1 6. t ime -c ost o ptimization objective: the optimization of project duration and cost by an...
DESCRIPTION
3 Can control the duration of an activity by varying the type and numbers of resources used, and the number of hours they are employed. To reduce activity duration, or bring forward its completion date: –can add resources; –change to higher performance resources; –employ more hours per day (overtime); –increase the number of shifts; –increase the number of working days; this is termed Activity Crashing.TRANSCRIPT
1
6. TIME-COST OPTIMIZATION
Objective: The optimization of project duration and cost by an appropriate crashing of activities.
Summary:6.1 Finding the Minimum Project Duration
and Corresponding Minimum Cost.
6.2 Sensitivity Analysis to Determinethe Minimum Project Cost.
6.3 Determining the Minimum Project Costfor a Target Project Duration.
2
6.1 FINDING THE MINIMUM PROJECT DURATION AND
CORRESPONDING MINIMUM COST
• Find the minimum practicable project duration that can be achieved, and then find the corresponding minimum project cost. – Eg: highway construction, reduce project
duration to minimize inconvenience to road users.
3
• Can control the duration of an activity by varying the type and numbers of resources used, and the number of hours they are employed.
• To reduce activity duration, or bring forward its completion date:– can add resources;– change to higher performance resources;– employ more hours per day (overtime);– increase the number of shifts;– increase the number of working days;
this is termed Activity Crashing.
4
• Typically there is a time-cost trade-off in that reducing the duration of a task tends to:– increase direct costs (labor, equipment, materials, subcontractors).
Why?• However, reducing the project duration will tend to:
– reduce indirect costs (site staff, head-office expenses, and penalty clauses).
• Also, increasing the duration of a task can:– increase direct costs by introducing idle time.
• There is a practical limit on how far an activity can be crashed. Why?
5
• In reducing the project duration, there is no point in crashing an activity to a point where it is no longer critical. Why?– Will not reduce project duration.– Likely to add to the costs.
• Also, where there is a choice, crash the activities that give rise to the least increase in costs.
6Fig. 6-1: Affect of Crashing an Activity on its Direct Costs
(a) activity 1-2
time
directcosts $
3 4 5
900500
normal duration
crash duration
(b) activity 2-3
time
directcosts $
4 5 6 7
1600
700
crashcost
normal cost
directcosts $
(c) activity 2-4
time6 7 8 9 10
200100
(d) activity 3-5
time
directcosts $
5 6
900
500
(e) activity 4-6
time
directcosts $
6 7 8 9 10
400200
directcosts $
(f) activity 5-7 & 6-7
time3 4 5 6 7
500300100
act 5-7
act 6-7
7
Fig. 6-2: Initial Attempt at Reducing Project Duration
(a) progress using normal activities for foundation operation
continued...
5
7
10
0
6
10
0
5
7
1 2
3
4
5
6
70 5
12
15 25
25
32 32
27
2515
15
50TF = 0
TF = 3
TF = 0
TF = 9
TF = 3
TF = 0
TF = 2
TF = 2
TF = 0
Normal Duration = 32
Normal cost = 500 + 700 + 100 + 500 + 200 + 300 + 100 = $2,400
8
Fig. 6-2: Initial Attempt at Reducing Project Duration
(b) progress with all activities crashed
3
4
6
0
5
6
0
3
4
1 2
3
4
5
6
70 3
7
9 15
15
19 19
16
159
9
30TF = 0
TF = 2
TF = 0
TF = 4
TF = 2
TF = 0
TF = 1
TF = 1
TF = 0Note, activities usecrashed durations
Crashed Duration= 19 (down 13)
Crashed cost = 900 + 1600 + 200 + 900 + 400 + 500 + 200 = $4,700 (an increase of $2,300)
9
Fig. 6-3: Optimization of Cost by Relaxing Non-Critical Activities
(a) first step in relaxing non-critical activities
continued...
Save costs by relaxingnon-critical activities
Start where the great-est savings can be made
3
4
6
0
6
6
0
3
4
1 2
3
4
5
6
70 3
7
9 15
15
19 19
16
159
9
30TF = 0
TF = 2
TF = 0
TF = 3
TF = 2
TF = 0
TF = 1
TF = 1
TF = 0
relaxed by 1
Crashed Duration= 19 (unchanged)
Crashed cost = 900 + 1600 + 200 + 500 + 400 + 500 + 200 = $4,300 (a saving of $400)
10
Fig. 6-3: Optimization of Cost by Relaxing Non-Critical Activities
(b) second step in relaxing non-critical activities
continued...
