1. Project Scheduling Critical Path Method
Based on material from Chapter 6 of Project Management and Teamwork, by Karl Smith

2. How do you schedule complex projects?
Make a list of things to do?
Use an outline?
Draw a concept map?
Focus on those things we know how to do first?
Use project management software?

3. Dinner & Concert How much time do you need to prepare and consume the meal?
Menu consists of soup and baked chicken
Soup must be boiled 35 minutes and will allow 15 minutes to serve and consume
Chicken dish requires 30 minutes to boil rice, 15 minutes to brown chicken in frying pan, 15 minutes to bake rice and chicken in baking dish
Sauce takes 5 minutes to prepare in frying pan and 15 minutes to boil peas
Only have two pots and one frying pan
Wine takes 5 minutes to uncork and 30 minutes to let breath before serving
Allow 25 minutes to serve and consume entrée and wine

4. Meal Planning Exercise Work Breakdown Structure
Boil Soup
(Pot 1)
Eat Soup
(Pot 1)
Eat Entree
Boil Peas
(Pot 2)
Boil Rice
(Pot 2)
Bake Entree
Brown Chicken
(Fry Pan)
Prepare Sauce
(Fry Pan)
Activity Name
(Resource)
Open Wine
Wine Breathes

5. Critical Path Method
Work breakdown structure ok for simple task with few activities
When number of task large, a systematic solution is to use the Critical Path Method (CPM)
to use CPM must know the duration of each activity and the predecessors of each

6. CPM - Forward Pass
Early Start (ES) - Earliest time that each activity can start
- obtained by adding the earliest start of its latest starting predecessor to the that predecessor’s duration
- when two or more activities must be competed before the next one can start, then the maximum must be used
Early Finish (EF) - Determined by summing the early start (ES) and duration

7. Meal Planning Exercise Critical Path Method - Forward Pass35 50 35
Boil Soup 35
Eat Soup 15 50 75
Eat Entree 25 30 45
Boil Peas 15 30 30 45
Boil Rice 30
Bake Entree 15 15 15 20
Brown Chicken 15
Prepare Sauce 5 5 5 35 ES EF
Open Wine 5
Wine Breathes 30
Activity Name
duration

8. CPM - Backward Pass
Late Start (LS) - Latest possible starting time that each activity can have
- calculated as the earliest starting successor, less the duration of the activity under consideration
Late Finish (LF) - The resulting finish time based on late start (LS)

9. Meal Planning Exercise Critical Path Method - Backward Pass35 50 35
Boil Soup 35
Eat Soup 15 35 50 50 75 35
Eat Entree 25 30 45 50 75
Boil Peas 15 30 30 45 35 50
Boil Rice 30
Bake Entree 15 5 35 35 50 15 15 20
Brown Chicken 15
Prepare Sauce 5 15 30 30 35 5 5 35 ES EF
Open Wine 5
Wine Breathes 30
Activity Name
duration 15 20 20 50 LS LF

10. CPM - Critical Path & Floats
Critical Path - The path for which activities cannot be delayed
- activities on critical path will have equal earliest and latest times and are call critical
Floats - The amount the termination of an activity can be delayed before delaying a successor is called free float (FF). FFi = (ESi+1) min - ESi - Di
The amount of slack an activity has before it would cause the path on which it lies to become critical is called the total float (TF). TFi = LFi - EFi

11. Meal Planning Exercise
Critical Path 35 50 35
Boil Soup 35
Eat Soup 15 35 50 50 75 35
Eat Entree 25 30 45 50 75
Boil Peas 15 30 30 45 35 50
Boil Rice 30
Bake Entree 15 15 35 35 50 15 15 20
Brown Chicken 15
Prepare Sauce 5
FF = = 5 15 30 30 35 5 5 35 ES EF
Open Wine 5
Wine Breathes 30
Activity Name
duration 15 20 20 50 LS LF

12. CritPath Program http://www.ce.umn.edu/~smith
Allows easy entry of activites
Provides critical path calculations (ES, EF, LS, LF, Float) and algorithm stepper
Calculates critical path
Gives associated Gantt Chart - a time-scaled network (Gantt Chart does not show interdependence)