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Chapter 06 - Process Selection and Facility Layout
6-49
Education.
The distance (in feet) between departments for the first option is shown below:
From
To
1
2
3
4
5
6
1
80
80
20
40
40
2
160
40
120
40
3
100
40
120
4
60
20
5
80
6
Then, for each department pair, we must multiply Number of Trips x Distance.
Number of Trips x Distance
Total distance traveled per day = 40,200 feet.
From
To
1
2
3
4
5
6
1
0
3200
2200
3200
2000
2
0
2000
4800
4800
5
1600
6
Chapter 06 - Process Selection and Facility Layout
6-50
17. Given: Department 1 must be assigned to Location A.
The possible approach described below assumes that we will try to optimize a subset of
department pairs (those with the highest number of trips between departments).
First, we can start by rank ordering department pairs based on the number of trips between them.
Below is a list of department pairs that includes each department at least once. We are treating
these department pairs as A (Absolutely necessary) conditions.
Dept. Pair
No. of Trips
Ranking
1-3
51
1
3-7
50
2
9-10
47
3
6-8
44
4
8-9
43
5
6-9
42
6
1-2
40
7
2-10
36
8
3-10
36
9
1-10
35
10
4-5
35
11
Second, we can start assigning departments using different heuristics to locate the departments
with high traffic between them next to each other. One such heuristic is demonstrated next.
Heuristic 1: We will assign departments counterclockwise based on those department pairs with
high traffic between them. Note that Department 1 is fixed in the middle at Location A, Locations
B & J are adjacent to Location A, and Locations E & F are considered adjacent to each other.
Step 1: Department Pair 1-3 is #1 on the list of No. of Trips. In addition, we see that Department
3 is linked to Department 7 in 3-7 (#2 on the list) and Department 10 in 3-10 (#9 on the list). We
will make our assignments to meet the higher-level conditions first. We assign Department 3 to
Location B and Department 7 to Location C.
Step 2: Next on our list of unaddressed department pairs is 9-10 (#3 on the list). We see that
Department 9 is linked to Department 8 in 8-9 (#5 on the list) and Department 6 in 6-9 (#6 on the
list). Department 10 is linked to Department 2 in 2-10 (#8 on the list), Department 3 in 3-10 (#9
on the list), and Department 1 (#10 on the list). We will make our assignments to meet the higher-
level conditions first. We assign Department 9 in between Departments 8 and 10. We assign
Dept. 10 to Location D, Department 9 to Location E, and Department 8 to Location F. These
assignments will leave 3-10 two departments apart and 1-10 three departments apart.
the list). We assign Department 6 as close as possible to Department 8 by placing it at Location
G. This assignment leaves 6-8 one department apart and 6-9 two departments apart.
Step 4: Next on our list of unaddressed department pairs is 1-2 (#7 on the list). We see that
Department 2 is linked to Department 10 in 2-10 (#8 on the list). We address the higher-level
condition first by locating Department 2 next to Department 1 at Location J. This assignment
Chapter 06 - Process Selection and Facility Layout
6-52
Education.
18. Given: Rebalance the assembly line in Problem 7. Use the longest operation time heuristic. Break
ties with the most following tasks heuristic. Then, determine the percent idle time. Cycle time =
50 seconds per unit.
Precedence diagram (all times are in seconds):
Task
Operation Time
Number of
Following Tasks
A
45
6
B
11
5
C
9
4
D
50
4
E
26
3
F
11
2
G
12
2
H
10
2
I
9
1
J
10
0
A
B
C
E
D
G
F
45
11
9
12
10
9
10
Chapter 06 - Process Selection and Facility Layout
Education.
Longest Operation Time Solution (Cycle time = 50 seconds per unit)
Station
Time
Remaining
Eligible
Will Fit
Assign
(task time)
Revised
Time
Remaining
Idle
1
50
A, D
A, D
D (50)
(see Note 1)
0
0
2
50
A, E
A, E
A (45)
(see Note 2)
5
5
B, E
None
---
5
3
50
B, E
B, E
E (26)
(see Note 3)
24
24
B, F
B, F
B (11)
(see Note 4)
13
13
C, F
C, F
F (11)
(see Note 5)
2
2
C
None
---
2
4
50
C
C
C (9)
41
41
G, H
G, H
G (12)
(see Note 6)
29
29
H
H
H (10)
19
19
I
I
I (9)
10
10
J
J
J (10)
0
0
Note 1) Assign Task D because it has the longest operation time of Tasks A & D.
