Part 1. The jobs A,B,C,D,E, arrived in that order to be processed on two machine
ID: 467588 • Letter: P
Question
Part 1.
The jobs A,B,C,D,E, arrived in that order to be processed on two machines.
Job
A
B
C
D
E
Time on Machine 1
35
41
49
28
53
Time on Machine 2
32
56
36
48
55
How many of the statements are correct?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Statement 1. In the FIFO schedule, the total time of completion is 271.
Statement 2. In the FIFO schedule, the flow time of job D is 216.
Statement 3. In the FIFO schedule, the total queue time of job C is 76.
Statement 4. In the FIFO schedule, the total idle time of machine 2 is 35.
Part 4. Questions 6-7
An organization that continuously processes proposals is addressing a large backlog due to an historical FIFO sequencing rule. You have been asked to determine a schedule that minimizes the processing time of project proposals through the editing department and revision department. The editing department identifies changes and the revision department incorporates the changes and produces a final proposal document for release. A proposal must pass through each department. Each department has personnel to service only one document at a time. The editing time is dependent on the type of proposal and the revision time is dependent on the size of the proposal. The time estimates below have been provided to you for scheduling.
Question 6. What is the minimum processing time in minutes?
(A) 525 (B) 1025 (C) 522 (D) 502 (E) none of the above
Question 7. What is the minimum average jobs per minute that can be achieved?
(A) 281 (B) 21 (C) 41 (D) 13 (E) none of the above
Proposal #
Editing Time (minutes)
Revision Time (minutes)
1
17
18
2
24
26
3
18
17
4
13
15
5
24
23
6
28
26
7
20
21
8
22
20
9
16
17
10
12
10
11
21
22
12
30
28
13
18
19
14
20
19
15
12
13
16
25
27
17
22
25
18
23
21
19
17
16
20
26
29
21
14
16
22
19
18
23
29
27
24
16
15
25
26
25
Question 8. Using the aggregate run-out method for the assembly line schedule problem below, what is the production for product C in hours?
(A) 3 (B) 4 (C) 6 (D) 28 (E) None of the above
Available production = 53 hours.
Product
Line
Production
Inventory
Demand
Products
Hours/Item
Items
Items/week
A
0.1
120
50
B
0.2
100
80
C
0.1
110
50
D
0.3
200
80
E
0.2
90
40
Job
A
B
C
D
E
Time on Machine 1
35
41
49
28
53
Time on Machine 2
32
56
36
48
55
Explanation / Answer
Part 1:.
Scheduling done as per FIFO method:
Job
Time on Machine 1
Time on Machine 2
Machine 1 Start
Machine 1 Finish
Machine 2 Start
Machine 2 Finish
Machine 2 Idle
Job Idle time
A
35
32
0
35
35
67
35
0
B
41
56
35
76
76
132
9
0
C
49
36
76
125
132
168
0
7
D
28
48
125
153
168
216
0
15
E
53
55
153
206
216
271
0
10
The last job E finishes at 271 period on Machine 2. The total time of completion = 271, Statement 1 is correct.
The Job D finish time of Machine 2 is 216, thus, the flow time of Job D = 216, Statement 2 is correct.
The Job C has to wait till period 76 to start processing on machine 1, thus, total queue time of job C = 76, Statement 3 is correct.
Total idle time on Machine 2 = 35 + 9 = 44 periods, the us the statement 4 is incorrect.
Thus, only three statements are correct.
Correct Option: (D) 3
Part 2:
For reducing the idle time for N jobs scheduling on two workstations Johnson’s Rule is applied.
Steps for Johnson’s Rule
For “n” jobs on two machines, the steps to follow for Johnson’s rules are:
Repeat steps 1, 2, and 3 until all jobs have been scheduled.
For example, process time of proposal#10 is minimum 10 at the WS#2, thus, sequence the Proposal#10 in last. Remove that proposal from the list. Again the minimum processing time of 12 minutes is for Proposal#15 at WS#1, thus, sequence Proposal#15 first.
WS#1
WS#2
Sequence
Proposal #
Editing Time (minutes)
Revision Time (minutes)
WS#1 Start Time
WS#1 Finish time
WS#2 Start
WS#2 finish time
1
15
12
13
0
12
12
25
2
4
13
15
12
25
25
40
3
21
14
16
25
39
40
56
4
9
16
17
39
55
56
73
5
1
17
18
55
72
73
91
6
13
18
19
72
90
91
110
7
7
20
21
90
110
110
131
8
11
21
22
110
131
131
153
9
17
22
25
131
153
153
178
10
2
24
26
153
177
178
204
11
16
25
27
177
202
204
231
12
20
26
29
202
228
231
260
13
12
30
28
228
258
260
288
14
23
29
27
258
287
288
315
15
6
28
26
287
315
315
341
16
25
26
25
315
341
341
366
17
5
24
23
341
365
366
389
18
18
23
21
365
388
389
410
19
8
22
20
388
410
410
430
20
14
20
19
410
430
430
449
21
22
19
18
430
449
449
467
22
3
18
17
449
467
467
484
23
19
17
16
467
484
484
500
24
24
16
15
484
500
500
515
25
10
12
10
500
512
515
525
Question 6. What is the minimum processing time in minutes?
(A) 525 (B) 1025 (C) 522 (D) 502 (E) none of the above
Minimum processing time for all the proposal in WS#2 is 525 minutes.
Correct Option: (A)
Question 7. What is the minimum average jobs per minute that can be achieved?
(A) 281 (B) 21 (C) 41 (D) 13 (E) none of the above
Minimum Average job per minute = no. of Jobs/minimum total processing time = 25/525 = 0.05
Correct Option: (E)
Question #8:
Aggregate Run-out Method attempts to use the total production capacity available to produce just enough of each product so that if all production stops, inventory of each product runs out at the same time.
Aggregate Run-out time in months
= Total Inventory and Machine hours Available/Machine Hours required
Aggregate ROT = (53 + 121)/58 = 3 weeks
1
2
3
4=1x2
5=1*3
6=ROTx3
7=3+6
8=7-2
9=1x8
Product Line
Production
Inventory
Demand
Inventory
Demand
week Desired ending inve,
Weeks desired End Inv + Forecast
Req. Prod.
Assembly time Allocated
Products
Hours/Item
Items
Items/week
Hours
Hours
Items
units
Hours
A
0.1
120
50
12
5
150
200
80
8
B
0.2
100
80
20
16
240
320
220
44
C
0.1
110
50
11
5
150
200
90
9
D
0.3
200
80
60
24
240
320
120
36
E
0.2
90
40
18
8
120
160
70
14
121
58
111
Thus, processing time reuired for product C = 9 hours.
Correct Option: (E)
Job
Time on Machine 1
Time on Machine 2
Machine 1 Start
Machine 1 Finish
Machine 2 Start
Machine 2 Finish
Machine 2 Idle
Job Idle time
A
35
32
0
35
35
67
35
0
B
41
56
35
76
76
132
9
0
C
49
36
76
125
132
168
0
7
D
28
48
125
153
168
216
0
15
E
53
55
153
206
216
271
0
10