CB2201 Quantitative Methods Project Management (Solutions) Q12.12
Sid Davidson is the personnel director of Babson and Willcount, a company that specializes in consulting and research. One of the training programs that Sid is considering for the middle-level managers of Babson and Willcount is leadership training. Sid has listed a number of activities that must be completed before a training program of this nature could be conducted. The activities and immediate predecessors appear in the folloing table!
AC!"!#
!MM$%!A$ P&$%$C$SS'&S
A
--
B
--
C
--
D
B
E
A,D
F
C
G
E,F
Develop a netor" for this problem. Solution
%
#
Start
B
$
D
&
'inish
'
(
Q12.1
Sid Davidson as able to determine the activity times for the leadership training program. )e ould li"e to determine the total pro*ect completion time and the critical path. The activity times appear in the folloing table +see roblem (.(!
AC!"!#
!M$ (%A#S)
A
B
/
C
(
D
(0
E
1
F
2
G
3 1/
Solution
S 5 (1
S50
# 0 (1 (/
S50
Start
B /0
/0 /
S 5 (( $ (0 ((( (
% 1(/ (3(/ (3
S50
S50 D (0/ (// (/
& 3(3 2(3 2
'inish
S 5 (( ' 2( 4( (3
$ritical path is B-D-%-& Total pro*ect completion time is 2 days
Q12.1
6onohan 6achinery specializes in developing eed-harvesting e7uipment that is used to clear small la"es of eeds. &eorge 6onohan, president of 6onohan 6achinery, is convinced that harvesting eeds is far better than using chemicals to "ill eeds. $hemicals cause pollution, and the eeds seem to gro faster after chemicals have been used. &eorge is contemplating the construction of a machine that ould harvest eeds on narro rivers and aterays. The activities that are necessary to build one of these e8perimental eed-harvesting machines are listed in the folloing table. $onstruct a netor" for these activities.
AC!"!#
!MM$%!A$ P&$%$C$SS'&S
A
--
B
--
C
A
D
A
E
B
F
B
G
C,E
H
D,F
Solution
$ &
# D Start
'inish % ) B '
1
Q12.1*
#fter consulting ith Butch 9ander, &eorge 6onhan as able to determine the activity times for constructing the eed-harvesting machine to be used on narro rivers. &eorge ould li"e to determine %S, %', :S, :', and slac" for each activity. The total pro*ect completion time and the critical path should also be determined. +See roblem (-(2 for details. The activity times are shon in the folloing table!
AC!"!#
!M$ (+$$,S)
A
2
B
/
C
1
D
E
;
F
2
G
(0
H
4 Slac"50
Slac"50 # 20
20 2
$ 2 2
1 < <
Slac"50
Slac"5;
& (0< (<< (<
D 2 3(0 (
Start
'inish
Slac"50 B /0 /0 /
%
;/ <
Slac"50
) 4(( (3( (<
Slac"5(
' 2/ ((2 (
$ritical paths are #-$-& and B-%-&.
Slac"5(
Total pro*ect completion time is (< ee"s. ;
Q1.2-
Boman Builders manufactures steel storage sheds for commercial use. =oe Boman, president of Boman Builders, is contemplating producing sheds for home use. The activities necessary to build an e8perimental model and related data are given in the accompanying table.
+a. What is the pro*ect completion date>
+b. 'ormulate an : problem to crash this pro*ect to (0 ee"s.
Activit
/ormal ime
Crash ime /ormal Cost ()
Crash Cost ()
!mmediate Predecessors
A
1
(000
(200
-
B
(
000
400
-
C
(
(
100
100
-
D
4
1
(100
(200
A
E
2
1
3/0
(000
B
F
(
;000
/000
C
G
;
(/00
000
D,E
Solution
+a
Thus the pro*ect completion date is (; ee"s. /
+b ?o the pro*ect is crashed to (0 ee"s, the : formulation ill be! Solution Activit /ormal
Crash
/ormal
Crash
!mmediate
Crash Cost
ime
ime
Cost ()
Cost ()
Predecessors
er ee3 ()
A
1
(,000
(,200
-
200
B
(
,000
,400
-
400
C
(
(
100
100
-
0
D
4
1
(,100
(,200
A
4/
E
2
1
3/0
(,000
B
/0
F
(
;,000
/,000
C
(,000
G
;
(,/00
,000
D,E
/0
here $rash $ost per ee" 5
$rash $ost - ?ormal $ost ?ormal Time - $rash Time
%ecision "aria4les5
:et @i be the earliest finish time for activity i +here i 5 a, b, c,A, g @start be the start time for ro*ect @finish be the earliest finish time of pro*ect i be the amount of time reduced C crashed for activity i
'4jective 6unction5
6in 5 200# E 400B E 0$ E 4/D E /0% E (,000' E /0&
Constraints5 Precedence relationshi
'or #ctivity #, @#
≥ @start E
1 F #,
i.e. @# F @start E #
≥
1
Grerite the e7uationH
Similarly, @B F @start E B
≥
@$ F @start E $
≥
(
2
'or #ctivity D, @D
≥ @# E
4 F D,
i.e. @D F @# E D ≥ 4
Similarly, @% F @B E % ≥ 2 @' F @$ E ' ≥ @& F @D E & ≥ ; @& F @% E & ≥ ;
Activit Crash ime 7imit
#
≤ (I
B
≤ (I
$
≤ 0I
D
≤ ;I
% ≤ 1I '
≤ (I
&
≤
Project Comletion
@finish F @&
≥0
@finish F @'
≥0
@finish
≤ (0
ee"s
/on8negativit
@i, @start, @finish, i J 0
4
