Software Ltd has established a project team to undertake some important market research work. It is possible to reduce the expected or 'normal' times for certain activities in units of one week (but not in fractions of a week) but at an extra cost. The relevant information is given below.

activity Predecessor. Normal Time (weeks). Normal Cost crash time. crash cost

a 5 5000. 3 6000

b 4 3000 4 3000

c a 2 6000 1 21000

d c 4 1000. 4 1000

e b 5 4000. 3 7000

f b 5 8000. 1 14000

g b,c 4 4000. 2 24000

h f 3 5000. 2 15000

In addition to the costs shown there is a cost of retainer fees and administration overheads of $10000 for each week that the project lasts.

a) What is the normal expected duration of the project? What is the critical path?

The normal expected duration of the project is:

The critical path is:

b) What would be the cost of completing the project using the normal durations?

The cost of completing the project using the normal durationsis:

c) What would be the duration of the project if costs are to be minimized?

activity maximum crash time crash cost

a

b

c

d

e

f

g

h

stage crash activity time reduction. Resulting Critical Path(s). Project Duration (weeks) Project Direct Costs ($)

Crash Cost ($) Total Indirect Costs ($) Total Project Costs ($)

0

1

2

Therefore the optimal project duration is

weeks, and the optimal project cost is

.