Planning of Barus

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Planning of Barus Holley Addition
Activity Duration, Days
Predecessors
215
Procurement
60
Site Preparation
SP
31
Pour Foundation
P, PF
15
Erect Steel
ES
40
Roof, Ext. Wall
ES
50
Fabricate Glass
REW
85
Int Walls Gl.
REW
55
Landscaping
280
Acquire Furn.
IWG, AF, FG
15
Install Furn.
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Arrow Diagram (Network)
Nodes (I) Events
Arrows (I,J) Activities (Tasks)
2
5
PF
L
REW
SP
IWG
P
ES
FG
9
3
4
1
6
7
AF
IF
8
4
Forward Pass Find ES(I)
ES(I) Earliest Start of Activities emanating
from node I
60
270
2
5
PF
L
REW
SP
IWG
P
ES
FG
9
3
4
1
6
7
370
215
230
280
355
0
AF
IF
8
355
5
Backward Pass Find LC(I)
LC(I) Latest Completion of Activities
terminating at Node I.
184
270
60
270
2
5
PF
L
REW
SP
IWG
P
ES
FG
9
3
4
1
6
7
370
215
230
280
355
0
215
370
230
355
0
355
AF
IF
8
355
355
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Determining the Critical Path
An Activity (I,J) is on the Critical Path if the
following three conditions are met ES(I)
LC(I) ES(J) LC(J) ES(J) ES(I) LC(J)
LC(I) D(I,J) where D(I,J) is the duration of
Activity (I,J).
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Identify Critical Path
184
270
60
270
2
5
PF
L
REW
SP
IWG
P
ES
FG
9
3
4
1
6
7
370
215
230
355
280
0
370
215
230
355
355
0
AF
IF
355
355
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Determining the Slack Times (Floats)
The Slack Time, ST(I,J), of an Activity (I,J) is
the difference between the maximum time
available to perform the Activity (i.e. LC(J)
ES(I)) and its duration D(I,J) that
is, ST(I,J) LC(J) ES(I) D(I,J). For
Activities on the Critical Path the Slack Time is
zero.
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Determine Slack Times
184
270
60
270
2
5
SP(124)
L (45)
PF(124)
REW
IWG
ES
P
P
FG(75)
9
3
4
1
6
7
370
215
230
355
280
0
370
215
230
355
355
0
AF(75)
IF
355
355
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Construct Time Chart
1
5
4
3
7
9
8
1
2
2
3
6
4
5
9
8
1
200
400
300
100
0
Elapsed Time, Days
Critical Tasks
Non-Critical Tasks
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Schedule Project
1
5
4
3
7
9
8
SP
1
2
PF
2
3
FG
6
4
L
5
9
AF
8
1
200
400
300
100
0
Elapsed Time, Days
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LINGO Model Tasks
MODEL SETS TASKS / START, PROCUREMENT,
SITE_PREPARATION, POUR_FOUNDATION, ERECT_STEEL,
ROOF_EXT_WALL, FABRICATE_GLASS, INT_WALLS_GLASS,
LANDSCAPING, ACQUIRE_FURN, INSTALL_FURN, FINISH/
TIME, ES, LS, SLACK PRED( TASKS, TASKS)
/ START, SITE_PREPARATION, START,
PROCUREMENT, START, ACQUIRE_FURN, SITE_PREPARATI
ON, POUR_FOUNDATION, PROCUREMENT, ERECT_STEEL,
POUR_FOUNDATION, ERECT_STEEL, ERECT_STEEL,
ROOF_EXT_WALL, ERECT_STEEL, FABRICATE_GLASS,
ROOF_EXT_WALL, INT_WALLS_GLASS,
FABRICATE_GLASS, INSTALL_FURN,
ROOF_EXT_WALL, LANDSCAPING, INT_WALLS_GLASS,
INSTALL_FURN, ACQUIRE_FURN, INSTALL_FURN, LANDS
CAPING, FINISH, INSTALL_FURN, FINISH / ENDSETS


