1 By: Prof. Y. Peter Chiu Scheduling ~ HOMEWORK SOLUTION ~
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Transcript of 1 By: Prof. Y. Peter Chiu Scheduling ~ HOMEWORK SOLUTION ~
1
By: Prof. Y. Peter Chiu
Scheduling
~ HOMEWORK SOLUTION ~
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HW # 4 Four trucks, 1, 2, 3, and 4, are waiting on a loading dock at XYZ
Company that has only a single service bay. The trucks are labeled in the order that they arrived at the dock.
Assume the current time is 1:00 p.m. The times required to unload each truck and the times that the goods they contain are due in the plant are given in the table below:
Determine the schedules that result for each of the rules: (1) FCFS ; (2) SPT ; (3) EDD ; and (4) CR. In each case compute the mean flow time, average tardiness, and number of tardy jobs.
Truck# Unloading time
Time Material Is Due
1 20 mins 1:25 p.m.
2 14 mins 1:45 p.m.
3 35 mins 1:50 p.m.
4 10 mins 1:30 p.m.
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HW # 4
FCFS
Mean flow time = 202/4 = 50.5Avg. Tardiness = 68/4 = 17Number of Tardy trucks = 2
Truck#
ti Fi di Ti
1 20 20 25 0
2 14 34 45 0
3 35 69 50 19
4 10 79 30 49
Total 202 68
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HW # 4
SPT
F’=157/4=39.25Avg. Ti=48/4=12# of Tardy Trucks = 2
Truck# ti Fi di Ti
4 10 10 30 0
2 14 24 45 0
1 20 44 25 19
3 35 79 50 29
Total 157 48
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HW # 4
EDD
F’=43.25T’=7.25# of Tardy job = 1
Truck# ti Fi di Ti
1 20 20 25 0
4 10 30 30 0
2 14 44 45 0
3 35 79 50 29
Total 173 29
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HW # 4
CR : Current Time = 1:00pm
Truck# ti di CR
1 20 25 25/20 =1.25*
2 14 45 45/14 =3.21
3 35 50 50/35 =1.43
4 10 30 30/10 =3
Pick!
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HW # 4
CR : Current Time = 1:00pm+20min = 1:20pm
Truck# ti di di-CurTime
CR
2 14 45 25 25/14 =1.79
3 35 50 30 30/35 =0.86*
4 10 30 10 10/10 =1
Pick!
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HW # 4
Current Time = 1:20pm+35min = 1:55pm
Late Jobs use “SPT” order, pick #4, then #2
Truck# ti di di-CurTime CR
2 14 45 -10
4 10 30 -25 Pick!
Truck# ti Fi di Ti
1 20 20 25 0 F’=54.75
3 35 55 50 5 T’=18.50
4 10 65 30 35 #of Tardy Jobs=3
2 14 79 45 34
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HW # 5 p.414 Five jobs must be scheduled for batch processing on a
mainframe computer system. The processing times and the promised times for each of the jobs are listed here.
job 1 2 3 4 5
processing time 40 min 2.5 hr 20 min 4 hr 1.5 hr
promised time 11:00 A.M. 2:00 P.M. 2:00 P.M. 1:00 P.M. 4:00 P.M.
Assume that the current time is 10:00 A.M.
(a) If the jobs are scheduled according to SPT, find the tardiness of each job and the mean tardiness of all jobs.
(b) Repeat the calculation in part (a) for EDD scheduling.
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HW # 5
SPT : Current Time 10:00 AM
3 – 1 – 5 – 2 – 4
Job ti Fi di Ti
3 20 10:20 240 0
1 40 11:00 60 0
5 1:30 12:00 360 0
2 2:30 15:00 240 60
4 4:00 19:00 180 360 T’=84 mins
420
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HW # 5 EDD : 1 – 4 – 3 – 2 – 5
(Tie uses ‘SPT’ ), otherwise : 1 – 4 – 2 – 3 – 5 ; T’=136
Job ti Fi di Ti
1 40 10:40 60 0
4 4:00 14:40 180 100
3 20 15:00 240 60
2 2:30 17:30 240 210
5 1:30 19:00 360 180 T’=110550
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HW # 6Consider the information given in Problem 4. Determine the
sequence that the truck should be unload in order to minimize (a) Mean flow time. (b) Maximum lateness. (c) Number of tardy jobs.
Four trucks, 1, 2, 3, and 4, are waiting on a loading dock at XYZ Company that has only a single service bay. The trucks are labeled in the order that they arrived at the dock.
Assume the current time is 1:00 p.m. The times required to unload each truck and the times that the goods they contain are due in the plant are given in the table below:
Truck# Unloading time
Time Material Is Due
1 20 mins 1:25 p.m.
2 14 mins 1:45 p.m.
3 35 mins 1:50 p.m.
4 10 mins 1:30 p.m.
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HW # 6 From #4
(a) SPT minimizes F’ : 4 – 2 – 1 – 3
(b) EDD minimizes maximum lateness
: 1 – 4 – 2 – 3
(c) By Moore’s Algorithm
: 1 – 4 – 2 – 3
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HW # 7 On May 1, a lazy MBA student suddenly realizes that he
has done nothing on seven different homework assignments and projects that are due in various courses. He estimates the time required to complete each project (in days) and also notes their due dates:
Project 1 2 3 4 5 6 7
Time (days) 4 8 10 4 3 7 14 Due date 4/20 5/17 5/28 5/28 5/12 5/7 5/15
Because projects 1, 3, and 5 are from the same class, he decides to do those in the sequence that they are due. Furthermore, project 7 requires results from projects 2 and 3, so project 7 must be done after 2 and 3 are completed. Determine the sequence in which he should do the projects in order to minimize the maximum lateness.
