CHAPTER 5: SCHEDULE COMPRESSION AND TIME-COST TRADE OFF

WHAT IS NETWORK COMPRESSION (CRASHING)?Crashing a project means shortening the normal duration of

the project schedule.

WHY CRASHING A PROJECT?There are many reasons for crashing a project:1- to avoid late penalties.2- to take advantages of monetary incentives for early

completion of a project.3- to beat the competition

OPTIONS TO ACCELERATE ACTIVITIES Improving productivity of existing resources Changing the working methods employed by

altering technology and types of resources

The most common method is increasing project resources. There are 2 approaches:

Adding number of resources Working longer: overtime & weekends

COST SLOPE = CRASH COST - NORMAL COST NORMAL TIME - CRASH TIME

COST SLOPE = CRASH COST - NORMAL COST

NORMAL TIME - CRASH TIME

NOTE Because the line shows the slope

between the normal and crash points, it is also understood that a project activity can be speeded up to some degree less than the complete crash point, relative to the slope of the crash line.

In analyzing crash options for project activities, the goal is to find the point at which time and cost trade-offs are optimized

Example1:Figure below shows a simple activity network model for a project

composed of three activities A,B, and C. project duration equals 30 days. What will be the cost to fully crash all activities

Activity Immediate predecessors

Normal time

Crash time

Cost per day to crash

ABC

------B

121020

3410

$100 300 200

1

3

4

A

B C

EXAMPLE1 CONTINUED

Act Cn Tn Tc Nb of days

Cost to crash

Cc

A $1100 12 3 9 $100/ day

= (9*100)+ 1100=$2000

B $3200 10 4 6 $300/day

= (6*300)+ 3200=$5000

C $2000 20 10 10 $200/day

= (10*200)+2000=$4000

The basic procedure for crashing a network is to crash activities along the critical path. Thus, activities on the critical path are potential candidates for crashing, because shortening non-critical activities would not have an impact on total project duration

From an economic standpoint, activities should be crashed according to crashing costs: crash those with the lowest crash costs first (having the flattest cost slope)

In order to make a rational decision on which activities, if any, to crash and on the extent of crashing desirable, a manager needs certain information:

1. Regular time and crash time estimates for each activity

2. Regular cost and crash cost estimates for each activity3. A list of activities that are on the critical path.

EXAMPLE 2 Suppose we have a project with only

eight activities, as illustrated in Table 1 which shows normal activity durations and costs and crashed durations and their costs.

We wish to determine which activities are the optimal candidates for crashing.

TABLE 1PROJECT ACTIVITIES AND COSTS

Normal Crashed

Activity Duration Cost Duration Cost

A 5 days $ 1,000 3 days $ 1,500

B 7 days 700 6 days 1,000

C 3 days 2,500 2 days 4,000

D 5 days 1,500 5 days 1,500

E 9 days 3,750 6 days 9,000

F 4 days 1,600 3 days 2,500

G 6 days 2,400 4 days 3,000

H 8 days 9,000 5 days 15,000

Total costs $22,450 $37,500

EXAMPLE 2 Normal Crashed cost slopeAct Duration Cost Duration CostA 5 days $ 1,000 3 days $ 1,500 $250/ dayB 7 days 700 6 days 1,000 300 C 3 days 2,500 2 days 4,000 1500D 5 days 1,500 5 days 1,500 ---E 9 days 3,750 6 days 9,000 1750F 4 days 1,600 3 days 2,500 900G 6 days 2,400 4 days 3,000 300H 8 days 9,000 5 days 15,000 2000

Total costs = $22,450

The calculations suggest that the least expensive activities to crash would be first, activity A ($250/day),

followed by activities B and G ($300/day). On the other hand, the project would incur

the greatest cost increases through crashing activities H, E, and C ($2,000/day, $1,750/day, and $1,500/day, respectively).

Note that in this example, we are assuming that activity D cannot be shortened, so no crashing cost can be calculated for it.

A-D-E-H= 27 DAYS

B,7 F,4

A,5 C,3 E,9

D,5 G,6

H,8

CHOOSE TO CRASH CRITICAL ACTIVITIESActivity Cost slope (per day) Critical

Path? A $ 250

Yes B 300

No C 1,500

No D —

Yes E 1,750

Yes F 900

No G 300

No H 2,000

Yes

Crashing activity A (lowest at $250) by 1 day will increase the project budget from $22,450 to $22,700. Fully crashing activity A will shorten the project duration to 25 days while increasing the cost to $22,950.

Activities B and G are the next candidates for crashing at $300 per day each.

Neither activity is on the project’s critical path, however, so the overall benefit to the project from shortening these activities may be minimal

The per unit cost to crash E is $1,750, and the cost to crash H is higher ($2,000). Thus, crashing activity E by 1 day will increase the project budget from $22,950 to $24,700

NORMAL COST= $22,450 @ 27 DAYS

Project Duration Costs crashed activity

27 days $22,450 none 26 days 22,700 A by

1 day 25 days 22,950 A by

1 day 24 days 24,700 E by

1 day 23 days 26,450 E by

1 day 22 days 28,200 E by

1 day 21 days 30,200 H by

1 day 20 days 32,200 H by

1 day 19 days 34,200 H by

1 day

  Relationship Between Cost and Days Saved in a Crashed Project

At each stage of the network compression calculations, a logical analysis must be made in accordance with the following rules:

1. List the activities on the critical path.2. Delete those with zero potential for compression; these will

include activities whose normal and crash durations are identical, as well as those already fully crashed in previous stages.

3. Select the activity with the lowest crash cost since it will give the cheapest compression.

4. Determine the amount by which this activity can be crashed and its relevant cost.

5. Determine if any network limitations to this compression exist and the reasons for their existence

6. Carry out the compression within the limitations imposed7. Compute the new project duration and the corresponding project

cost