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LINGO Model Data

DATA TIME 0, 215, 60, 31, 15, 40, 50, 85,
55, 280, 15 ,0 ENDDATA

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LINGO Model Algorithm

_at_FOR( TASKS( J) J GT 1 ES( J) _at_MAX( PRED(
I, J) ES( I) TIME( I))) _at_FOR( TASKS( I) I
LT LTASK LS( I) _at_MIN( PRED( I, J) LS( J) -
TIME( I))) _at_FOR( TASKS( I) SLACK( I) LS( I)
- ES( I)) ES( 1) 0 LTASK _at_SIZE(
TASKS) LS( LTASK) ES( LTASK) END

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LINGO Solution Input Data
Feasible solution found at step 0
Variable
Value
LTASK 12.00000
TIME( START)
0.0000000 TIME(
PROCUREMENT) 215.0000
TIME( SITE_PREPARATION) 60.00000
TIME( POUR_FOUNDATION)
31.00000
TIME( ERECT_STEEL) 15.00000
TIME( ROOF_EXT_WALL)
40.00000 TIME(
FABRICATE_GLASS) 50.00000
TIME( INT_WALLS_GLASS) 85.0000
TIME( LANDSCAPING)
55.00000
TIME( ACQUIRE_FURN) 280.0000
TIME( INSTALL_FURN)
15.0000
TIME( FINISH) 0.0000000
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LINGO Solution Earliest Starts
ES( START)
0.0000000 ES( PROCUREMENT)
0.0000000 ES( SITE_PREPARATION)
0.0000000 ES( POUR_FOUNDATION)
60.00000 ES( ERECT_STEEL)
215.0000 ES( ROOF_EXT_WALL)
230.0000 ES( FABRICATE_GLASS)
230.0000 ES( INT_WALLS_GLASS)
270.0000 ES( LANDSCAPING)
270.0000 ES( ACQUIRE_FURN)
0.0000000 ES( INSTALL_FURN)
355.0000 ES( FINISH)
370.0000
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LINGO Solution Latest Starts
Latest Start is defined by LS(I,J) LC(I,J)
D(I,J).
LS( START)
0.0000000 LS( PROCUREMENT)
0.0000000 LS( SITE_PREPARATION)
124.0000 LS( POUR_FOUNDATION)
184.0000 LS( ERECT_STEEL)
215.0000 LS( ROOF_EXT_WALL)
230.0000 LS( FABRICATE_GLASS)
305.0000 LS( INT_WALLS_GLASS)
270.0000 LS( LANDSCAPING)
315.0000 LS( ACQUIRE_FURN)
75.00000 LS( INSTALL_FURN)
355.0000 LS( FINISH)
370.0000
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LINGO Solution Slack Times
SLACK( START) 0.0000000
SLACK( PROCUREMENT) 0.000000 SLACK(
SITE_PREPARATION) 124.0000 SLACK(
POUR_FOUNDATION) 124.0000 SLACK(
ERECT_STEEL) 0.0000000 SLACK(
ROOF_EXT_WALL) 0.0000000 SLACK(
FABRICATE_GLASS) 75.00000 SLACK(
INT_WALLS_GLASS) 0.0000000 SLACK(
LANDSCAPING) 45.00000 SLACK(
ACQUIRE_FURN) 75.00000 SLACK(
INSTALL_FURN) 0.0000000 SLACK(
FINISH) 0.0000000