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HW # 7 1 53
2 7
4 6
last. #4 JOBS },,min{
}{min)}({min{4,6,7} VJOBS
FJ
LATENESS MAXIMUM MINIMIZE To
Vj
7
1ii
2314506502750
dFFg
50
iiVjii
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PROJ# 1 2 3 4 5 6 7
Time 4 8 10 4 3 7 14
Due Date -11 16 27 27 11 6 14
4}-7-3-2-{....5 far, so last JOB#5 3 6}-11,14-min{14
{5,6} V 148-22J4}-7-3-2-{.... far, so
last JOB#2 6 6}-11,22-16,22-min{22 {2,5,6} V 2210-32J4}-7-3-{... far, so
Last #3 JOB 5 6}-32 27,-32 16,-min{32 {2,3,6} V 3214-46J
Last. #7 JOB 3214}-6,46-min{46 {6,7} V 464-50J
HW # 7
17
4-7-3-2-5-6-1
Last JOB#6 5 6}-11 (-11),-min{11{1,6} V 113-14J
PROJ# ti Fi di Fi-di
1 4 4 -11 15
6 7 11 6 5
5 3 14 11 3
2 8 22 16 6
3 10 32 27 5
7 14 46 14 32
4 4 50 27 23
HW # 7
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8-7-3-5-6-4-1-2 1select {1,2}V8-7-3-5-6-4 4select {2,4}V8-7-3-5-6 6select {4,6}V8-7-3-5 5select {4,5,6}V8-7-3 3select {3,4,5}V8-7 7select {3,5,7}V8 8select {3,5,8}V
41362
m/c 1 JOBS 8
7
6
5
4
3
2
1
587
HW # 8
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HW # 9
(a) To minimize mean flow time SPT: 6-4-2-1-3-5
(b) To minimize “Number of Tardy Jobs”
Moore’s Algorithm
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Job ti Delivery ti di
1 1:12 15 1:27 3:30
2 :40 15 55 2:00
3 2:12 15 2:27 3:00
4 :30 15 45 5:00
5 3:06 15 3:21 4:00
6 :25 15 40 6:00
HW # 9
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HW # 9 (b) Moore’s Algorithm starting from EDD
Job ti’ Fi’ di Li
2 55 55 2:00 -1:05
3 2:27 3:22 3:00 22
1 1:27 4:49 3:30 1:19
5 3:21 8:10 4:00 4:10*
4 45 8:55 5:00 3:55
6 40 9:35 6:00 3:35
Delete Job # 3
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Job ti’ Fi’ di
2 55 55 2:00
1 1:27 2:22 3:30
5 3:21 5:43 4:00
4 45 5:00
6 40 6:00
Job ti’ Fi’ di
2 55 55 2:00
1 1:27 2:22 3:30
4 45 3:07 5:00
6 40 3:47 6:00
HW # 9
(b) Moore’s Algorithm
Delete Job # 5
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2-1-4-6-3*-5* (by SPT for tardy jobs)
or 2-1-4-6-5*-3*
# of Tardy Jobs = 2
(c) To minimize maximum lateness
EDD: 2-3-1-5-4-6
Max Li=4:10
HW # 9
(b) Moore’s Algorithm
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HW # 10
Seven jobs are to be processed through a single machine. The processing times and due dates are given here.
Project 1 2 3 4 5 6 7
Processing time 3 6 8 4 2 1 7
Due date 4 8 12 15 11 25 21
Determine the sequence of the jobs in order to minimize:
(a) Mean flow time.
(b) Number of tardy jobs.
(c) Maximum lateness & compute the maximum lateness.
(d) What is the makespan for any sequence?
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HW # 10
(a) SPT minimize F’
6 – 5 – 1 – 4 – 2 – 7 – 3
(b) To minimize Number of Tardy Jobs
Use Moore’s Algorithm
first EDD: 1 – 2 – 5 – 3 – 4 – 7 – 6
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Job ti Fi di Li
1 3 3 4 -1
2 6 9 8 1
5 2 11 11 0
3 8 19 12 7
4 4 23 15 8
7 7 30 21 9*
6 1 31 25 6
Delete Job # 2
HW # 10 (b) By Moore’s Algorithm
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Job ti Fi di
1 3 3 4
5 2 5 11
3 8 13 12
4 4 15
7 7 21
6 1 25
Delete Job # 3
HW # 10 (b) By Moore’s Algorithm
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∴ 1 – 5 – 4 – 7 – 6 – 2* - 3* ( tardy jobs by SPT)
or 1 – 5 – 4 – 7 – 6 – 3* - 2* Number Of Tardy Jobs = 2
Job ti Fi di
1 3 3 4
5 2 5 11
4 4 9 15
7 7 16 21
6 1 17 25
HW # 10 (b) By Moore’s Algorithm
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(C) EDD minimize Maximum lateness
1 – 2 – 5 – 3 – 4 – 7 – 6
maximum lateness = 9
(d)
31 same the is sequence any for
tmakespann
1ii
HW # 10
30
#37• To minimize maximum lateness subject to the
precedence constraints. Lawler’s Algorithm
Job# ti Di
1 4 5
2 10 10
3 2 7
4 1 9
5 8 22
6 3 25
7 2 18
8 6 20
1→ 2→ 5→ 6
4→ 7→ 8
3
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By Chiu’s algorithm
V1={3,6,8} max Di → 6
V2={3,5,8} max Di → 5
V3={2,3,8} → 8
V4={2,3,7} → 7
V5={2,3,4} → 2
V6={1,3,4} → 4
V7={1,3} → 3
Last → 1
The Optimal sequence is 1-3-4-2-7-8-5-6
#37
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The EndThe End