Question

For the set of tasks given below, do the following:

Task	Task Time(seconds)			Immediate Predecessor
A		45		-
B		11		A
C		9		B
D		50		-
E		26		D
F		11		E
G		12		C
H		10		C
I		9		F, G, H
J		10		I
		193

b. Determine the minimum and maximum cycle times in seconds for a desired output of 500 units in a seven-hour day. (Round your answers to 1 decimal place.)
  

The minimum cycle time	seconds
The maximum cycle time	seconds

c. Determine the minimum number of workstations for output of 500 units per day. (Round up your answer to the next whole number.)
  
Minimum number of workstations            

d. Balance the line using the greatest positional weight heuristic. Break ties with the most following tasks heuristic. Use a cycle time of 50 seconds.

Work stations	Following Tasks
I	(Click to select)  E  B  C  A  D
II	(Click to select)  D  F  C  B  A
III	(Click to select)  A  C  B, E, C  B  A, E, C
IV	(Click to select)  G  F, A, G  G, H  G, F, H, I  C
V	(Click to select)  J  A  B  D  C

e. Calculate the percentage idle time for the line using the 50 second cycle time. (Round your answer to 1 decimal place. Omit the "%" sign in your response.)
  
Percentage of idle time             %

Answer 1

B) Determine the maximum and minimum cycle times.

Maximum Cycle time = total time of completing al the task by single worker = total task time = 193 seconds

Minimum Cycle time = highest task time = 50 seconds of activity D

c) What is the minimum number of stations needed?

First determine desired cycle time for producing 500 unit per day in 7 hours per day

Demand = 500 units per day

Available time = 7 hours/day = 7*60*60 = 25200 seconds per day

Cycle time = Available time/Demand = 25200/500= 50.4 seconds per unit

Cycle time = 50.4 seconds per unit

Total work content =193 seconds

Theoretical number of workstation required = Total work content/Cycle time = 193/50.4 = 3.83

Minimum theoretical number of WS = 4 workstation

d)

a precedence diagram.

Determine Positional weights:

Start with extreme right task of the line. Positional weight for task is sum of the task’s time and the time of all following tasks.

TASK	Calculation	Positional Weights
A	=45+11+9+12+9+10+10	106
B	=11+9+12+9+10+10	61
C	=9+12+9+10+10	50
D	=50+26+11+9+10	106
E	=26+11+9+10	56
F	=11+9+10	30
G	=12+9+10	31
H	=10+9+10	29
I	=9+10	19
J	10	10

Assignment of Tasks:

For the first workstation, select the task with highest positional weight, prerequisite that preceding task of the selected task is completed and the duration is less than the desired cycle time (C).

Obtain remaining time on the workstation by subtracting the cumulative assigned time from cycle time.

If remaining time becomes less than cycle time, move for next workstation. Repeat the procedure till all the tasks are assigned.

Station	Cycle time Available	Task	Time (Seconds)	Time left (Seconds)	Ready tasks (positional wt)
					A(106),D(106)
1	50	A (45)	45	5	D(106),B(61)
2	50	D (50)	50	0	B(61),E(56)
3	50	B (11)	11	39	E(56),C(50)
	39	E (26)	26	13	C(50),F(30)
	13	C (9)	9	4	F(30),G(31),H(29)
4	50	G (12)	12	38	F(30),H(29)
	38	F (11)	11	27	H(29)
	27	H (10)	10	17	I(19)
	17	I (9)	9	8	J(10)
5	50	J (10)	10	40

Assignments are as follows:

WS	Task	Total time	Idle time
1	A	45	5
2	D	50	0
3	B, E, C	46	4
4	G, F, H, I	42	8
5	J	10	40
		Total	57

e.

Total idle time = 57

% of idle time = total Idle time/(cycle time x # of Workstations) x 100 = 57/(50 x 5) x 100

% of idle time = 22.8%