Note 2) Assign Task A because it has the longest operation time of Tasks A & E.
Note 3) Assign Task E because it has the longest operation time of Tasks B & E.
Note 4) Tasks B & F are tied with operation time = 11. We break the tie by assigning Task B because it
Chapter 06 - Process Selection and Facility Layout
6-54
Education.
Overview of Workstations: Longest Operation Time Solution
Station
Tasks Assigned
Total Time Used at Station
Idle Time at Station
1
D
50
0
2
A
45
5
3
E, B, F
48
2
4
C, G, H, I, J
50
0
Note: Calculated cycle time equals the actual bottleneck station time used. As shown above, Stations 1 &
4 are bottlenecks and use all 50 seconds.
Percent Idle Time:
Percent idle time for longest operation time solution:
Enrichment Module: Process Design and Facility Layout Problem
Job shop layout problem
Donald Rice sold the building that housed the restaurant/lounge he owned and operated for the last 10
years and has recently purchased a larger building in a new location. Mr. Rice hopes to operate a new
restaurant and expand his growing business. The building has four equal size rooms. Donald’s restaurant
consists of four major departments (areas of his operation):
1. Dining area
2. Lounge/Bar
3. Kitchen
4. Storage/Refrigeration/Loading area
Donald envisioned using the four rooms to occupy four areas of his operation. The distance matrix among
the four rooms is as follows (all distance values are given in feet):
Distance Matrix
Room
1
2
3
4
1
–
25
45
35
2
–
60
20
3
–
10
4
–
Chapter 06 - Process Selection and Facility Layout
6-55
Education.
Based on his experience from his previous restaurant, he estimated the following number of trips per hour
between departments:
Load Matrix
Dining
Lounge
Kitchen
Storage
Dining
60
80
10
Lounge
40
20
Kitchen
100
Storage
a. Donald is thinking about using the following departmental layout.
Room 1
Room 2
Room 3
Room 4
Dining
Kitchen
Lounge
Storage
Determine the (distance x trip) matrix for the above layout. What is the total distance?
b. Determine a layout and the associated trip x distance matrix that will result in a lower total
distance (Hint: Locate the departments that have high traffic close to each other).
Chapter 06 - Process Selection and Facility Layout
6-56
Education.
Solution of Problem 1
a. Distance x Load Matrix
To
Dining
Lounge
Kitchen
Storage
Dining
–
*2,700
**2,000
***350
From
Lounge
–
2,400
200
Kitchen
–
2,000
Storage
–
* (45 x 60) = 2,700
**(25 x 80) = 2,000
***(35 x 10) = 350
Total distance = 2,700 + 2,000 + 350 + 2,400 + 200 + 2,000 = 9,650 feet
b. The objective is to arrange the departments such that the departments with high interdepartment
movements (# of trips) are close to one another.
Because the number of trips between kitchen and storage is the highest and room 3 and room 4
(100) have the closest proximity (shortest distance of 10 feet), we will place kitchen and storage
in rooms 3 and 4. However, at this point we have not decided which of the two departments will
be placed in room 1 and room 2.
We can observe that the next highest number of trips is between dining and kitchen (80). In
addition, the shortest distance from rooms 1 and 2 to rooms 3 and 4 is 20 feet (room 2 to room 4).
Therefore, kitchen is placed in room 4, storage is placed in room 3, dining is placed in room 2,
and the lounge is placed in room 1. The summary of the room assignments are given below:
Room 1—Lounge
Room 2—Dining
Room 3—Storage
Room 4—Kitchen
Updated (Distance) x (Load) Matrix
To
Dining
Lounge
Kitchen
Storage
Dining
–
*1,500
**1,600
***600
From
Lounge
–
1,400
900
Kitchen
–
1,000
Storage
–
* (45 x 60) = 2,700
