 D-F 60

B-C 30 ' E-F 30

6.17 Five machines located in a manufacturing cell are arranged in a "U" configuration asshown in the layout below. The material handling system employed is a.bidirectionalconveyor system. Determine the bestmachine arrangement given the product routinginformation and production rates in the table.

3^Part Two DEVELOPING ALTERNATIVES: CONCEPTS AND TECHNIQUES

BI-DIRECTIONALCONVEYOR SYSTEM

Product iVIachine Sequence Prod, Rate

1 B-E-A-C 100

2 C-E-D 200

3 B-C-E-A-D 500

4 A-C-E-B 150 .

5 B-C-A 200

M/C Distance M/C Distance

A-B 20' B-D 100'

A-C 70' B-E 120'

A-D 120' C-D 50'

A-E 140' C-E 70'

B-C 50' D-E 20'

6.18 The ABC Cooling and Heating Company manufactures several different types ofair conditioners. Five departments are involved in the processing required for the products. Asummary ofthe processing sequences required for the five major products and the weeklyproduction volumes for the products are shown inthe tables below along with the department area. Based on thegraph-based construction metliod, develop a block layout.

Product Process Sequence Weeldy Production1 ABC 150

2 ABED 200

3 ACE 50

4 • ACBE - 200

5 ADE 250

Department Area (ft^)A 1500

B 1500

C 1000

D 2000

E 2000

1

3Z5. 6 LAYOUT PLANNING MODELS AND DESIGN ALGORITHMS

6.19 The activity relationship chart for Walter's machine shop is shown in the figure below.The space requirements are in square feet. Construct the relationship diagram and develop a block layout using the graph-based method.

CELL A 1,000

CELL B 1,200

CELLC 1,000

CELLD 1,200

CELLE 2,000

CELLF 1,000

CFH G 1,600

CELL H . 800

Dept. A B C D E F G H

A —302 0 0 0 66 0 68

B 0 — 504 20 136 154 56 40

C 0 0 — 76 352 0 122 94 .

D 0 0 0- — 0 0 180 8

E 0 0 0 0 —122 0 282

F 0 0 0 0 0 . — 188- 24

G 0 0 0 0 • 0 0 — • 296

H 0 0 0 0 0 0 0 —

6.20 The from-to material flow matrix for an eight-departmeint facility is given in the tablebelow. Construct a relationship diagram based on the material flow matrix, and construct a block layout using the graph-based method.

Dept. Area Required (ft^)A 2800

B 2100

C 2600

. D 400

E 600

F . 400

G 2300

IT 1800

6.21 Consider the layout of five equal-sized departments. The material flow matrix is givenin the figure below.a. Develop the final adjacency graph using the graph-based procedure.b. Develop a block layout based on the final adjacency graph obtained in part a.

37&Part Two DEVELOPING AlTEmATIVES: CONCEPTS AND TECHNIQUES

A B C D E

A — 0 5 25 • 15

B 0 — 20 30 25

C 0 25 — • 40 30

D 30 5 20 — 0

E 20 30 5 10 ^—

6.22 The material flow matrix for 10 departments is given below.

A B C D E F G H I J

A — 0 12 0 132 16 0 220 20 24

B 0 — 176 0 216 0 144 128 0 0

C 0 0— 0 0 184 0 0 28 0

D 212 136 240— 36 0 236 0 164 0

E 0 0 140 0 — 0 192 0 0 160

F 0 180 0 188 108— 248 228 0 0

G 172 0 156 0 0 0 — 112 224 152

H 0 0 32 40 204 0 0 — 0 0

I 0 168 0 0 104 156 0 148 — 200

J 0 124 196 120 0 116 0 108 0 —

The area requirements are

Dept. Area (ft^)

A 400

B 1000

C 2600

D - 400

E 2400

F 1000

G 3600

H 1200

I 400

J 2400

a. Determine a final adjacency graph using the graph-based procedure.b. Construct a block layout based on the adjacency graph in part a.

6.23 Suppose the efficiency rating is designated by E, and the cost computed by CRAFT isdesignated by K. Further suppose that four departments (labeled A, B, C, and D) aregiven for a layout problem. Each department is assumed to be of equal area, and eachdepartment is represented by a unit square. The unit cost used in computing i?" isassumed to be equal to 1.0 for all deparUnent pairs. (That is, c,y = 1.0 for all i, j.) Theflow between the above departments is given as follows:

a

•^

ii.-•it•Aji

IM-

ISSi'"

m

377

5 LAYOUT PIANNING MODELS AND DESIGN AI^GORITHIvIS'

A B c D

A — To 10 0 .

