ISYE 3104 Summer 2003
Chapter 9
Homework 5 Solution
Layout Strategy
DISCUSSION QUESTIONS
1. How would you obtain data and determine the number of trips in:
(a) a hospital?
(b) a machine shop?
(c) an auto-repair shop?
Most organizations have some procedure for documenting movement of
their product. For instance, a hospital has doctor’s orders indicating the tests and
procedures that a patient is to undergo. A machine shop has routing documents
indicating the operations that an order is to follow as the product moves through the
shop. And an auto repair shop knows what repairs, parts, and labor are used on a
particular job and as a result where the job was done and the trips made necessary.
In each of the above examples a matrix would be made showing the number
of trips. And the distance (or time or cost) of each trip would be determined.
2. What are the two major trends influencing office layout?
Two major trends influencing office layout are: technology and virtual companies.
3. What layout variables would you consider particularly important in an office
layout where computer programs are written?
Some of the layout variables you might want to consider as particularly important in
an office where computer programs are to be written are:
 Ease of communication
 Provision of privacy and a quiet work environment
 Lighting –especially as it related to glare on CRT screens
 Consideration of ergonomic or human factor issues in equipment
layout and construction
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ISYE 3104 Summer 2003
Homework 5 Solution
PROBLEMS
Problem 9.2
What is the appropriate layout of the new building?
This matrix includes movements in both directions:
M
W
D
L
G
B
M
-
W
125
-
D
75
0
-
L
0
75
0
-
G
50
0
150
20
-
B
60
0
20
0
0
-
Based on the above matrix, we can establish the following closeness ratings among
the different processes:
M
W
D
L
G
B
M
-
W
A
-
D
E
U
-
L
U
E
U
-
G
I
U
A
O
-
B
E
U
O
U
U
-
Here are two optimal layouts:
Room 1
Room 2
Room 3
B
M
W
D
G
L
Room 4
Room 5
Room 6
Room 1
Room 2
Room 3
W
M
B
L
G
D
Room 4
Room 5
Room 6
Or
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ISYE 3104 Summer 2003
M  W:
M  D:
M  G:
M  B:
W  L:
D  G:
D  B:
L  G:
125
75
50
60
75
150
20
20
Homework 5 Solution
Movement-Distance Calculations
x 20 =
2,500
x 40 =
3,000
x 20 =
1,000
x 20 =
1,200
x 20 =
1,500
x 20 =
3,000
x 20 =
400
x 20 =
400
13,000 = Minimum distance movement
for both (symmetrical layouts)
To compute the optimal solution of this problem, in a strict sense, one would
employ the following mathematical programming formulation:
Parameters:
dij : distance between available areas (rooms) i and j, i,j{1,…,6}
fkl : number of trips between processes ik and l, k,l  {1,…,6}
Variables:
xki binary variable with a value of 1 indicating that process k is assigned to
location i, k,i  {1,…,6}
Objective:
min i,j,k,l dij*fkl*xki*xlj
Constraints
i xki = 1, k (i.e., every process k must be assigned to one and only one
location)
k xki = 1, i (i.e., every location i must be assigned to one and only one
process)
xki{0,1},  i, k (i.e., the decision variables are all binary)
The above formulation is known as a quadratic assignment problem. (it is an assignment
because as it is stated by the problem constraints, we are essentially trying to match the
processes with the available areas/rooms, and it is quadratic because the objective is a
quadratic function of the decision variables). However, the non-linear structure (quadratic)
of the objective, combined with the binary nature of the decision variables, makes it a
computationally hard problem. i.e., there are no readily available efficient algorithms for its
solution.
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ISYE 3104 Summer 2003
Homework 5 Solution
Problem 9.4
You have been asked to evaluate these two kitchen layouts and to prepare a
recommendation for your boss, Mr.Reid, so that he can proceed to place the contract for
building the kitchens.
Layout 1:
Refrig.
(1)
1
2
3
4
5
1
0
5
3
3
0
Counter
(2)
Trip Matrix
2
3
4
8 13
0
0
3
3
12
0
4
0
0
0
8
4 10
Sink
(3)
5
0
8
0
5
0
Storage
(4)
1
2
3
4
5
Stove
(5)
Distance Matrix
1
2
3
4
5
0
4
8 12 16
4
0
4
8 12
8
4
0
4
8
12
8
4
0
4
16 12
8
4
0
ΣΣTij x Dij = 600 with rooms fixed (504, if not fixed; 560, if the sink is fixed in one
location)
Layout 2:
Sink
(3)
Refrig.
(1)
1
2
3
4
5
1
0
5
3
3
0
Trip Matrix
2
3
4
8 13
0
0
3
3
12
0
4
0
0
0
8
4 10
Storage
(4)
Counter
(2)
5
0
8
0
5
0
Stove
(5)
1
2
3
4
5
Distance Matrix
1
2
3
4
5
0
7
8 12 14
7
0
5
6
7
8
5
0
4
9
12
6
4
0
6
14
7
9
6
0
ΣΣTij x Dij = 602 (if rooms are fixed; 566 if not; and 595 if the sink is fixed in one location)
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