Project Management Practice ProblemBragg’s Bakery is building a new automated bakery downtown Sandusky. Here are the activities that need to be completed to get the new bakery built and the equipment installed.
ACTIVITYPREDECESSORNORMAL TIME (WEEK)CRASH TIME (WEEK)EXPEDITING COST/WEEKA-963000BA853500CA15104000DB,C532000EC1062500FD,E215000
Hint: I have directly provided the crashing cost per unit time.
a. What is the normal project length?
b. What is the critical path in this project?
c. Which activity will you choose to crash first to reduce the duration of the project by one week?
d. What is the project length if all activities are crashed to their minimum?
e. What is the slack for activity D?

Answer:

a. The normal project length is 36 weeks.

b. The critical path in this project is A-C-E-F.

c. The activity that you choose to crash first to reduce the duration of the project by one week is E because it has the least expediting cost/week amongst A, C, E, F.

d. The project length if all activities are crashed to their minimum is 23 weeks.

e. The slack for activity D is 5 weeks.

Explanation:

a) The normal length of the project = completion time of last activity = 36 weeks.

b) The criteria for critical activity:

[tex]LC_{i} = ES_{i} ,\\LC_{j} = ES_{j} ,\\[/tex]

[tex]ES_j - ES_i = LF_j - LF_{i} =[/tex] duration of the activity

where ES = Earliest start time, EF = Earliest finish time , LC = latest completion time, LF = latest finish time ,

The suffix- i refers to the preceding node, suffix-j refers to the succeeding node.

activities satisfying above all criteria are A, C, E, F

therefore critical path is A-C-E-F.

c) To reduce the project duration by 1 week. we should choose to crash among critical activities A, C, E, F. thus we choose to crash activity E because it has the least expediting cost/week amongst A, C, E, F.

d) if we crash all the activities to their minimum, then the project length = sum of crash time of all critical activities

= [6 + 10 + 6 + 1]

= 23 weeks.

e) The slack of activity d = LS - ES = 34 - 29

= 5 weeks

The critical path is given in the diagram,