DE4-DE6 Refining models, Gantt charts and resource levelling Quiz: AQA Further Maths, Unit 5

The 20 questions

1. What is a Gantt (cascade) diagram in critical path analysis?

   • A histogram showing the number of resources used in each time period
   • A chart that shows the total float of each activity as a single number
   • A bar chart in which each activity is drawn as a bar from its start time to its finish time against a time axis
   • A network diagram with nodes showing durations and arcs showing precedence only

2. What is a resource histogram in critical path analysis?

   • A chart showing only the activities on the critical path
   • A chart showing how much of a resource is needed at each point in time, based on a schedule
   • A bar chart of the total duration of each activity
   • A graph of earliest start times plotted against latest start times

3. What is resource levelling?

   • Adjusting the timing of non-critical activities within their float to reduce peaks in resource use, usually without extending the project
   • Starting every activity at its latest start time
   • Increasing the number of resources until every activity becomes critical
   • Removing all non-critical activities from the project

4. What is meant by a heuristic procedure, as used in resource levelling?

   • An algorithm that proves the project cannot be completed
   • A method that always gives the exact optimal schedule
   • A rule requiring every activity to be on the critical path
   • A practical method that gives a good schedule quickly, but does not guarantee the optimal schedule

5. A model of a project assumes unlimited resources, but the real site has only a few workers. Which refinement is most appropriate?

   • Add resource limits to the model, so that activities cannot run together when the workers available would be exceeded
   • Replace every activity duration with the average duration of all activities
   • Ignore the critical path, since the resources are assumed to be unlimited
   • Remove all precedence constraints so that activities can start at once

6. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). Workers: A 2, B 1, C 2, D 2, E 1, all started at earliest start times. What is the earliest time at which activity E can start in the early start schedule?

   • Time 5
   • Time 9
   • Time 4
   • Time 12

7. In a Gantt chart with activities drawn from their earliest start times, how is the total float of a non-critical activity usually shown?

   • As a marker placed at the start of the critical path
   • As a separate bar showing its latest start time only
   • As a bar twice as long as its duration
   • As a line or extension after its bar, showing how far it can slip without delaying the project

8. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). Workers: A 2, B 1, C 2, D 2, E 1, all started at earliest start times. What is the peak number of workers needed at any time in the early start schedule?

   • 6
   • 4
   • 3
   • 5

9. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). Workers: A 2, B 1, C 2, D 2, E 1, all started at earliest start times. In which time interval does the peak demand of workers occur in the early start schedule?

   • Between time 4 and time 5
   • Between time 0 and time 3
   • Between time 9 and time 12
   • Between time 5 and time 9

10. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). Workers: A 2, B 1, C 2, D 2, E 1, all started at earliest start times. What is the total number of worker-days needed for the whole project?

    • 12
    • 27
    • 30
    • 24

11. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). Workers: A 2, B 1, C 2, D 2, E 1, all started at earliest start times. Activity C has float 4. Why might resource levelling move C later within its float?

    • Because moving C reduces the total number of worker-days needed
    • Because moving C within its float can reduce peak demand without delaying the project
    • Because C has zero float and so cannot be moved at all
    • Because C is critical and must be moved to finish earlier

12. Activities: A (3, no predecessors), B (4, none), C (2, after A), D (5, after B), E (3, after C and D). Workers: A 2, B 1, C 2, D 2, E 1, all started at earliest start times. If only 3 workers are available at any time, is the early start schedule feasible?

    • No, because the project duration of 12 exceeds the number of workers
    • Yes, because the peak demand is only 3 between time 0 and time 3
    • Yes, because the total of 27 worker-days is below the limit
    • No, because the demand of 4 workers between times 4 and 5 exceeds the limit of 3

13. If resource levelling delays a critical activity, what is the effect on the project?

    • The critical path changes so that it includes only non-critical activities
    • The project duration is extended, since critical activities have no float
    • The project is unchanged, because levelling moves only non-critical activities
    • The project finishes earlier, since levelling shortens activity durations

14. When an activity is moved during resource levelling, what must remain true?

    • It must stay within its float, so its predecessors and successors remain satisfied and the project duration is unchanged
    • It must be moved onto the critical path
    • Its float must be exactly equal to its duration
    • It must always start at time zero

15. Which statement about a Gantt chart showing float is correct?

    • Critical activities are drawn with float lines longer than those of non-critical activities
    • A Gantt chart cannot show critical activities
    • Float lines show the duration of each activity
    • Float lines show how far each non-critical activity can slip, while critical activities show no float

16. A model assumes that one worker can carry out two activities at the same time. Which refinement is most appropriate?

    • Replace each activity with a single node of zero duration
    • Delete all activities with positive float from the network
    • Add a constraint that each worker can do only one activity at a time, and check the resource histogram against this limit
    • Remove the resource constraint, since the model is already accurate

17. What is the main purpose of a resource histogram when refining a critical path model?

    • To show whether the schedule needs more resources than are available at any time, so that the schedule can be adjusted
    • To replace the whole network with a single activity
    • To find the critical path directly from the resource numbers
    • To calculate the float of every activity exactly

18. Activity D needs 2 workers for 5 days. How many worker-days does D require?

    • 5
    • 10
    • 2
    • 7

19. Two activities that run in parallel each need 3 workers, but only 4 workers are available. Which statement is correct?

    • They can run together, because each needs fewer than four workers
    • They can run together, because their total of six workers is small
    • They cannot run together without exceeding the resources, so one must be delayed within its float or extra workers must be provided
    • They must be run in sequence, which leaves the project duration unchanged

20. Which statement about heuristic resource levelling is correct?

    • It may not find the best possible schedule, but gives a practical schedule that respects precedence and resource limits
    • It guarantees the smallest total float across the network
    • It always finds the minimum possible project duration
    • It requires that every activity be on the critical path

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