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Networks and Project Analysis : Critical Path, Precedence Diagrams Start and Finish Dates

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The marketing department at Bodnar Industries is developing a promotional campaign to introduce a new product. A listing of the various activities required, their immediate predecessors, and estimates of their times (in days) is given below.

a) Draw the precedence diagram for this network.
b) Find the means and standard deviations of the activity times.
c) Find the expected early and late start and finish times.
d) Identify the critical path, the expected length of the critical path and the expected slack times for each activity.
e) What is the probability that the project will be completed in less than 60 days? More than 65 days?
f) How many days should the marketing manager allow for completion of the project if he wants to be 99% sure that the project will be completed within this allowed time?

Activity Description Immediate Predecessors Optimistic Time Most Likely Time Pessimistic Time
A Rough brochure layout -- 2 3 5
B Review brochure A 6 8 10
C Final brochure layout B 4 6 8
D Final brochure artwork C 5 7 11
E Design display -- 12 15 20
F Rough display artwork E 2 3 4
G Review display E 6 8 10
H Revise display G 2 3 4
I Final display artwork F,H 1 2 4
J Make display plates I 18 23 26
K Make brochure plates D,I 10 13 16
L Make and ship displays J 7 10 14
M Print and ship brochures K 6 8 10

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Solution Summary

Project Critical Path, Precedence Diagrams Start and Finish Dates are investigated. The solution is detailed and well presented.

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Operations Management

Two problems (attached is better formatting):

Environment Recycling, Inc. must clean up a large autormobile tire dump under a state environmental cleanup contract. The tasks, durations (weeks), costs, and predecessor relationships are shown in the table below.

Activity Predecessor(s) Normal Time Crash Time Normal Cost Crash Cost
A - 5 4 400 750
B A 12 9 1000 2200
C A 7 6 800 1100
D C 6 5 600 1000
E B, D 8 6 1200 2200
F D 3 2 800 1000
G D 3 2 500 650
H E 4 3 400 600
F, G, H 6 5 900 1300

a. Draw the project network.
b. Identify the critical path(s).
c. What is the total project-completion time and total cost?
d. What is the total project-completion time and lowest-cost solution if the state wants to complete the project 3 weeks early?


A competitor of Kozar International, Inc. has begun marketing a new instant-developing film project. Kozar has had a similar product under study in its R&D department but has not yet been able to begin production. Because of the competitor's action, top managers have asked for a speedup of R&D activities so that Kozar can produce and market instant film at the earliest possible date. The predecessor information and activity time estimates in months are shown here:

Activity Immediate Predecessors Optimistic Time Most Probable Time Pessimistic Time
A - 1 1.5 5
B A 3 4 5
C A 1 2 3
D B, C 3.5 5 6.5
E B 4 5 12
F C, D, E 6.5 7.5 11.5
G F 5 9 13

a. Draw the project network.
b. Develop an activity schedule for this project using early and late start and finish times, compute activity slack time, and define the critical activities.
c. What is the probability the project will be completed in time for Kozar to begin marketing the new product within 24 months?

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