Select activitywith next bestcost savings
3
6
6
0
6
6
0
3
4
1 2
3
4
5
6
70 3
9
9 15
15
19 19
16
159
9
30TF = 0
TF = 0
TF = 0
TF = 1
TF = 0
TF = 0
TF = 1
TF = 1
TF = 0
relaxed by 2
Crashed Duration= 19 (unchanged)
Crashed cost = 900 + 1000 + 200 + 500 + 400 + 500 + 200 = $3,700 (a saving of $1,000 from complete crash)
11
Fig. 6-3: Optimization of Cost by Relaxing Non-Critical Activities
(c) third step in relaxing non-critical activities
Select activitywith next bestcost savings
3
6
6
0
6
6
0
4
4
1 2
3
4
5
6
70 3
9
9 15
15
19 19
15
159
9
30TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
relaxed by 1
Crashed Duration= 19 (unchanged)
Crashed cost = 900 + 1000 + 200 + 500 + 400 + 400 + 200 = $3,600 (a saving of $1,100 from complete crash)
Note, increase in number ofcritical activities
12
6.2 SENSITIVITY ANALYSIS TO DETERMINE MINIMUM PROJECT
COST• Find the minimum project cost, and then find the corresponding minimum project duration.• Two methods:
– Start with normal activity network and gradually crash:• Crash critical activities with smallest rate of change in cost.
– Start with crashed activity network (after optimized for cost) and gradually relax:• Relax activities with largest rate of change in cost.
13
Fig. 6-4: Cost Senstivity Analysis by Relaxing Critical Activities(a) first step in cost sensitivity analysis
continued...
Start with crashedactivity network
optimized for cost
PRIMAVERA
BCN Mouse
Crashingactivities !!! CRASH !!!
3
6
6
0
6
6
0
4
4
1 2
3
4
5
6
70 3
9
9 15
15
19 19
15
159
9
30TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
Project Duration= 19 days
Direct Cost = 900 + 1000 + 200 + 500 + 400 + 400 + 200= $3,600
Relax activities, slowlyextending project duration
(for all parallel paths).
Which activity(ies)give the greatest cost
reduction rate ?
There aresix alternatives !
1) Relaxing activity 1-2gives what rate ?
$200/day
2) Relaxing activities2-3 & 2-4 gives ?
300+25=$325/day
3) Relaxing activities3-5 & 2-4 gives ?
0+25=$25/day
activity 3-5is alreadyat itsnormalduration
4) Relaxing activities3-5 & 4-6 gives ?
0+50=$50/day
5) Relaxing activities3-5 & 6-7 gives ?
0+33.3=$33.3/day
6) Relaxing activities5-7 & 6-7 gives ?
100+33.3=$133.3/day
So, relax activities2-3 & 2-4 by 1 daysaving 300+25=$325
7
730
6
6
0
4
4
1 2
3
4
5
6
70 3
10
10 16
16
20 20
16
1610
10
30TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
Project Duration= 20 days
Direct Cost = 900 + 700 + 175 + 500 + 400 + 400 + 200= $3,275
14Fig. 6-5: Senstivity of Costs to Varying the Project Duration
5000 4600 4200 3800 3400 3000 2600 2200 1800 1400
19 20 21 22 23 24 25 26 27 28 29 30 31 32
project duration (days)
cost ($) = Indirect Costs @ $75/day= Direct Costs= Combined Costs
15
Fig. 6-4: Cost Senstivity Analysis by Relaxing Critical Activities(b) second step in cost sensitivity analysis
continued...
30
6
6
0
4
4
1 2
3
4
5
6
70 3
10
10 16
16
20 20
16
1610
10
30TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 07
7
Project Duration= 20 days
Direct Cost = 900 + 700 + 175 + 500 + 400 + 400 + 200= $3,275
Relax activity 1-2 by 2 days
saving 2x200=$400
53
0
6
6
0
4
4
1 2
3
4
5
6
70 5
12
12 18
18
22 22
18
1812
12
50TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 07
7
Project Duration= 22 days
Direct Cost = 500 + 700 + 175 + 500 + 400 + 400 + 200= $2,875
16Fig. 6-5: Senstivity of Costs to Varying the Project Duration
5000 4600 4200 3800 3400 3000 2600 2200 1800 1400
19 20 21 22 23 24 25 26 27 28 29 30 31 32
project duration (days)
cost ($) = Indirect Costs @ $75/day= Direct Costs= Combined Costs
17
Fig. 6-4: Cost Senstivity Analysis by Relaxing Critical Activities(c) third step in cost sensitivity analysis
continued...