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CPM with Crashing LINGO Model (a)
MODEL ! A CPM model with crashing
SETS TASKS / START, PROCUREMENT,
SITE_PREPARATION, POUR_FOUNDATION,
ERECT_STEEL, ROOF_EXT_WALL, FABRICATE_GLASS,
INT_WALLS_GLASS, LANDSCAPING, ACQUIRE_FURN,
INSTALL_FURN, FINISH/ TIME, !
Normal time for task TMIN, ! Min
time at max crash CCOST, ! Crash
cost/unit time EF, ! Earliest
finish CRASH ! Amount of
crashing
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Accessing LINGO
Go to Engineering Instructional Computer
Facility Prince Engineering Laboratory Balcony
(Enter from Brook Street follow corridor to
third stairwell on the right, go up two flights
of stairs) Logon Name First 6 characters of
last name followed by first and second letters
of first name. Password Rightmost 6 numbers
and letters of student ID number. Open
Lingo Go to the Start menu.
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PRINCE LAB COMPUTING FACILITY
LINK TO Logon FAQ
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CPM with Crashing LINGO Model (b)
! Here are the precedence relations PRED(
TASKS, TASKS)/ START, SITE_PREPARATION, START,
PROCUREMENT, START, ACQUIRE_FURN, SITE_PREPARATI
ON, POUR_FOUNDATION, PROCUREMENT, ERECT_STEEL,
POUR_FOUNDATION, ERECT_STEEL, ERECT_STEEL,
ROOF_EXT_WALL, ERECT_STEEL, FABRICATE_GLASS,
ROOF_EXT_WALL, INT_WALLS_GLASS,
FABRICATE_GLASS, INSTALL_FURN,
ROOF_EXT_WALL, LANDSCAPING, INT_WALLS_GLASS,
INSTALL_FURN, ACQUIRE_FURN INSTALL_FURN, LANDSC
APING, FINISH, INSTALL_FURN, FINISH /
ENDSETS
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CPM with Crashing LINGO Model (c)
DATA TIME 0, 215, 60, 31, 15, 40, 50, 85,
55, 280, 15, 0 ! Normal times TMIN
0, 195, 50, 28, 12, 35, 45, 50, 40,
240, 13, 0 ! Crash times CCOST 0, 2, 3, 3,
4, 4, 5, 3, 2, 1, 2, 0 ! Cost
(K)/day to crash DUEDATE 348 !
Project due date ENDDATA
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CPM with Crashing LINGO Model (d)
! The crashing LP model ! Define earliest
finish, each predecessor of a task constrains
when the earliest time the task can be
completed. The earliest the preceding task can
be finished plus the time required for the
task minus any time that could be reduced by
crashing this task. _at_FOR( PRED( I, J) EF(
J) gt EF( I) TIME( J) - CRASH( J) )
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CPM with Crashing LINGO Model (e)
! For each task, the most it can be crashed is
the regular time of that task minus minimum time
for that task _at_FOR( TASKS( J) CRASH( J)
lt TIME( J) - TMIN( J) ) ! Meet the due date !
This assumes that there is a single last task
EF( _at_SIZE( TASKS)) lt DUEDATE
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CPM with Crashing LINGO Model (f)
! Minimize the sum of crash costs MIN _at_SUM(
TASKS CCOST CRASH) END
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CPM with Crashing LINGO Solution
Optimal solution found at step 13
Objective value 44.00000
Variable Value Reduced Cost
EF( START) 0.0000000
2.000000 EF( PROCUREMENT)
195.0000 0.0000000 EF(
SITE_PREPARATION) 60.00000
0.0000000 EF( POUR_FOUNDATION)
91.00000 0.0000000 EF(
ERECT_STEEL) 210.0000 0.0000000
EF( ROOF_EXT_WALL) 250.0000
0.0000000 EF( FABRICATE_GLASS)
335.0000 0.0000000 EF(
INT_WALLS_GLASS) 335.0000
0.0000000 EF( LANDSCAPING)
305.0000 0.0000000 EF(
ACQUIRE_FURN) 280.0000 0.0000000
EF( INSTALL_FURN) 348.0000
0.0000000 EF( FINISH)
348.0000 0.0000000
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CPM with Crashing LINGO Solution(Crash Times)
Variable Value Reduced Cost
CRASH( START) 0.0000000
0.0000000 CRASH( PROCUREMENT)
20.00000 0.0000000 CRASH(
SITE_PREPARATION) 0.0000000 3.000000
CRASH( POUR_FOUNDATION) 0.0000000
3.000000 CRASH( ERECT_STEEL)
0.0000000 2.000000 CRASH(
ROOF_EXT_WALL) 0.0000000 2.000000
CRASH( FABRICATE_GLASS) 0.0000000
5.000000 CRASH( INT_WALLS_GLASS)
0.0000000 1.000000 CRASH(
LANDSCAPING) 0.0000000 2.000000
CRASH( ACQUIRE_FURN) 0.0000000
1.000000 CRASH( INSTALL_FURN)
2.000000 0.0000000 CRASH(
FINISH) 0.0000000 0.0000000