B— 0 4

C —• 4

D —

a. Compute the values of E and K for the following layout:

A C

B' D

b.' Compute the values of E and K for the following layout.

B

A DC

c. Compute the values of E and K for the following layout.

A B

C D

d. What can you say regarding the consistencyof the two measures. That is, if a layoutis "good" when measured by its lvalue, would it still be "good" when it is measured by its K value or vice versa? Justify your answer.

6.24 Consider four departments labeled A, B, C, and D. Each department is represented bya 1 X 1 square. The following data are given;

Initial Layout

A B

C D

Flow-Between Matrix Unit Cost Matrix

A B C D A B c D

A — 6 0 3 A —2 0 3

B — 5 0 B 2 — 1 0

C — 0 C 0 1 —0

D —D 3 0 0 —

The location of department A is fixed. Answer the following questions using CRAFTwith two-way exchanges only.a. List all the.department pairs that CRAFT would consider exchanging. (Do not com

pute their associated cost.)b. Compute the actual cost of exchanging departments C and D.c. Given that department A is fixed and that each department must remain as a 1 X 1

square, is the layout obtained by exchanging departments C and D optimum? Whyor why not? (Hint; Examine the properties of the resulting layout and consider theobjective function of CRAFT.)

375Part Two DEVELOPING ALTEIWATTVES: CONCEPTS AND TECHNIQUES

6.25 The following layout is an illegal CRAFT layout. Nevertheless, given that the volume offlow from Ato Bis 4, Ato Cis 3, and Bto Cis 9, and that all move costs are 1, whatis the layout cost?

c c C C C C

c B B B B C

c B A A B C

c B B B B C

c C C C C C

6.26 When CRAFT evaluates the exchange of departments, instead of actually exchangingthe departments, it only exchanges the centroids ofdepartments.a. What is the impact of this method ofexchanging if all departments are the same

size?

b. Given the following from-to chart and scaled layout (each square is 1 X 1), whatdoes the evaluation of the exchange of departments B and Cindicate should besaved over the existing layout, and what is actually saved once this exchange ismade?

To

From • A B C

A — 10 6

B 2 —• 7

C —

From-To Chart

A A A C B B B B

A A A C B B B B

A A A C B B B B

Initial Layout

6.27 Explain the steps CRAFT would take with the following problem and determine thefinal layout. Only two-way exchanges are to be considered.

To

From A B C D E

A— 3 2 1 A A A B B B

B— 1 3 A A A C C C

C 1 •— 4 A A A C C C

D—• D D D E E E

E— D D D E E E

From-To Chart Initial Layout

6.28 Amanufacturing concern has five departments (labeled Athrough E) located ina rectangular building as shown below:

3796 LAYOUT PLANNING MODELS AND DESIGN ALGORITHMS

i C

E

c)

Suppose the flow data, the unit cost data, and the distance matrix are givenas follows;

Flow-Between Matrix

A B c D • E

A — 0 5 0 5

B —• 6 2 0

C — 3 0

D — 7

E —

Unit Cost ($/Unit Dist.) Distance Matrix

A B C D E A B C D E

A — 0 1 0 1 A — 6 20 18 11

B —• 1 4- 0 B — 12 22 15

C — 3 0 C — 10 8

D .— 1 D — 7

E — E —

a. Using the CRAFT two-way exchange procedure, indicate all the department pairsCRAFT would consider exchanging in the above layout.

b. Compute the estimatedcost of exchanging departments A and E.6.29 Suppose thefollowing layout isprovided asthe initial layout to CRAFT. The flow-between

matrix and the distance matrix are given as follows. (All the c,y values are equal to 1.0.)