50
6
6
0
4
4
1 2
3
4
5
6
70 5
12
12 18
18
22 22
18
1812
12
50TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 07
7
Project Duration= 22 days
Direct Cost = 500 + 700 + 175 + 500 + 400 + 400 + 200= $2,875
Relax activities5-7 & 6-7 by 1 day
saving 100+33.3=$133.3
5
5
50
6
6
0
4
4
1 2
3
4
5
6
70 5
12
12 18
18
23 23
18
1812
12
50TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 07
7
Project Duration= 23 days
Direct Cost = 500 + 700 + 175 + 500 + 400 + 300 + 166.7= $2,741.7
18Fig. 6-5: Senstivity of Costs to Varying the Project Duration
5000 4600 4200 3800 3400 3000 2600 2200 1800 1400
19 20 21 22 23 24 25 26 27 28 29 30 31 32
project duration (days)
cost ($) = Indirect Costs @ $75/day= Direct Costs= Combined Costs
19
Fig. 6-4: Cost Senstivity Analysis by Relaxing Critical Activities(d) fourth step in cost sensitivity analysis
continued...
50
6
6
0
5
5
1 2
3
4
5
6
70 5
12
12 18
18
23 23
18
1812
12
50TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 0
TF = 07
7
Project Duration= 23 days
Direct Cost = 500 + 700 + 175 + 500 + 400 + 300 + 166.7= $2,741.7
Relax activity4-6 by 4 days
saving 4x50 = $200
10
50
6
6
0
5
5
1 2
3
4
5
6
70 5
12
12 22
22
27 27
22
2212
12
50TF = 0
TF = 0
TF = 0
TF = 4
TF = 0
TF = 0
TF = 0
TF = 0
TF = 07
7
Project Duration= 27 days
Direct Cost = 500 + 700 + 175 + 500 + 200 + 300 + 166.7= $2,541.7
20Fig. 6-5: Senstivity of Costs to Varying the Project Duration
5000 4600 4200 3800 3400 3000 2600 2200 1800 1400
19 20 21 22 23 24 25 26 27 28 29 30 31 32
project duration (days)
cost ($) = Indirect Costs @ $75/day= Direct Costs= Combined Costs
21
Fig. 6-4: Cost Senstivity Analysis by Relaxing Critical Activities(e) fifth step in cost sensitivity analysis
50
6
10
0
5
5
1 2
3
4
5
6
70 5
12
12 22
22
27 27
22
2212
12
50TF = 0
TF = 0
TF = 0
TF = 4
TF = 0
TF = 0
TF = 0
TF = 0
TF = 07
7
Project Duration= 27 days
Direct Cost = 500 + 700 + 175 + 500 + 200 + 300 + 166.7= $2,541.7
Relax activity6-7 by 2 days
saving 2x33.3 = $66.7
7
50
6
10
0
5
5
1 2
3
4
5
6
70 5
12
12 22
22
29 29
24
2212
12
50TF = 0
TF = 0
TF = 0
TF = 6
TF = 0
TF = 0
TF = 2
TF = 2
TF = 07
70
Project Duration= 29 days
Direct Cost = 500 + 700 + 175 + 500 + 200 + 300 + 100= $2,475
22Fig. 6-5: Senstivity of Costs to Varying the Project Duration
5000 4600 4200 3800 3400 3000 2600 2200 1800 1400
19 20 21 22 23 24 25 26 27 28 29 30 31 32
project duration (days)
cost ($) = Indirect Costs @ $75/day= Direct Costs= Combined Costs
Finally, relaxing activity 2-4by 3 days takes us back to
the normal network.
Optimum combinedcosts @ 23 days
23
6.3 DETERMINING MINIMUM PROJECT COST FOR A TARGET
DURATION• Find the minimum project cost for a given
target project duration. – Eg: speed-up of the project to meet the
contractual target date.
24Fig. 6-5: Senstivity of Costs to Varying the Project Duration
5000 4600 4200 3800 3400 3000 2600 2200 1800 1400
19 20 21 22 23 24 25 26 27 28 29 30 31 32
project duration (days)
cost ($)
= Combined Costs
If target project duration= 20 days; use network
in Fig. 6-4a.
If target project duration= 21 days; use network
in Fig 6-4b, relaxing act 1-2by 1 day only to 6 days
If target project duration= 27 days; might use networkrelaxed to 23 days (Fig. 6-4c)