Seminar 8:
Critical Path Method
Problem 1: (Hillier and Lieberman, 10.3-1.)
You and several friends are about to prepare a lasagna dinner. The tasks to be
performed, their immediate predecessors, and their estimated durations are as
follows:
Task Task Description Tasks that Must Precede Time
A Buy the mozzarella cheese 30 minutes
B Slice the mozzarella 5 minutes
C Beat 2 eggs 2 minutes
D Mix eggs and ricotta cheese 3 minutes
E Cut up onions and mushrooms 7 minutes
F Cook the tomato sauce 25 minutes
G Boil large quantity of water 15 minutes
H Boil the lasagna noodles 10 minutes
I Drain the lasagna noodles 2 minutes
J Assemble all the ingredients 10 minutes
K Preheat the oven 15 minutes
L Bake the lasagna 30 minutes
a) Complete the table.
b) Construct the project network for preparing this dinner.
c) Use CPM to find minimal realization time and determine the critical path
d) Because of a phone call, you were interrupted for 6 minutes when you
should have been cutting the onions and mushrooms. By how much will
the dinner be delayed? If you use your food processor, which reduces the
cutting time from 7 to 2 minutes, will the dinner still be delayed?
Problem 2:
The project is defined by the table:
Activity duration immediate predecessors
A 5 B
9 C
11 A, B
D 6 B
E 7 A
F 5 C,D
G 9 C, E
a) Construct the project network
b) Use CPM to find minimal realization time and determine the critical path
Problem 3: The project is defined by the table:
Activity duration immediate predecessors
A 4 B
1 C
3 B
D 3 A, B
E 1 B
F 5 B
G 4 C, D
H 4 C, D, F
a) Construct the project network
b) Use CPM to find minimal realization time and determine the critical path
c) Use Excel template http://www.vertex42.com/ExcelTemplates/critical-pathmethod.html
for the construction of Gantt chart.