Flow-Between Matrix Distance Matrix

A B C D E F A B C D E F

A — 0 8 0 4 0 A — • 30 25 55 50 80

B —• 0 5 0 2 B — 45 25, 60 50

C — 0 1 0 C — 30 25 55

D. — 6 0 D — 45 25

E — 4 E —30

F — F —

1A

t ^ •

(%

1

— E33 • •

[3t

1

Given the above data and initial layout, which department pairs will not be considered for exchange.

b. Compute the cost of the initial layout.c. Compute the eslimated layout cost assuming that departments EandFareexchanged.d. In general, when the same data and initial layoutare supplied to CRAFr and MUL

TIPLE, why would one expect MULTIPLE to often (but not always) outperformCRAFT? Also, what type of data and/or initial layout would allow CRAFT to consis-tendy generate layout costs that are comparableto those obtained fromMULTIPLE?

6.30 Answer the following questions for CRAFT.a. State two principal weaknesses and two principal strengths of CRAFT.b. CRAFT uses the estimated cost in evaluating the potential impact of exchanging two

or three department locations. Suppose we modify the original computer code to

a.

380

Part Two DEVELOPING ALTERNATIVES: CONCEPTS AND TECHNIQUES

obtain a new code, say, NEWCRAFT, where we always use the actual cost in evaluating the potential impact of exchanging two or three departments. Assuming thatwe start with the same initial layout and that we use the same exchange option(such as two-way exchanges only, or any other exchange option), the cost of the final layout obtained from NEWCRAFT will not necessarily be less than the cost of thefinal layout obtained from CRAFT. True or false? Why?

6.31 Using BLOCPLAN's procedure, convert the following from-to chart to a relationship chart.

To

From A B C D E F G • H

A— 8 3 6

B 1 — 5

C — 4

D 9 — 18

E 4 1 •—

F 4 4 —

G 2— 20

H 7 —

6.32 Consider BLOCPLAN. Suppose the following REL-chart and layout are given for a fivedepartment problem. (It is assumed that each grid in the layout represents a unitsquare.) Further suppose that the following scoring vector is being used: A = 10, E =5, I = 2, O = 1, U = 0, and X = -10.

6.33

6.34

1 2 3 4 5

1 — A U E U

2— U U • I

3 — U X

4— A

5 —

4 1

5 3 2

a. Compute the "efficiency rating."b. Compute the REL-DIST score.c. In improving a layout, BLOCPLAN can exchange only those departments that are

either adjacent or equal in area. True or false? Why? (If true, then explain why thereis such a limitation. If false, then explain how two departments that do not meet theabove constraint are exchanged.)

d. In constructing and improving a layout, BLOCPLAN maintains rectangular department shapes. Discuss the advantages and limitations of maintaining such department shapes in facility layout.

Use the MIP model to obtain an optimal layout with the data given for Problem 6.28.(You may assume that each grid measures 20' X 20'.)

Use the MIP model to obtain an optimal layout with the data given for Problem 6.29.(You may assume that each grid measures 10' X 10'.)

''M..

W&l

«

ite'»systi:'W^t

W-te''-

il

HS:Btev

#•

®p-'

5 - '

V'

6.35

6.36

6.37

6.38

6.39

381

6 LAYOUT PLANNING MODELS AND DESIGN ALGORITHMS

Consider the layout shown in Figure 6.26d. Use LOGIC and the cut-tree shown inFigure 6.27 to exchange departments B and F.

Re-solve Problem 6.35 by exchanging departments D and H in the layout shown inFigure 6.26c?.

Re-solve Problem 6.35 by exchanging departments G and H in the layout shown inFigure 6.29.

Answer the following questions for MULTIPLE.a. Consider four departments (labeled A through D) witli the following area requirements:

A = 7 grids, B = 3 grids, C = 4 grids, and D = 2 grids. Using the spacefilling curveshown below, show the layout that would be obtained from the sequence A-B-C-D.

Start End

b. Using the data given for part a and the spacefilling curve shown above, show thelayout that would be obtained by exchanging departments B and D.

c. Discuss the advantages and limitations of using spacefilling curves in the mannerthey have been used in MULTIPLE. Your discussion should include the treatment offixed departments, dummy departments, unusable floor space (i.e., obstacles), andextra (i.e., empty) floor space.

Consider the initial layout and flow/cost data given for Problem 6.28.a. Using the following conforming curve and MULTIPLE, improve the initial layout via

two-way department exchanges.

b. In general, what is the disadvantage of using conforming curves?

6.40 Consider the initial layout and flow data given for Problem 6.29. Use MULTIPLE andthe following conforming curve to obtain a two-opt layout.