Decision - Critical Path Analysis

Question 1

What is the float of an activity?

Answer 1

The time that its start may be delayed without affecting the duration of the project.

Total float = latest finish time - duration - earliest start time

Question 2

What is a critical activity?

Answer 2

An activity between 2 critical events, AND they have a float of 0

Question 3

What is a critical event?

Answer 3

An event where the early time is equal to the late time

Question 4

How do you calculate the early event times?

Answer 4

Perform a forward pass, the largest possible value is taken for this (as it is not possible to get to this event until all preceding activities have been completed)

Question 5

How do you calculate the late event times?

Answer 5

Perform a backward pass, the smallest possible value is always taken (as if you left the event later than that the prokect would be delayed)

Question 6

What are the early and late event times of the source and sink nodes?

Answer 6

The source (start) and sink (end) nodes always have the same value for their early and late times respectively

Question 7

What is a precedence table?

Answer 7

A table showing which activity each activity depends on

Question 8

What is a dummy and when is a dummy used?

Answer 8

A dummy is a dotted line used to show dependencies between activities, it has not time or cost.
* It is used when an activity is dependent on 2 events, but another activity is dependent on JUST ONE of those 2 events
* It is also used to ensure that each activity is uniquely represented in terms of its events. There can be at most one activity between 2 events and therefore a dummy can be used to get around this

Question 9

What activites are linked to the source node?

Answer 9

Only those which are not dependent on any previosu events

Question 10

How do you draw a gantt chart?

Answer 10

• Draw the critical activites on the top row
• Draw the other activities on their own lines, starting at their early event time for the length of time it takes to complete
• Then draw a dotted line from the end of the activity to the late event time (this is the float of the activity)
• THE BOXES (NOT LINES) REPRESENT DAYS, THE DAY BEGGINING WITH 4 IS THE 5th DAY, STARTING WITH 8 IS THE 9th DAY ETC

Question 11

How do you calculate the lower bound for the number of workers required to complete the project in the minimum time?

Answer 11

(sum of length of each activity) / (minimum time to complete project)

(Σ activity length) / (finish time)

Question 12

What are the rules when constructing scheduling diagrams?

Answer 12

• Each activity must only require 1 worker
• You should always choose the first worker available
• If you have a choice of activities for a worker, you should always choose the one with the lowest value for its late finish time

Question 13

Explain how to construct a scheduling diagram

Answer 13

1. Start by drawing the critical activities along the top row (as you would for a gantt chart)
2. Choose the activitiy with the earliest finish time and put that on the next row
3. Choose the next activity with the next earliest finish time and either put this following a previous activity on an existing row (you can delay the activity within its float) but start a new row if the activity does not fit onto a previous row due to dependencies or overlap of activities (timing). If there is a period of inactivity for the worker shade it in.
4. Repeat step 3 for all activities
5. Check dependencies and timings for each activity

Question 14

What does each row of a scheduling diagram represent?

Answer 14

Each worker

Question 15

What is a resource histogram?

Answer 15

A diagram to determine how many workers are required to complete a project in the minimum time

Question 16

What are the rules for constructing a resource histogram?

Answer 16

• No worker can do more tha one job at a time
• Once a worker has started an activity, they must finish it
• Once a worker has finished an activity they immediately become available to start another
• An activity can require more than one worker

Question 17

Explain how to construct a resource histogram:

Answer 17

1. First split the process into blocks by determining how many workers are required on each specific day (it helps if you have a gantt chart avaialble)
2. Draw this onto the resource histogram and label each square with the activity each worker is performing
3. Delay certain activities in order to “level out” the number of workers available

Question 18

What is resource levelling?

Answer 18

The process of adjusting the start and finish times of activities in order to take into account the constraints on resources (such as the number of workers)