Intro to operations management (final exam today)
Chapter 9: Line Balancing (longest task approach)
Formulas
Line balancing
Available Time = Net time available excluding meeting time, lunch break etc…
Cycle Time = !"#$%#&$' )%*' +,%-. /'01%2'3
Theoretical minimum number of workstations = ∑)#.5 )%*'
)6-#$ 78'2#-%6, )%*'
• To measure the effectiveness, we have to find the efficiency and idle time by using the following formulas:
Efficiency = ∑)#.5 )%*'
!9-1#$ ,1*&'2 6: ;625.-#-%6,. < $#2='.- #..%=,'3 9>9$' -%*' x 100
Idle Time = (Actual number of workstations x largest assigned cycle time)- ∑Task Time
Remember
• The theoretical number of workstation is not always possible to reach when tasks are actually assigned to stations.
• Cycle time is the maximum time that a product is allowed at each workstation.
Chapter 9: Line Balancing (longest task approach)
Question 1. If the goal is to produce 180 units per hour. The tasks, task times, and immediate predecessors for the tasks are as follows:
Task Task Time (in sec) Precedence
A 12 -
B 15 A
C 8 A
D 5 B,C
E 20 D
a) What is the available time? b) What is the cycle time? c) What is the theoretical minimum number of workstations? d) Use the longest task time approach to Assign tasks to work station
Solution
a) One hour = 60 min, since the task time is given in seconds we have to convert the available time to seconds. So the available time = 60*60 = 3600 sec
b) Cycle Time = ?26319-%6, !"#$%#&$' )%*' +,%-. /'01%2'3
= @ABB CDB
= 20 seconds per units
c) Theoretical minimum number of workstations = ∑)#.5 )%*' E>9$' )%*'
= AB FB
= 3 workstation
d) Workstations assignment
Task WS1/CT R T
A+C 20 20 – 20 = 0
Task WS2/CT RT
B+D 20 20 – 20 = 0
Task WS3/CT RT
E 20 20 – 20 = 0
Chapter 9: Line Balancing (longest task approach)
Question 2. There are 500 minutes available during the day, lunch break is 20 min, and the average daily demand has been 60 chairs. There are 5 tasks:
Task Task Time (min) Precedence
A 4 —
B 7 —
C 8 B
D 5 C
E 6 A
a) Draw a precedence diagram of this operation b) What is the available time? c) What is the cycle time for this operation? d) What is the theoretical minimum number of workstations? e) Use the longest task time approach to Assign tasks to work station f) What is the idle time? g) What is the efficiency percentage of the assembly line?
Solution
a) Precedence Diagram
a) Available time = 500 min – 20 min = 480 min b) Cycle Time = ?26319-%6, !"#$%#&$' )%*'
+,%-. /'01%2'3
= GDB *%, AB 1,%-.
= 8 min (we have to produce 1 chair every 8 min)
c) Theoretical minimum number of workstations = ∑)#.5 )%*' E>9$' )%*'
= @B D = 3.5 stations = 4 workstations
A
4
C
8
D
5
E
6
B
7
S
Fin
Chapter 9: Line Balancing (longest task approach)
d)
Task WS1/CT RT
B 7 1
Task WS2/CT** RT
C 8 0
Task WS3/CT RT
D 5 3
Task WS4/CT RT
A 4 4
Task WS5/CT RT
E 6 2
**largest assigned cycle time
e) Idle Time = (Actual number of workstations x largest assigned cycle time)- ∑Task Time
= (5 * 8) – 30 = 10 min per cycle
f) Efficiency = ∑)#.5 )%*' !9-1#$ ,1*&'2 6: ;625.-#-%6,. < $#2='.- #..%=,'3 9>9$' -%*'
= @B H∗D
x 100 = 75 %
Chapter 9: Line Balancing (longest task approach)
Question 3. Develop a solution for the following line balancing problem, allowing a cycle time of 5 minutes.
a) Calculate the theoretical minimum number of workstations. b) Use the longest task time approach to Assign tasks to work c) Does the solution have the minimum number of stations? Explain. d) How much idle time is there? e) What is the efficiency of this line?
Work Task Task Time (seconds) Task Predecessor(s)
A 70 -
B 60 A
C 120 B
D 60 -
E 240 C, D
F 100 A
G 190 E, F
Solution
CT = 300 sec
a) No. w/s = 2.8 = 3 REMEMBER ALWAYS ROUND UP
b) Line balancing
Task WS1/CT** R T
A+F+D+B 290 10
Task WS2/CT RT
C 120 180
Task WS3/CT RT
E 240 60
Task WS4/CT RT
G 190 110
c) No, the solution uses 4 stations, not 3 d) Idle time = 320 sec e) Efficiency = 72%
Chapter 9: Line Balancing (longest task approach)
Question 4. A company is designing a product layout for a new product. It plans to use this production line eight hours a day in order to meet a schedule of 400
units per day. The tasks necessary to produce this product are detailed in the
table below.
Task Predecessor Time (seconds)
A - 50
B A 36
C - 26
D - 22
E B, D 70
F C, E 30
a. What is the required cycle time? b. What is the theoretical minimum number of workstations needed to meet the
schedule?
c. Use the longest task time approach to Assign tasks to work d. What is the idle time? e. What is the efficiency? f. Does the solution have the minimum number of stations?
Solution
a) Cycle time = 72 sec b) w/s = 3.25 = 4 REMEMBER ALWAYS ROUND UP c) balance
Task WS1/CT** RT
A+D 72 0
Task WS2/CT RT
B+C 62 10
Task WS3/CT RT
E 70 2
Task WS4/CT RT
F 30 42
d) idle time = 54 sec e) efficiency = 81.25% f) yes