3D.4.5-3D.4.6 Resource histograms and scheduling with workers Quiz: Pearson Edexcel Further Maths, Unit 38

The 20 questions

1. A resource histogram plots

   • cost against activity
   • event times against event number
   • the number of workers needed against time
   • float against duration

2. Resource levelling aims to

   • shorten the project below its critical path length
   • smooth the number of workers needed over time, by using floats
   • maximise the number of workers at any time
   • remove the dummy activities

3. A lower bound on the number of workers needed to finish in time T is

   • T multiplied by the number of activities
   • the number of activities divided by T
   • the largest number of workers on any one activity
   • total worker-time divided by T, rounded up

4. In the scheduling problems here, the number of workers needed for each activity

   • is always exactly one
   • is always zero
   • is chosen freely by the planner
   • is given and may be more than one

5. The height of a resource histogram at a given time shows

   • the total number of workers working at that time
   • the cost of the workers
   • the duration of the project
   • the float of the critical path

6. Delaying non-critical activities within their float can

   • increase the peak number of workers
   • remove activities from the critical path
   • reduce the peak number of workers needed
   • always shorten the project

7. The minimum project duration when workers are unlimited is

   • the sum of all activity durations
   • the largest total float
   • the total worker-time
   • the length of the critical path

8. Activity X runs from time 0 to 4 with 2 workers. Activity Y runs from time 1 to 3 with 1 worker. How many workers are needed at time 2?

   • 2
   • 4
   • 1
   • 3

9. Activities A (3 days, 2 workers), B (4 days, 1 worker) and C (2 days, 3 workers) are in a project. What is the total worker-days?

   • 16
   • 24
   • 12
   • 9

10. A project needs 30 worker-days and must finish in 6 days. What is the lower bound on the number of workers?

    • 5
    • 3
    • 6
    • 30

11. An activity uses 3 workers for 2 days and has 3 days of float. What is its worker-time?

    • 6
    • 5
    • 9
    • 3

12. The project has capacity for 4 workers. Two activities need 3 and 2 workers at the same time. What must happen?

    • more workers are hired automatically
    • one must be delayed, within its float, so they do not overlap
    • the project duration must shorten
    • both can run since 5 is close to 4

13. Days 1 and 2 use 3 workers each day, and days 3 to 5 use 1 worker each day. What is the total worker-days?

    • 9
    • 11
    • 12
    • 6

14. A project has total worker-time 20 and must finish in 7 days. What is the minimum number of workers?

    • 7
    • 2
    • 3
    • 20

15. Daily worker numbers over five days are 2, 4, 3, 5 and 1. What is the peak number of workers?

    • 15
    • 4
    • 3
    • 5

16. A project has total worker-time 26 and must finish in 5 days. What is the minimum number of workers?

    • 6
    • 26
    • 5.2
    • 5

17. Two activities each need 2 workers for 3 days. One may start up to 3 days later without delaying the project. What is the lowest achievable peak?

    • 6
    • 3
    • 2
    • 4

18. Why can the minimum number of workers exceed the worker-time lower bound?

    • the lower bound is always wrong
    • work cannot always be split evenly over time because of precedence and fixed activity durations
    • each activity needs exactly one worker
    • histograms count dummy activities

19. Why can scheduling with the fewest workers lengthen the project?

    • delaying activities to share workers can push critical activities back and extend the finish
    • workers cannot be reassigned between activities
    • the critical path is ignored when workers are shared
    • fewer workers always lower costs

20. Daily peaks of workers over five days are 3, 5, 2, 6 and 1. What is the maximum number of workers needed?

    • 17
    • 5
    • 3
    • 6

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